[{"data":1,"prerenderedAt":6660},["ShallowReactive",2],{"navigation_docs":3,"learnalog_locale_counterpart__zh_financial-economic-time-series_05-unit-roots-cointegration":1782,"-en-financial-economic-time-series-05-unit-roots-cointegration":1783,"-en-financial-economic-time-series-05-unit-roots-cointegration-surround":6655},[4,1038],{"title":5,"path":6,"stem":7,"children":8},"En","\u002Fen","en",[9,12,58,250,406,477,534,715,798,824,943],{"title":10,"path":6,"stem":11},"","en\u002Findex",{"title":13,"path":14,"stem":15,"children":16},"Research Skills and Academic Writing","\u002Fen\u002Facademic-writing","en\u002Facademic-writing\u002Findex",[17,18,22,26,30,34,38,42,46,50,54],{"title":13,"path":14,"stem":15},{"title":19,"path":20,"stem":21},"1. Research Questions, Scope, and Feasibility","\u002Fen\u002Facademic-writing\u002F01-research-questions-and-planning","en\u002Facademic-writing\u002F01-research-questions-and-planning",{"title":23,"path":24,"stem":25},"2. Search, Evaluate, and Read Evidence","\u002Fen\u002Facademic-writing\u002F02-reading-and-literature-matrix","en\u002Facademic-writing\u002F02-reading-and-literature-matrix",{"title":27,"path":28,"stem":29},"3. From Sources to Synthesis and Argument","\u002Fen\u002Facademic-writing\u002F03-arguments-outlines-and-paragraphs","en\u002Facademic-writing\u002F03-arguments-outlines-and-paragraphs",{"title":31,"path":32,"stem":33},"4. Literature Review and a Defensible Gap","\u002Fen\u002Facademic-writing\u002F04-writing-the-literature-review","en\u002Facademic-writing\u002F04-writing-the-literature-review",{"title":35,"path":36,"stem":37},"5. Research Design, Evidence, and Core Sections","\u002Fen\u002Facademic-writing\u002F05-core-sections-and-evidence","en\u002Facademic-writing\u002F05-core-sections-and-evidence",{"title":39,"path":40,"stem":41},"6. Citation, Paraphrasing, Integrity, and AI","\u002Fen\u002Facademic-writing\u002F06-citation-paraphrasing-and-integrity","en\u002Facademic-writing\u002F06-citation-paraphrasing-and-integrity",{"title":43,"path":44,"stem":45},"7. Revision, Review, and Submission","\u002Fen\u002Facademic-writing\u002F07-revision-style-and-submission","en\u002Facademic-writing\u002F07-revision-style-and-submission",{"title":47,"path":48,"stem":49},"8. Research Workbook","\u002Fen\u002Facademic-writing\u002F08-literature-review-checklist-and-template","en\u002Facademic-writing\u002F08-literature-review-checklist-and-template",{"title":51,"path":52,"stem":53},"9. Research Workflow and Tools","\u002Fen\u002Facademic-writing\u002F09-tools-for-academic-writing-and-literature-management","en\u002Facademic-writing\u002F09-tools-for-academic-writing-and-literature-management",{"title":55,"path":56,"stem":57},"10. Worked Project — From Question to Defensible Conclusion","\u002Fen\u002Facademic-writing\u002F10-worked-example-from-block-structure-to-question-chain","en\u002Facademic-writing\u002F10-worked-example-from-block-structure-to-question-chain",{"title":59,"path":60,"stem":61,"children":62,"page":249},"Accounting","\u002Fen\u002Faccounting","en\u002Faccounting",[63,69,87,93,193],{"title":64,"path":65,"stem":66,"children":67},"Accounting — From Evidence to Decisions","\u002Fen\u002Faccounting\u002F00-index","en\u002Faccounting\u002F00-index",[68],{"title":64,"path":65,"stem":66},{"title":70,"path":71,"stem":72,"children":73},"Accounting Appendix","\u002Fen\u002Faccounting\u002Fappendix","en\u002Faccounting\u002Fappendix\u002Findex",[74,75,79,83],{"title":70,"path":71,"stem":72},{"title":76,"path":77,"stem":78},"Worked Examples and Error Diagnosis","\u002Fen\u002Faccounting\u002Fappendix\u002F24-examples-pitfalls","en\u002Faccounting\u002Fappendix\u002F24-examples-pitfalls",{"title":80,"path":81,"stem":82},"Accounting Glossary","\u002Fen\u002Faccounting\u002Fappendix\u002F26-glossary","en\u002Faccounting\u002Fappendix\u002F26-glossary",{"title":84,"path":85,"stem":86},"Reading and Evidence Map","\u002Fen\u002Faccounting\u002Fappendix\u002F27-reading-map","en\u002Faccounting\u002Fappendix\u002F27-reading-map",{"title":88,"path":89,"stem":90,"children":91},"Northstar Record-to-Decision Capstone","\u002Fen\u002Faccounting\u002Fcapstone","en\u002Faccounting\u002Fcapstone\u002Findex",[92],{"title":88,"path":89,"stem":90},{"title":94,"path":95,"stem":96,"children":97},"Financial Accounting","\u002Fen\u002Faccounting\u002Ffinancial-accounting","en\u002Faccounting\u002Ffinancial-accounting\u002Findex",[98,99,117,131,165,179],{"title":94,"path":95,"stem":96},{"title":100,"path":101,"stem":102,"children":103},"1. Foundations","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations","en\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002Findex",[104,105,109,113],{"title":100,"path":101,"stem":102},{"title":106,"path":107,"stem":108},"Objectives and Qualitative Characteristics","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F01-objectives-qualitative-characteristics","en\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F01-objectives-qualitative-characteristics",{"title":110,"path":111,"stem":112},"Equation and Elements","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F02-equation-elements","en\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F02-equation-elements",{"title":114,"path":115,"stem":116},"Accrual Basis, Estimates and Periods","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F03-accounting-bases-principles","en\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F03-accounting-bases-principles",{"title":118,"path":119,"stem":120,"children":121},"2. Recording Transactions","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions","en\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002Findex",[122,123,127],{"title":118,"path":119,"stem":120},{"title":124,"path":125,"stem":126},"Double-Entry and Debit\u002FCredit","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F04-double-entry-dr-cr","en\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F04-double-entry-dr-cr",{"title":128,"path":129,"stem":130},"Accounting Cycle","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F05-accounting-cycle","en\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F05-accounting-cycle",{"title":132,"path":133,"stem":134,"children":135},"3. Measurement and Adjustments","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002Findex",[136,137,141,145,149,153,157,161],{"title":132,"path":133,"stem":134},{"title":138,"path":139,"stem":140},"Revenue Recognition","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F07-revenue-recognition","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F07-revenue-recognition",{"title":142,"path":143,"stem":144},"Inventory","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F08-inventory","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F08-inventory",{"title":146,"path":147,"stem":148},"Receivables and Expected Credit Losses","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F09-receivables","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F09-receivables",{"title":150,"path":151,"stem":152},"Property, Plant and Equipment","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F10-ppe","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F10-ppe",{"title":154,"path":155,"stem":156},"Intangible Assets","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F11-intangibles","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F11-intangibles",{"title":158,"path":159,"stem":160},"Leases","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F12-leases","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F12-leases",{"title":162,"path":163,"stem":164},"Current and Deferred Income Tax","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F13-income-tax","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F13-income-tax",{"title":166,"path":167,"stem":168,"children":169},"4. Reporting and Cash","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash","en\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002Findex",[170,171,175],{"title":166,"path":167,"stem":168},{"title":172,"path":173,"stem":174},"Linked Financial Statements","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F06-financial-statements","en\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F06-financial-statements",{"title":176,"path":177,"stem":178},"Cash, Reconciliation and Internal Control","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F14-cash-control","en\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F14-cash-control",{"title":180,"path":181,"stem":182,"children":183},"5. Analysis and Comparison","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison","en\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002Findex",[184,185,189],{"title":180,"path":181,"stem":182},{"title":186,"path":187,"stem":188},"Ratio Analysis","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F15-ratio-analysis","en\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F15-ratio-analysis",{"title":190,"path":191,"stem":192},"IFRS versus US GAAP","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F25-ifrs-gaap","en\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F25-ifrs-gaap",{"title":194,"path":195,"stem":196,"children":197},"Management Accounting","\u002Fen\u002Faccounting\u002Fmanagement-accounting","en\u002Faccounting\u002Fmanagement-accounting\u002Findex",[198,199,217,235],{"title":194,"path":195,"stem":196},{"title":200,"path":201,"stem":202,"children":203},"1. Cost Foundations","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations","en\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002Findex",[204,205,209,213],{"title":200,"path":201,"stem":202},{"title":206,"path":207,"stem":208},"Cost Concepts and Behaviour","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F16-cost-concepts","en\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F16-cost-concepts",{"title":210,"path":211,"stem":212},"Costing Systems","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F17-costing-systems","en\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F17-costing-systems",{"title":214,"path":215,"stem":216},"Variable and Absorption Costing","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F19-variable-vs-absorption","en\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F19-variable-vs-absorption",{"title":218,"path":219,"stem":220,"children":221},"2. Planning and Control","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control","en\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002Findex",[222,223,227,231],{"title":218,"path":219,"stem":220},{"title":224,"path":225,"stem":226},"Cost–Volume–Profit Analysis","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F18-cvp-analysis","en\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F18-cvp-analysis",{"title":228,"path":229,"stem":230},"Budgeting and Variance Analysis","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F20-budgeting-variances","en\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F20-budgeting-variances",{"title":232,"path":233,"stem":234},"Performance Measurement","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F21-performance-measurement","en\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F21-performance-measurement",{"title":236,"path":237,"stem":238,"children":239},"3. Decisions and Investment","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment","en\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002Findex",[240,241,245],{"title":236,"path":237,"stem":238},{"title":242,"path":243,"stem":244},"Short-Term Decisions","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F22-short-term-decisions","en\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F22-short-term-decisions",{"title":246,"path":247,"stem":248},"Capital Budgeting","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F23-capital-budgeting","en\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F23-capital-budgeting",false,{"title":251,"path":252,"stem":253,"children":254,"page":249},"Business Analytics","\u002Fen\u002Fbusiness-analytics","en\u002Fbusiness-analytics",[255,261,279,305,335,365,383,400],{"title":256,"path":257,"stem":258,"children":259},"Business Analytics — From Data to Defensible Action","\u002Fen\u002Fbusiness-analytics\u002F00-index","en\u002Fbusiness-analytics\u002F00-index",[260],{"title":256,"path":257,"stem":258},{"title":262,"path":263,"stem":264,"children":265},"0. Decision and Data Foundations","\u002Fen\u002Fbusiness-analytics\u002F00-intro","en\u002Fbusiness-analytics\u002F00-intro\u002Findex",[266,267,271,275],{"title":262,"path":263,"stem":264},{"title":268,"path":269,"stem":270},"Decision Framing","\u002Fen\u002Fbusiness-analytics\u002F00-intro\u002F01-decision-framing","en\u002Fbusiness-analytics\u002F00-intro\u002F01-decision-framing",{"title":272,"path":273,"stem":274},"Data Contracts","\u002Fen\u002Fbusiness-analytics\u002F00-intro\u002F02-data-contracts","en\u002Fbusiness-analytics\u002F00-intro\u002F02-data-contracts",{"title":276,"path":277,"stem":278},"Reproducible Analytics Workflow","\u002Fen\u002Fbusiness-analytics\u002F00-intro\u002F03-reproducible-workflow","en\u002Fbusiness-analytics\u002F00-intro\u002F03-reproducible-workflow",{"title":280,"path":281,"stem":282,"children":283},"1. Descriptive Analytics","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive","en\u002Fbusiness-analytics\u002F01-descriptive\u002Findex",[284,285,289,293,297,301],{"title":280,"path":281,"stem":282},{"title":286,"path":287,"stem":288},"Distributions and Exploratory Data Analysis","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F04-distributions-eda","en\u002Fbusiness-analytics\u002F01-descriptive\u002F04-distributions-eda",{"title":290,"path":291,"stem":292},"KPIs and Denominators","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F05-kpis-denominators","en\u002Fbusiness-analytics\u002F01-descriptive\u002F05-kpis-denominators",{"title":294,"path":295,"stem":296},"Segments, Cohorts and Funnels","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F06-segmentation-cohorts-funnels","en\u002Fbusiness-analytics\u002F01-descriptive\u002F06-segmentation-cohorts-funnels",{"title":298,"path":299,"stem":300},"Visual Evidence and Data Stories","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F07-visualisation-story","en\u002Fbusiness-analytics\u002F01-descriptive\u002F07-visualisation-story",{"title":302,"path":303,"stem":304},"Experiments and Causal Boundaries","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F08-experiments-causal-boundary","en\u002Fbusiness-analytics\u002F01-descriptive\u002F08-experiments-causal-boundary",{"title":306,"path":307,"stem":308,"children":309},"2. Predictive Analytics","\u002Fen\u002Fbusiness-analytics\u002F02-predictive","en\u002Fbusiness-analytics\u002F02-predictive\u002Findex",[310,311,315,319,323,327,331],{"title":306,"path":307,"stem":308},{"title":312,"path":313,"stem":314},"Validation, Baselines and Leakage","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F09-validation-leakage","en\u002Fbusiness-analytics\u002F02-predictive\u002F09-validation-leakage",{"title":316,"path":317,"stem":318},"Regression and Forecasting","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F10-regression-forecasting","en\u002Fbusiness-analytics\u002F02-predictive\u002F10-regression-forecasting",{"title":320,"path":321,"stem":322},"Classification and Calibration","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F11-classification-calibration","en\u002Fbusiness-analytics\u002F02-predictive\u002F11-classification-calibration",{"title":324,"path":325,"stem":326},"Trees and Ensembles","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F12-trees-ensembles","en\u002Fbusiness-analytics\u002F02-predictive\u002F12-trees-ensembles",{"title":328,"path":329,"stem":330},"Decision Metrics and Thresholds","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F13-decision-metrics-thresholds","en\u002Fbusiness-analytics\u002F02-predictive\u002F13-decision-metrics-thresholds",{"title":332,"path":333,"stem":334},"Explainability, Monitoring and Drift","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F14-explainability-drift","en\u002Fbusiness-analytics\u002F02-predictive\u002F14-explainability-drift",{"title":336,"path":337,"stem":338,"children":339},"3. Prescriptive Analytics","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive","en\u002Fbusiness-analytics\u002F03-prescriptive\u002Findex",[340,341,345,349,353,357,361],{"title":336,"path":337,"stem":338},{"title":342,"path":343,"stem":344},"Decision-Making under Uncertainty","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F15-decision-uncertainty","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F15-decision-uncertainty",{"title":346,"path":347,"stem":348},"Linear Optimisation","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F16-linear-optimization","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F16-linear-optimization",{"title":350,"path":351,"stem":352},"Inventory and Allocation","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F17-inventory-allocation","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F17-inventory-allocation",{"title":354,"path":355,"stem":356},"Queueing and Simulation","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F18-queueing-simulation","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F18-queueing-simulation",{"title":358,"path":359,"stem":360},"Pricing and Revenue Management","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F19-pricing-experimentation","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F19-pricing-experimentation",{"title":362,"path":363,"stem":364},"Causal Targeting and Policy Learning","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F20-causal-targeting","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F20-causal-targeting",{"title":366,"path":367,"stem":368,"children":369},"4. Deployment and Governance","\u002Fen\u002Fbusiness-analytics\u002F04-deployment","en\u002Fbusiness-analytics\u002F04-deployment\u002Findex",[370,371,375,379],{"title":366,"path":367,"stem":368},{"title":372,"path":373,"stem":374},"Data Products and Monitoring","\u002Fen\u002Fbusiness-analytics\u002F04-deployment\u002F21-data-products-monitoring","en\u002Fbusiness-analytics\u002F04-deployment\u002F21-data-products-monitoring",{"title":376,"path":377,"stem":378},"Governance, Fairness and Privacy","\u002Fen\u002Fbusiness-analytics\u002F04-deployment\u002F22-governance-fairness-privacy","en\u002Fbusiness-analytics\u002F04-deployment\u002F22-governance-fairness-privacy",{"title":380,"path":381,"stem":382},"Adoption and Business Value","\u002Fen\u002Fbusiness-analytics\u002F04-deployment\u002F23-adoption-value","en\u002Fbusiness-analytics\u002F04-deployment\u002F23-adoption-value",{"title":384,"path":385,"stem":386,"children":387},"Appendix and Revision Tools","\u002Fen\u002Fbusiness-analytics\u002Fappendix","en\u002Fbusiness-analytics\u002Fappendix\u002Findex",[388,389,393,397],{"title":384,"path":385,"stem":386},{"title":390,"path":391,"stem":392},"Formula and Decision Map","\u002Fen\u002Fbusiness-analytics\u002Fappendix\u002F24-formula-map","en\u002Fbusiness-analytics\u002Fappendix\u002F24-formula-map",{"title":394,"path":395,"stem":396},"Worked Examples and Pitfalls","\u002Fen\u002Fbusiness-analytics\u002Fappendix\u002F25-worked-examples-pitfalls","en\u002Fbusiness-analytics\u002Fappendix\u002F25-worked-examples-pitfalls",{"title":84,"path":398,"stem":399},"\u002Fen\u002Fbusiness-analytics\u002Fappendix\u002F26-reading-map","en\u002Fbusiness-analytics\u002Fappendix\u002F26-reading-map",{"title":401,"path":402,"stem":403,"children":404},"Capstone — The Evening Delivery Promise","\u002Fen\u002Fbusiness-analytics\u002Fcapstone","en\u002Fbusiness-analytics\u002Fcapstone\u002Findex",[405],{"title":401,"path":402,"stem":403},{"title":407,"path":408,"stem":409,"children":410,"page":249},"Financial Economic Time Series","\u002Fen\u002Ffinancial-economic-time-series","en\u002Ffinancial-economic-time-series",[411,417,423,429,435,441,447,453,459,465,471],{"title":412,"path":413,"stem":414,"children":415},"Financial and Economic Time Series — Course Guide","\u002Fen\u002Ffinancial-economic-time-series\u002F00-intro","en\u002Ffinancial-economic-time-series\u002F00-intro\u002Findex",[416],{"title":412,"path":413,"stem":414},{"title":418,"path":419,"stem":420,"children":421},"Three Versions of Time Series","\u002Fen\u002Ffinancial-economic-time-series\u002F01-bridge","en\u002Ffinancial-economic-time-series\u002F01-bridge\u002Findex",[422],{"title":418,"path":419,"stem":420},{"title":424,"path":425,"stem":426,"children":427},"Data, Clocks, and Transformations","\u002Fen\u002Ffinancial-economic-time-series\u002F02-data-transformations","en\u002Ffinancial-economic-time-series\u002F02-data-transformations\u002Findex",[428],{"title":424,"path":425,"stem":426},{"title":430,"path":431,"stem":432,"children":433},"Predictive Regressions and Persistent Predictors","\u002Fen\u002Ffinancial-economic-time-series\u002F03-predictive-regressions","en\u002Ffinancial-economic-time-series\u002F03-predictive-regressions\u002Findex",[434],{"title":430,"path":431,"stem":432},{"title":436,"path":437,"stem":438,"children":439},"Volatility, Tails, and Financial Risk","\u002Fen\u002Ffinancial-economic-time-series\u002F04-volatility-risk","en\u002Ffinancial-economic-time-series\u002F04-volatility-risk\u002Findex",[440],{"title":436,"path":437,"stem":438},{"title":442,"path":443,"stem":444,"children":445},"Unit Roots, Cointegration, and Error Correction","\u002Fen\u002Ffinancial-economic-time-series\u002F05-unit-roots-cointegration","en\u002Ffinancial-economic-time-series\u002F05-unit-roots-cointegration\u002Findex",[446],{"title":442,"path":443,"stem":444},{"title":448,"path":449,"stem":450,"children":451},"VAR, Structural Identification, and Local Projections","\u002Fen\u002Ffinancial-economic-time-series\u002F06-var-identification","en\u002Ffinancial-economic-time-series\u002F06-var-identification\u002Findex",[452],{"title":448,"path":449,"stem":450},{"title":454,"path":455,"stem":456,"children":457},"State Space, Mixed Frequency, and Nowcasting","\u002Fen\u002Ffinancial-economic-time-series\u002F07-state-space-nowcasting","en\u002Ffinancial-economic-time-series\u002F07-state-space-nowcasting\u002Findex",[458],{"title":454,"path":455,"stem":456},{"title":460,"path":461,"stem":462,"children":463},"Forecast Evaluation for Decisions","\u002Fen\u002Ffinancial-economic-time-series\u002F08-forecast-evaluation","en\u002Ffinancial-economic-time-series\u002F08-forecast-evaluation\u002Findex",[464],{"title":460,"path":461,"stem":462},{"title":466,"path":467,"stem":468,"children":469},"Integrated R Laboratory","\u002Fen\u002Ffinancial-economic-time-series\u002F09-r-laboratory","en\u002Ffinancial-economic-time-series\u002F09-r-laboratory\u002Findex",[470],{"title":466,"path":467,"stem":468},{"title":472,"path":473,"stem":474,"children":475},"Capstones, Data, and Reading Ladder","\u002Fen\u002Ffinancial-economic-time-series\u002F10-capstone-readings","en\u002Ffinancial-economic-time-series\u002F10-capstone-readings\u002Findex",[476],{"title":472,"path":473,"stem":474},{"title":478,"path":479,"stem":480,"children":481,"page":249},"Intro To Economics","\u002Fen\u002Fintro-to-economics","en\u002Fintro-to-economics",[482,486,490,494,498,502,506,510,514,518,522,526,530],{"title":483,"path":484,"stem":485},"Introduction to Economics — Decisions, Markets, and the Macroeconomy","\u002Fen\u002Fintro-to-economics\u002F00-intro","en\u002Fintro-to-economics\u002F00-intro",{"title":487,"path":488,"stem":489},"Chapter 1 — Choice, Opportunity Cost, and Trade","\u002Fen\u002Fintro-to-economics\u002F01-foundations","en\u002Fintro-to-economics\u002F01-foundations",{"title":491,"path":492,"stem":493},"Chapter 2 — Demand, Supply, Equilibrium, and Welfare","\u002Fen\u002Fintro-to-economics\u002F02-demand-and-supply","en\u002Fintro-to-economics\u002F02-demand-and-supply",{"title":495,"path":496,"stem":497},"Chapter 3 — Elasticity, Revenue, and Tax Incidence","\u002Fen\u002Fintro-to-economics\u002F03-elasticity","en\u002Fintro-to-economics\u002F03-elasticity",{"title":499,"path":500,"stem":501},"Chapter 4 — Firms, Market Power, and Market Failure","\u002Fen\u002Fintro-to-economics\u002F04-market-structures","en\u002Fintro-to-economics\u002F04-market-structures",{"title":503,"path":504,"stem":505},"Chapter 5 — GDP, Income, Wealth, and Welfare","\u002Fen\u002Fintro-to-economics\u002F05-gdp-and-wealth","en\u002Fintro-to-economics\u002F05-gdp-and-wealth",{"title":507,"path":508,"stem":509},"Chapter 6 — Inflation, Purchasing Power, and Labour Markets","\u002Fen\u002Fintro-to-economics\u002F06-inflation-and-unemployment","en\u002Fintro-to-economics\u002F06-inflation-and-unemployment",{"title":511,"path":512,"stem":513},"Chapter 7 — Productivity, Technology, and Economic Growth","\u002Fen\u002Fintro-to-economics\u002F07-economic-growth","en\u002Fintro-to-economics\u002F07-economic-growth",{"title":515,"path":516,"stem":517},"Chapter 8 — Money, Credit, and Banking","\u002Fen\u002Fintro-to-economics\u002F08-money-and-banking","en\u002Fintro-to-economics\u002F08-money-and-banking",{"title":519,"path":520,"stem":521},"Chapter 9 — Business Cycles, AD–AS, and Monetary Policy","\u002Fen\u002Fintro-to-economics\u002F09-monetary-policy-and-ad-as","en\u002Fintro-to-economics\u002F09-monetary-policy-and-ad-as",{"title":523,"path":524,"stem":525},"Chapter 10 — Fiscal Policy, Distribution, and Public Debt","\u002Fen\u002Fintro-to-economics\u002F10-fiscal-policy","en\u002Fintro-to-economics\u002F10-fiscal-policy",{"title":527,"path":528,"stem":529},"Chapter 11 — Trade, Capital Flows, and Exchange Rates","\u002Fen\u002Fintro-to-economics\u002F11-open-economy-and-exchange-rates","en\u002Fintro-to-economics\u002F11-open-economy-and-exchange-rates",{"title":531,"path":532,"stem":533},"Chapter 12 — Integrated Economic Analysis Studio","\u002Fen\u002Fintro-to-economics\u002F12-review-and-case-studies","en\u002Fintro-to-economics\u002F12-review-and-case-studies",{"title":535,"path":536,"stem":537,"children":538,"page":249},"Microeconometrics","\u002Fen\u002Fmicroeconometrics","en\u002Fmicroeconometrics",[539,557,563,581,603,629,651,673,691,709],{"title":540,"path":541,"stem":542,"children":543},"0. Causal Questions and Designs","\u002Fen\u002Fmicroeconometrics\u002F00-foundations","en\u002Fmicroeconometrics\u002F00-foundations\u002Findex",[544,545,549,553],{"title":540,"path":541,"stem":542},{"title":546,"path":547,"stem":548},"Causal Questions and Estimands","\u002Fen\u002Fmicroeconometrics\u002F00-foundations\u002F01-causal-question-estimands","en\u002Fmicroeconometrics\u002F00-foundations\u002F01-causal-question-estimands",{"title":550,"path":551,"stem":552},"Potential Outcomes and Experiments","\u002Fen\u002Fmicroeconometrics\u002F00-foundations\u002F02-potential-outcomes-experiments","en\u002Fmicroeconometrics\u002F00-foundations\u002F02-potential-outcomes-experiments",{"title":554,"path":555,"stem":556},"Causal Diagrams and Controls","\u002Fen\u002Fmicroeconometrics\u002F00-foundations\u002F03-dags-controls","en\u002Fmicroeconometrics\u002F00-foundations\u002F03-dags-controls",{"title":558,"path":559,"stem":560,"children":561},"Microeconometrics — Designing Credible Counterfactuals","\u002Fen\u002Fmicroeconometrics\u002F00-index","en\u002Fmicroeconometrics\u002F00-index",[562],{"title":558,"path":559,"stem":560},{"title":564,"path":565,"stem":566,"children":567},"1. Regression and Inference","\u002Fen\u002Fmicroeconometrics\u002F01-regression","en\u002Fmicroeconometrics\u002F01-regression\u002Findex",[568,569,573,577],{"title":564,"path":565,"stem":566},{"title":570,"path":571,"stem":572},"OLS as a Projection","\u002Fen\u002Fmicroeconometrics\u002F01-regression\u002F04-ols-projection","en\u002Fmicroeconometrics\u002F01-regression\u002F04-ols-projection",{"title":574,"path":575,"stem":576},"FWL, Selection and Controls","\u002Fen\u002Fmicroeconometrics\u002F01-regression\u002F05-fwl-selection-controls","en\u002Fmicroeconometrics\u002F01-regression\u002F05-fwl-selection-controls",{"title":578,"path":579,"stem":580},"Inference and Clustering","\u002Fen\u002Fmicroeconometrics\u002F01-regression\u002F06-inference-clustering","en\u002Fmicroeconometrics\u002F01-regression\u002F06-inference-clustering",{"title":582,"path":583,"stem":584,"children":585},"2. Instruments and Panel Data","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel","en\u002Fmicroeconometrics\u002F02-iv-panel\u002Findex",[586,587,591,595,599],{"title":582,"path":583,"stem":584},{"title":588,"path":589,"stem":590},"Instrumental Variables","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel\u002F07-iv-identification","en\u002Fmicroeconometrics\u002F02-iv-panel\u002F07-iv-identification",{"title":592,"path":593,"stem":594},"Weak Instruments and LATE","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel\u002F08-weak-iv-late","en\u002Fmicroeconometrics\u002F02-iv-panel\u002F08-weak-iv-late",{"title":596,"path":597,"stem":598},"Panel Fixed Effects","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel\u002F09-panel-fixed-effects","en\u002Fmicroeconometrics\u002F02-iv-panel\u002F09-panel-fixed-effects",{"title":600,"path":601,"stem":602},"Dynamic Panels and Limits","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel\u002F10-dynamic-panel","en\u002Fmicroeconometrics\u002F02-iv-panel\u002F10-dynamic-panel",{"title":604,"path":605,"stem":606,"children":607},"3. Policy Evaluation Designs","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs","en\u002Fmicroeconometrics\u002F03-policy-designs\u002Findex",[608,609,613,617,621,625],{"title":604,"path":605,"stem":606},{"title":610,"path":611,"stem":612},"Difference-in-Differences","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F11-did-core","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F11-did-core",{"title":614,"path":615,"stem":616},"Staggered DID and Event Studies","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F12-staggered-event-studies","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F12-staggered-event-studies",{"title":618,"path":619,"stem":620},"Regression Discontinuity","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F13-rdd","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F13-rdd",{"title":622,"path":623,"stem":624},"Matching, Weighting and Overlap","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F14-matching-weighting","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F14-matching-weighting",{"title":626,"path":627,"stem":628},"Synthetic Control","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F15-synthetic-control","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F15-synthetic-control",{"title":630,"path":631,"stem":632,"children":633},"Module 4 — Choice and Limited Outcomes","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002Findex",[634,635,639,643,647],{"title":630,"path":631,"stem":632},{"title":636,"path":637,"stem":638},"Binary Choice","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F16-binary-choice","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F16-binary-choice",{"title":640,"path":641,"stem":642},"Multinomial and Ordered Choice","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F17-multinomial-choice","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F17-multinomial-choice",{"title":644,"path":645,"stem":646},"Count Outcomes","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F18-count-outcomes","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F18-count-outcomes",{"title":648,"path":649,"stem":650},"Censoring, Truncation and Selection","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F19-censoring-selection","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F19-censoring-selection",{"title":652,"path":653,"stem":654,"children":655},"Module 5 — Modern Causal Analysis","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal","en\u002Fmicroeconometrics\u002F05-modern-causal\u002Findex",[656,657,661,665,669],{"title":652,"path":653,"stem":654},{"title":658,"path":659,"stem":660},"Double Machine Learning","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal\u002F20-dml","en\u002Fmicroeconometrics\u002F05-modern-causal\u002F20-dml",{"title":662,"path":663,"stem":664},"Heterogeneity and Policy Learning","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal\u002F21-heterogeneity-policy","en\u002Fmicroeconometrics\u002F05-modern-causal\u002F21-heterogeneity-policy",{"title":666,"path":667,"stem":668},"Sensitivity and Partial Identification","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal\u002F22-sensitivity-partial-id","en\u002Fmicroeconometrics\u002F05-modern-causal\u002F22-sensitivity-partial-id",{"title":670,"path":671,"stem":672},"External Validity and Transport","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal\u002F23-external-validity","en\u002Fmicroeconometrics\u002F05-modern-causal\u002F23-external-validity",{"title":674,"path":675,"stem":676,"children":677},"Module 6 — From Data to Auditable Evidence","\u002Fen\u002Fmicroeconometrics\u002F06-workflow","en\u002Fmicroeconometrics\u002F06-workflow\u002Findex",[678,679,683,687],{"title":674,"path":675,"stem":676},{"title":680,"path":681,"stem":682},"Data Provenance","\u002Fen\u002Fmicroeconometrics\u002F06-workflow\u002F24-data-provenance","en\u002Fmicroeconometrics\u002F06-workflow\u002F24-data-provenance",{"title":684,"path":685,"stem":686},"Reproducibility and Reporting","\u002Fen\u002Fmicroeconometrics\u002F06-workflow\u002F25-reproducibility-reporting","en\u002Fmicroeconometrics\u002F06-workflow\u002F25-reproducibility-reporting",{"title":688,"path":689,"stem":690},"Paper and Evidence Audit","\u002Fen\u002Fmicroeconometrics\u002F06-workflow\u002F26-paper-audit","en\u002Fmicroeconometrics\u002F06-workflow\u002F26-paper-audit",{"title":692,"path":693,"stem":694,"children":695},"Appendix — Revision and Evidence Map","\u002Fen\u002Fmicroeconometrics\u002Fappendix","en\u002Fmicroeconometrics\u002Fappendix\u002Findex",[696,697,701,705],{"title":692,"path":693,"stem":694},{"title":698,"path":699,"stem":700},"Formula and Design Map","\u002Fen\u002Fmicroeconometrics\u002Fappendix\u002F27-formula-design-map","en\u002Fmicroeconometrics\u002Fappendix\u002F27-formula-design-map",{"title":702,"path":703,"stem":704},"Ten Worked Microeconometric Pitfalls","\u002Fen\u002Fmicroeconometrics\u002Fappendix\u002F28-worked-pitfalls","en\u002Fmicroeconometrics\u002Fappendix\u002F28-worked-pitfalls",{"title":706,"path":707,"stem":708},"Reading and Software Map","\u002Fen\u002Fmicroeconometrics\u002Fappendix\u002F29-reading-software-map","en\u002Fmicroeconometrics\u002Fappendix\u002F29-reading-software-map",{"title":710,"path":711,"stem":712,"children":713},"Capstone — Should Northbridge Expand Pathways?","\u002Fen\u002Fmicroeconometrics\u002Fcapstone","en\u002Fmicroeconometrics\u002Fcapstone\u002Findex",[714],{"title":710,"path":711,"stem":712},{"title":716,"path":717,"stem":718,"children":719,"page":249},"Microeconomics","\u002Fen\u002Fmicroeconomics","en\u002Fmicroeconomics",[720,726,732,738,744,750,756,762,768,774,780,786,792],{"title":721,"path":722,"stem":723,"children":724},"Advanced Microeconomics — Course Guide","\u002Fen\u002Fmicroeconomics\u002F00-intro","en\u002Fmicroeconomics\u002F00-intro\u002Findex",[725],{"title":721,"path":722,"stem":723},{"title":727,"path":728,"stem":729,"children":730},"Module 1 — Choice, Duality, and Revealed Preference","\u002Fen\u002Fmicroeconomics\u002F01-fundations","en\u002Fmicroeconomics\u002F01-fundations\u002Findex",[731],{"title":727,"path":728,"stem":729},{"title":733,"path":734,"stem":735,"children":736},"Module 2 — Comparative Statics and Welfare Measurement","\u002Fen\u002Fmicroeconomics\u002F02-comparative-statics","en\u002Fmicroeconomics\u002F02-comparative-statics\u002Findex",[737],{"title":733,"path":734,"stem":735},{"title":739,"path":740,"stem":741,"children":742},"Module 3 — Choice under Risk and Insurance","\u002Fen\u002Fmicroeconomics\u002F03-uncertainty","en\u002Fmicroeconomics\u002F03-uncertainty\u002Findex",[743],{"title":739,"path":740,"stem":741},{"title":745,"path":746,"stem":747,"children":748},"Module 4 — General Equilibrium and Welfare","\u002Fen\u002Fmicroeconomics\u002F04-general-equilibrium","en\u002Fmicroeconomics\u002F04-general-equilibrium\u002Findex",[749],{"title":745,"path":746,"stem":747},{"title":751,"path":752,"stem":753,"children":754},"Module 5 — Static, Dynamic, and Repeated Games","\u002Fen\u002Fmicroeconomics\u002F05-game-theory","en\u002Fmicroeconomics\u002F05-game-theory\u002Findex",[755],{"title":751,"path":752,"stem":753},{"title":757,"path":758,"stem":759,"children":760},"Module 6 — Oligopoly, Entry, and Algorithmic Pricing","\u002Fen\u002Fmicroeconomics\u002F06-oligopoly","en\u002Fmicroeconomics\u002F06-oligopoly\u002Findex",[761],{"title":757,"path":758,"stem":759},{"title":763,"path":764,"stem":765,"children":766},"Module 7 — Information Economics and Contracts","\u002Fen\u002Fmicroeconomics\u002F07-information-economics","en\u002Fmicroeconomics\u002F07-information-economics\u002Findex",[767],{"title":763,"path":764,"stem":765},{"title":769,"path":770,"stem":771,"children":772},"Module 8 — Mechanism Design and Auctions","\u002Fen\u002Fmicroeconomics\u002F08-mechanism-design","en\u002Fmicroeconomics\u002F08-mechanism-design\u002Findex",[773],{"title":769,"path":770,"stem":771},{"title":775,"path":776,"stem":777,"children":778},"Module 9 — Behavioural and Experimental Microeconomics","\u002Fen\u002Fmicroeconomics\u002F09-behavioural-economics","en\u002Fmicroeconomics\u002F09-behavioural-economics\u002Findex",[779],{"title":775,"path":776,"stem":777},{"title":781,"path":782,"stem":783,"children":784},"Module 10 — Externalities, Public Goods, and Collective Action","\u002Fen\u002Fmicroeconomics\u002F10-externalities-public-goods","en\u002Fmicroeconomics\u002F10-externalities-public-goods\u002Findex",[785],{"title":781,"path":782,"stem":783},{"title":787,"path":788,"stem":789,"children":790},"Module 11 — Matching and Market Design","\u002Fen\u002Fmicroeconomics\u002F11-market-design","en\u002Fmicroeconomics\u002F11-market-design\u002Findex",[791],{"title":787,"path":788,"stem":789},{"title":793,"path":794,"stem":795,"children":796},"Module 12 — Integrated Microeconomic Design Studio","\u002Fen\u002Fmicroeconomics\u002F12-review","en\u002Fmicroeconomics\u002F12-review\u002Findex",[797],{"title":793,"path":794,"stem":795},{"title":799,"path":800,"stem":801,"children":802},"Playground","\u002Fen\u002Fplayground","en\u002Fplayground\u002Findex",[803,804,808,812,816,820],{"title":799,"path":800,"stem":801},{"title":805,"path":806,"stem":807},"Typst Plugin Playground","\u002Fen\u002Fplayground\u002F01-typstex","en\u002Fplayground\u002F01-typstex",{"title":809,"path":810,"stem":811},"Citation Plugin Test","\u002Fen\u002Fplayground\u002F02-citation","en\u002Fplayground\u002F02-citation",{"title":813,"path":814,"stem":815},"Pyodide Playground","\u002Fen\u002Fplayground\u002F03-pyodide","en\u002Fplayground\u002F03-pyodide",{"title":817,"path":818,"stem":819},"WebR Playground","\u002Fen\u002Fplayground\u002F04-webr","en\u002Fplayground\u002F04-webr",{"title":821,"path":822,"stem":823},"Chart.js Visualizations","\u002Fen\u002Fplayground\u002F05-chartjs","en\u002Fplayground\u002F05-chartjs",{"title":825,"path":826,"stem":827,"children":828,"page":249},"Statistics For Insurance","\u002Fen\u002Fstatistics-for-insurance","en\u002Fstatistics-for-insurance",[829,835,857,883,905,927,937],{"title":830,"path":831,"stem":832,"children":833},"Statistics for General Insurance","\u002Fen\u002Fstatistics-for-insurance\u002F01-intro","en\u002Fstatistics-for-insurance\u002F01-intro\u002Findex",[834],{"title":830,"path":831,"stem":832},{"title":836,"path":837,"stem":838,"children":839},"Claims Development and Reserving","\u002Fen\u002Fstatistics-for-insurance\u002F02-chain-ladder","en\u002Fstatistics-for-insurance\u002F02-chain-ladder\u002Findex",[840,841,845,849,853],{"title":836,"path":837,"stem":838},{"title":842,"path":843,"stem":844},"Basic Chain Ladder","\u002Fen\u002Fstatistics-for-insurance\u002F02-chain-ladder\u002F01-basic-chain","en\u002Fstatistics-for-insurance\u002F02-chain-ladder\u002F01-basic-chain",{"title":846,"path":847,"stem":848},"Frequency–Severity Reserving","\u002Fen\u002Fstatistics-for-insurance\u002F02-chain-ladder\u002F02-average-per-claim","en\u002Fstatistics-for-insurance\u002F02-chain-ladder\u002F02-average-per-claim",{"title":850,"path":851,"stem":852},"Bornhuetter–Ferguson Method","\u002Fen\u002Fstatistics-for-insurance\u002F02-chain-ladder\u002F03-b-f-method","en\u002Fstatistics-for-insurance\u002F02-chain-ladder\u002F03-b-f-method",{"title":854,"path":855,"stem":856},"Uncertainty and Diagnostics","\u002Fen\u002Fstatistics-for-insurance\u002F02-chain-ladder\u002F04-uncertainty-diagnostics","en\u002Fstatistics-for-insurance\u002F02-chain-ladder\u002F04-uncertainty-diagnostics",{"title":858,"path":859,"stem":860,"children":861},"Frequency and Severity Models","\u002Fen\u002Fstatistics-for-insurance\u002F03-common-dist","en\u002Fstatistics-for-insurance\u002F03-common-dist\u002Findex",[862,863,867,871,875,879],{"title":858,"path":859,"stem":860},{"title":864,"path":865,"stem":866},"Core Severity Models","\u002Fen\u002Fstatistics-for-insurance\u002F03-common-dist\u002F01-loss-dist","en\u002Fstatistics-for-insurance\u002F03-common-dist\u002F01-loss-dist",{"title":868,"path":869,"stem":870},"Tail Models and Extreme Values","\u002Fen\u002Fstatistics-for-insurance\u002F03-common-dist\u002F02-more-dist","en\u002Fstatistics-for-insurance\u002F03-common-dist\u002F02-more-dist",{"title":872,"path":873,"stem":874},"Claim Count Models","\u002Fen\u002Fstatistics-for-insurance\u002F03-common-dist\u002F03-case-dist","en\u002Fstatistics-for-insurance\u002F03-common-dist\u002F03-case-dist",{"title":876,"path":877,"stem":878},"Fitting and Validating Loss Models","\u002Fen\u002Fstatistics-for-insurance\u002F03-common-dist\u002F04-fit-dist","en\u002Fstatistics-for-insurance\u002F03-common-dist\u002F04-fit-dist",{"title":880,"path":881,"stem":882},"Mixtures and Heterogeneity","\u002Fen\u002Fstatistics-for-insurance\u002F03-common-dist\u002F05-mix-dist","en\u002Fstatistics-for-insurance\u002F03-common-dist\u002F05-mix-dist",{"title":884,"path":885,"stem":886,"children":887},"Reinsurance as a Loss Transformation","\u002Fen\u002Fstatistics-for-insurance\u002F04-reinsurance","en\u002Fstatistics-for-insurance\u002F04-reinsurance\u002Findex",[888,889,893,897,901],{"title":884,"path":885,"stem":886},{"title":890,"path":891,"stem":892},"Proportional Reinsurance","\u002Fen\u002Fstatistics-for-insurance\u002F04-reinsurance\u002F01-proportional","en\u002Fstatistics-for-insurance\u002F04-reinsurance\u002F01-proportional",{"title":894,"path":895,"stem":896},"Excess-of-Loss Reinsurance","\u002Fen\u002Fstatistics-for-insurance\u002F04-reinsurance\u002F02-excess","en\u002Fstatistics-for-insurance\u002F04-reinsurance\u002F02-excess",{"title":898,"path":899,"stem":900},"Inflation and Layer Erosion","\u002Fen\u002Fstatistics-for-insurance\u002F04-reinsurance\u002F03-inflation","en\u002Fstatistics-for-insurance\u002F04-reinsurance\u002F03-inflation",{"title":902,"path":903,"stem":904},"Reinsurance Decision Lab","\u002Fen\u002Fstatistics-for-insurance\u002F04-reinsurance\u002F04-examples","en\u002Fstatistics-for-insurance\u002F04-reinsurance\u002F04-examples",{"title":906,"path":907,"stem":908,"children":909},"Aggregate Risk and Capital","\u002Fen\u002Fstatistics-for-insurance\u002F05-risk-theory","en\u002Fstatistics-for-insurance\u002F05-risk-theory\u002Findex",[910,911,915,919,923],{"title":906,"path":907,"stem":908},{"title":912,"path":913,"stem":914},"Collective Risk Model","\u002Fen\u002Fstatistics-for-insurance\u002F05-risk-theory\u002F01-collective","en\u002Fstatistics-for-insurance\u002F05-risk-theory\u002F01-collective",{"title":916,"path":917,"stem":918},"Individual Risk Model","\u002Fen\u002Fstatistics-for-insurance\u002F05-risk-theory\u002F02-individual","en\u002Fstatistics-for-insurance\u002F05-risk-theory\u002F02-individual",{"title":920,"path":921,"stem":922},"Aggregate Risk Computation Lab","\u002Fen\u002Fstatistics-for-insurance\u002F05-risk-theory\u002F03-examples","en\u002Fstatistics-for-insurance\u002F05-risk-theory\u002F03-examples",{"title":924,"path":925,"stem":926},"Tail Risk, Dependence, and Capital","\u002Fen\u002Fstatistics-for-insurance\u002F05-risk-theory\u002F04-tail-capital","en\u002Fstatistics-for-insurance\u002F05-risk-theory\u002F04-tail-capital",{"title":928,"path":929,"stem":930,"children":931},"Surplus and Ruin Theory","\u002Fen\u002Fstatistics-for-insurance\u002F06-ruin-theory","en\u002Fstatistics-for-insurance\u002F06-ruin-theory\u002Findex",[932,933],{"title":928,"path":929,"stem":930},{"title":934,"path":935,"stem":936},"Finite-Time Ruin Simulation","\u002Fen\u002Fstatistics-for-insurance\u002F06-ruin-theory\u002F01-finite-time-simulation","en\u002Fstatistics-for-insurance\u002F06-ruin-theory\u002F01-finite-time-simulation",{"title":938,"path":939,"stem":940,"children":941},"Portfolio Risk Capstone","\u002Fen\u002Fstatistics-for-insurance\u002F07-capstone","en\u002Fstatistics-for-insurance\u002F07-capstone\u002Findex",[942],{"title":938,"path":939,"stem":940},{"title":944,"path":945,"stem":946,"children":947,"page":249},"Time Series","\u002Fen\u002Ftime-series","en\u002Ftime-series",[948,958,964,970,976,982,988,994,1016],{"title":949,"path":950,"stem":951,"children":952},"Classical Time Series — Course Guide","\u002Fen\u002Ftime-series\u002F00-intro","en\u002Ftime-series\u002F00-intro\u002Findex",[953,954],{"title":949,"path":950,"stem":951},{"title":955,"path":956,"stem":957},"Preparation — Stationarity in 30 Minutes","\u002Fen\u002Ftime-series\u002F00-intro\u002F01-stationary","en\u002Ftime-series\u002F00-intro\u002F01-stationary",{"title":959,"path":960,"stem":961,"children":962},"Module 1 — Processes, Dependence, and Stationarity","\u002Fen\u002Ftime-series\u002F01-stochastic-process","en\u002Ftime-series\u002F01-stochastic-process\u002Findex",[963],{"title":959,"path":960,"stem":961},{"title":965,"path":966,"stem":967,"children":968},"Module 2 — ARMA, ARIMA, and Model Identification","\u002Fen\u002Ftime-series\u002F02-arma","en\u002Ftime-series\u002F02-arma\u002Findex",[969],{"title":965,"path":966,"stem":967},{"title":971,"path":972,"stem":973,"children":974},"Module 3 — Linear Prediction and State-Space Recursions","\u002Fen\u002Ftime-series\u002F03-prediction","en\u002Ftime-series\u002F03-prediction\u002Findex",[975],{"title":971,"path":972,"stem":973},{"title":977,"path":978,"stem":979,"children":980},"Module 4 — Estimation, Likelihood, and Inference","\u002Fen\u002Ftime-series\u002F04-estimation","en\u002Ftime-series\u002F04-estimation\u002Findex",[981],{"title":977,"path":978,"stem":979},{"title":983,"path":984,"stem":985,"children":986},"Module 5 — Systems, Seasonality, and Cointegration","\u002Fen\u002Ftime-series\u002F05-multi-ar","en\u002Ftime-series\u002F05-multi-ar\u002Findex",[987],{"title":983,"path":984,"stem":985},{"title":989,"path":990,"stem":991,"children":992},"Module 6 — Spectral Analysis, Cycles, and Filters","\u002Fen\u002Ftime-series\u002F06-spectral-analysis","en\u002Ftime-series\u002F06-spectral-analysis\u002Findex",[993],{"title":989,"path":990,"stem":991},{"title":995,"path":996,"stem":997,"children":998},"R Matrix Laboratory","\u002Fen\u002Ftime-series\u002F07-r-implementation","en\u002Ftime-series\u002F07-r-implementation\u002Findex",[999,1000,1004,1008,1012],{"title":995,"path":996,"stem":997},{"title":1001,"path":1002,"stem":1003},"R Matrix Lab 1 — Covariance Geometry","\u002Fen\u002Ftime-series\u002F07-r-implementation\u002F01-covariance-matrices","en\u002Ftime-series\u002F07-r-implementation\u002F01-covariance-matrices",{"title":1005,"path":1006,"stem":1007},"R Matrix Lab 2 — AR Recursions and Yule–Walker Equations","\u002Fen\u002Ftime-series\u002F07-r-implementation\u002F02-ar-recursions","en\u002Ftime-series\u002F07-r-implementation\u002F02-ar-recursions",{"title":1009,"path":1010,"stem":1011},"R Matrix Lab 3 — Prediction and Gaussian Likelihood","\u002Fen\u002Ftime-series\u002F07-r-implementation\u002F03-prediction-likelihood","en\u002Ftime-series\u002F07-r-implementation\u002F03-prediction-likelihood",{"title":1013,"path":1014,"stem":1015},"R Matrix Lab 4 — State Space and Kalman Filtering","\u002Fen\u002Ftime-series\u002F07-r-implementation\u002F04-state-space","en\u002Ftime-series\u002F07-r-implementation\u002F04-state-space",{"title":1017,"path":1018,"stem":1019,"children":1020},"Optional Python Appendix — Empirical Forecasting","\u002Fen\u002Ftime-series\u002F08-python-implementation","en\u002Ftime-series\u002F08-python-implementation\u002Findex",[1021,1022,1026,1030,1034],{"title":1017,"path":1018,"stem":1019},{"title":1023,"path":1024,"stem":1025},"Optional Python Lab 1 — Explore Before Modeling","\u002Fen\u002Ftime-series\u002F08-python-implementation\u002F01-exploration","en\u002Ftime-series\u002F08-python-implementation\u002F01-exploration",{"title":1027,"path":1028,"stem":1029},"Optional Python Lab 2 — Diagnose Stationarity","\u002Fen\u002Ftime-series\u002F08-python-implementation\u002F02-stationarity","en\u002Ftime-series\u002F08-python-implementation\u002F02-stationarity",{"title":1031,"path":1032,"stem":1033},"Optional Python Lab 3 — Fit and Audit ARMA Errors","\u002Fen\u002Ftime-series\u002F08-python-implementation\u002F03-arma-fitting","en\u002Ftime-series\u002F08-python-implementation\u002F03-arma-fitting",{"title":1035,"path":1036,"stem":1037},"Optional Python Lab 4 — Forecast, Backtest, and Monitor","\u002Fen\u002Ftime-series\u002F08-python-implementation\u002F04-forecasting","en\u002Ftime-series\u002F08-python-implementation\u002F04-forecasting",{"title":1039,"path":1040,"stem":1041,"children":1042},"Zh","\u002Fzh","zh",[1043,1045,1063,1247,1323,1365,1421,1467,1543,1625,1633,1731],{"title":10,"path":1040,"stem":1044},"zh\u002Findex",{"title":1046,"path":1047,"stem":1048,"children":1049},"学术写作与文献综述","\u002Fzh\u002Facademic-writing","zh\u002Facademic-writing\u002Findex",[1050,1051,1055,1059],{"title":1046,"path":1047,"stem":1048},{"title":1052,"path":1053,"stem":1054},"4. 文献综述的构建与写作","\u002Fzh\u002Facademic-writing\u002F04-writing-the-literature-review","zh\u002Facademic-writing\u002F04-writing-the-literature-review",{"title":1056,"path":1057,"stem":1058},"8. 文献综述清单与模板","\u002Fzh\u002Facademic-writing\u002F08-literature-review-checklist-and-template","zh\u002Facademic-writing\u002F08-literature-review-checklist-and-template",{"title":1060,"path":1061,"stem":1062},"10. 从分块结构到问题链：文献综述示例","\u002Fzh\u002Facademic-writing\u002F10-从分块结构到问题链-文献综述示例","zh\u002Facademic-writing\u002F10-从分块结构到问题链-文献综述示例",{"title":59,"path":1064,"stem":1065,"children":1066,"page":249},"\u002Fzh\u002Faccounting","zh\u002Faccounting",[1067,1073,1087,1191],{"title":1068,"path":1069,"stem":1070,"children":1071},"会计学学习路线图","\u002Fzh\u002Faccounting\u002F00-index","zh\u002Faccounting\u002F00-index",[1072],{"title":1068,"path":1069,"stem":1070},{"title":1074,"path":1075,"stem":1076,"children":1077},"附录","\u002Fzh\u002Faccounting\u002Fappendix","zh\u002Faccounting\u002Fappendix\u002Findex",[1078,1079,1083],{"title":1074,"path":1075,"stem":1076},{"title":1080,"path":1081,"stem":1082},"综合示例与常见陷阱","\u002Fzh\u002Faccounting\u002Fappendix\u002F24-examples-pitfalls","zh\u002Faccounting\u002Fappendix\u002F24-examples-pitfalls",{"title":1084,"path":1085,"stem":1086},"会计术语速查表","\u002Fzh\u002Faccounting\u002Fappendix\u002F26-glossary","zh\u002Faccounting\u002Fappendix\u002F26-glossary",{"title":1088,"path":1089,"stem":1090,"children":1091},"金融会计","\u002Fzh\u002Faccounting\u002Ffinancial-accounting","zh\u002Faccounting\u002Ffinancial-accounting\u002Findex",[1092,1093,1111,1125,1159,1173],{"title":1088,"path":1089,"stem":1090},{"title":1094,"path":1095,"stem":1096,"children":1097},"1. 基础","\u002Fzh\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations","zh\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002Findex",[1098,1099,1103,1107],{"title":1094,"path":1095,"stem":1096},{"title":1100,"path":1101,"stem":1102},"会计信息目标与质量特征","\u002Fzh\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F01-objectives-qualitative-characteristics","zh\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F01-objectives-qualitative-characteristics",{"title":1104,"path":1105,"stem":1106},"会计等式与要素","\u002Fzh\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F02-equation-elements","zh\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F02-equation-elements",{"title":1108,"path":1109,"stem":1110},"记账基础与原则","\u002Fzh\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F03-accounting-bases-principles","zh\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F03-accounting-bases-principles",{"title":1112,"path":1113,"stem":1114,"children":1115},"2. 交易记录","\u002Fzh\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions","zh\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002Findex",[1116,1117,1121],{"title":1112,"path":1113,"stem":1114},{"title":1118,"path":1119,"stem":1120},"复式记账与借贷规则","\u002Fzh\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F04-double-entry-dr-cr","zh\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F04-double-entry-dr-cr",{"title":1122,"path":1123,"stem":1124},"会计循环","\u002Fzh\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F05-accounting-cycle","zh\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F05-accounting-cycle",{"title":1126,"path":1127,"stem":1128,"children":1129},"3. 计量与调整","\u002Fzh\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments","zh\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002Findex",[1130,1131,1135,1139,1143,1147,1151,1155],{"title":1126,"path":1127,"stem":1128},{"title":1132,"path":1133,"stem":1134},"收入确认","\u002Fzh\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F07-revenue-recognition","zh\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F07-revenue-recognition",{"title":1136,"path":1137,"stem":1138},"存货","\u002Fzh\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F08-inventory","zh\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F08-inventory",{"title":1140,"path":1141,"stem":1142},"应收账款","\u002Fzh\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F09-receivables","zh\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F09-receivables",{"title":1144,"path":1145,"stem":1146},"固定资产","\u002Fzh\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F10-ppe","zh\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F10-ppe",{"title":1148,"path":1149,"stem":1150},"无形资产","\u002Fzh\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F11-intangibles","zh\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F11-intangibles",{"title":1152,"path":1153,"stem":1154},"租赁","\u002Fzh\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F12-leases","zh\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F12-leases",{"title":1156,"path":1157,"stem":1158},"所得税","\u002Fzh\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F13-income-tax","zh\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F13-income-tax",{"title":1160,"path":1161,"stem":1162,"children":1163},"4. 报表与现金","\u002Fzh\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash","zh\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002Findex",[1164,1165,1169],{"title":1160,"path":1161,"stem":1162},{"title":1166,"path":1167,"stem":1168},"财务报表","\u002Fzh\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F06-financial-statements","zh\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F06-financial-statements",{"title":1170,"path":1171,"stem":1172},"现金控制","\u002Fzh\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F14-cash-control","zh\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F14-cash-control",{"title":1174,"path":1175,"stem":1176,"children":1177},"5. 分析与比较","\u002Fzh\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison","zh\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002Findex",[1178,1179,1183,1187],{"title":1174,"path":1175,"stem":1176},{"title":1180,"path":1181,"stem":1182},"财务比率分析","\u002Fzh\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F15-ratio-analysis","zh\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F15-ratio-analysis",{"title":1184,"path":1185,"stem":1186},"IFRS 与 US GAAP 对比","\u002Fzh\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F25-ifrs-gaap","zh\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F25-ifrs-gaap",{"title":1188,"path":1189,"stem":1190},"2026 准则更新与报告案例","\u002Fzh\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F27-current-standards-2026","zh\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F27-current-standards-2026",{"title":1192,"path":1193,"stem":1194,"children":1195},"管理会计","\u002Fzh\u002Faccounting\u002Fmanagement-accounting","zh\u002Faccounting\u002Fmanagement-accounting\u002Findex",[1196,1197,1215,1233],{"title":1192,"path":1193,"stem":1194},{"title":1198,"path":1199,"stem":1200,"children":1201},"1. 成本基础","\u002Fzh\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations","zh\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002Findex",[1202,1203,1207,1211],{"title":1198,"path":1199,"stem":1200},{"title":1204,"path":1205,"stem":1206},"成本概念","\u002Fzh\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F16-cost-concepts","zh\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F16-cost-concepts",{"title":1208,"path":1209,"stem":1210},"成本核算系统","\u002Fzh\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F17-costing-systems","zh\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F17-costing-systems",{"title":1212,"path":1213,"stem":1214},"变动成本法 vs. 吸收成本法","\u002Fzh\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F19-variable-vs-absorption","zh\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F19-variable-vs-absorption",{"title":1216,"path":1217,"stem":1218,"children":1219},"2. 计划与控制","\u002Fzh\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control","zh\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002Findex",[1220,1221,1225,1229],{"title":1216,"path":1217,"stem":1218},{"title":1222,"path":1223,"stem":1224},"本量利分析","\u002Fzh\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F18-cvp-analysis","zh\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F18-cvp-analysis",{"title":1226,"path":1227,"stem":1228},"预算与差异分析","\u002Fzh\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F20-budgeting-variances","zh\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F20-budgeting-variances",{"title":1230,"path":1231,"stem":1232},"绩效评价","\u002Fzh\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F21-performance-measurement","zh\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F21-performance-measurement",{"title":1234,"path":1235,"stem":1236,"children":1237},"3. 决策与投资","\u002Fzh\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment","zh\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002Findex",[1238,1239,1243],{"title":1234,"path":1235,"stem":1236},{"title":1240,"path":1241,"stem":1242},"短期决策","\u002Fzh\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F22-short-term-decisions","zh\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F22-short-term-decisions",{"title":1244,"path":1245,"stem":1246},"资本预算","\u002Fzh\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F23-capital-budgeting","zh\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F23-capital-budgeting",{"title":1248,"path":1249,"stem":1250,"children":1251},"资产定价理论","\u002Fzh\u002Fasset-pricing","zh\u002Fasset-pricing\u002Findex",[1252,1253,1259,1265,1271,1277,1283,1289,1295,1301,1307,1313,1319],{"title":1248,"path":1249,"stem":1250},{"title":1254,"path":1255,"stem":1256,"children":1257},"第一章：引言与基础","\u002Fzh\u002Fasset-pricing\u002F01-intro","zh\u002Fasset-pricing\u002F01-intro\u002Findex",[1258],{"title":1254,"path":1255,"stem":1256},{"title":1260,"path":1261,"stem":1262,"children":1263},"第二章：效用理论与风险偏好","\u002Fzh\u002Fasset-pricing\u002F02-utility","zh\u002Fasset-pricing\u002F02-utility\u002Findex",[1264],{"title":1260,"path":1261,"stem":1262},{"title":1266,"path":1267,"stem":1268,"children":1269},"第三章：均值-方差分析","\u002Fzh\u002Fasset-pricing\u002F03-mean-variance","zh\u002Fasset-pricing\u002F03-mean-variance\u002Findex",[1270],{"title":1266,"path":1267,"stem":1268},{"title":1272,"path":1273,"stem":1274,"children":1275},"第四章：资本资产定价模型(CAPM)","\u002Fzh\u002Fasset-pricing\u002F04-capm","zh\u002Fasset-pricing\u002F04-capm\u002Findex",[1276],{"title":1272,"path":1273,"stem":1274},{"title":1278,"path":1279,"stem":1280,"children":1281},"第五章：因子模型","\u002Fzh\u002Fasset-pricing\u002F05-factor-models","zh\u002Fasset-pricing\u002F05-factor-models\u002Findex",[1282],{"title":1278,"path":1279,"stem":1280},{"title":1284,"path":1285,"stem":1286,"children":1287},"第六章：跨期资产定价","\u002Fzh\u002Fasset-pricing\u002F06-intertemporal","zh\u002Fasset-pricing\u002F06-intertemporal\u002Findex",[1288],{"title":1284,"path":1285,"stem":1286},{"title":1290,"path":1291,"stem":1292,"children":1293},"第七章：期权定价理论","\u002Fzh\u002Fasset-pricing\u002F07-options","zh\u002Fasset-pricing\u002F07-options\u002Findex",[1294],{"title":1290,"path":1291,"stem":1292},{"title":1296,"path":1297,"stem":1298,"children":1299},"第八章：固定收益证券","\u002Fzh\u002Fasset-pricing\u002F08-fixed-income","zh\u002Fasset-pricing\u002F08-fixed-income\u002Findex",[1300],{"title":1296,"path":1297,"stem":1298},{"title":1302,"path":1303,"stem":1304,"children":1305},"第九章：市场有效性与异象","\u002Fzh\u002Fasset-pricing\u002F09-efficiency","zh\u002Fasset-pricing\u002F09-efficiency\u002Findex",[1306],{"title":1302,"path":1303,"stem":1304},{"title":1308,"path":1309,"stem":1310,"children":1311},"第十章：数值方法与实证应用","\u002Fzh\u002Fasset-pricing\u002F10-empirical","zh\u002Fasset-pricing\u002F10-empirical\u002Findex",[1312],{"title":1308,"path":1309,"stem":1310},{"title":1314,"path":1315,"stem":1316,"children":1317},"第十一章：资产定价浏览器交互实验","\u002Fzh\u002Fasset-pricing\u002F11-interactive-labs","zh\u002Fasset-pricing\u002F11-interactive-labs\u002Findex",[1318],{"title":1314,"path":1315,"stem":1316},{"title":1320,"path":1321,"stem":1322},"第十二章：前沿文献与现代资产定价案例（2023—2026）","\u002Fzh\u002Fasset-pricing\u002F12-frontier-literature-2026","zh\u002Fasset-pricing\u002F12-frontier-literature-2026",{"title":1324,"path":1325,"stem":1326,"children":1327},"计量经济学","\u002Fzh\u002Feconometrics","zh\u002Feconometrics\u002Findex",[1328,1329,1333,1337,1341,1345,1349,1353,1357,1361],{"title":1324,"path":1325,"stem":1326},{"title":1330,"path":1331,"stem":1332},"第一章：数据、概率与回归对象","\u002Fzh\u002Feconometrics\u002F01-data-and-regression","zh\u002Feconometrics\u002F01-data-and-regression",{"title":1334,"path":1335,"stem":1336},"第二章：OLS、矩阵与几何解释","\u002Fzh\u002Feconometrics\u002F02-ols-and-geometry","zh\u002Feconometrics\u002F02-ols-and-geometry",{"title":1338,"path":1339,"stem":1340},"第三章：统计推断与稳健标准误","\u002Fzh\u002Feconometrics\u002F03-inference-and-robustness","zh\u002Feconometrics\u002F03-inference-and-robustness",{"title":1342,"path":1343,"stem":1344},"第四章：内生性、工具变量与两阶段最小二乘","\u002Fzh\u002Feconometrics\u002F04-endogeneity-and-iv","zh\u002Feconometrics\u002F04-endogeneity-and-iv",{"title":1346,"path":1347,"stem":1348},"第五章：面板数据与时间序列","\u002Fzh\u002Feconometrics\u002F05-panel-and-time-series","zh\u002Feconometrics\u002F05-panel-and-time-series",{"title":1350,"path":1351,"stem":1352},"第六章：估计方法与因果设计的共同基础","\u002Fzh\u002Feconometrics\u002F06-estimation-and-causal-design","zh\u002Feconometrics\u002F06-estimation-and-causal-design",{"title":1354,"path":1355,"stem":1356},"第七章：可重复计量实证项目","\u002Fzh\u002Feconometrics\u002F07-reproducible-project","zh\u002Feconometrics\u002F07-reproducible-project",{"title":1358,"path":1359,"stem":1360},"第八章：计量经济学浏览器回归实验","\u002Fzh\u002Feconometrics\u002F08-interactive-regression-labs","zh\u002Feconometrics\u002F08-interactive-regression-labs",{"title":1362,"path":1363,"stem":1364},"第九章：前沿文献与现代计量案例（2023—2026）","\u002Fzh\u002Feconometrics\u002F09-frontier-literature-2026","zh\u002Feconometrics\u002F09-frontier-literature-2026",{"title":478,"path":1366,"stem":1367,"children":1368,"page":249},"\u002Fzh\u002Fintro-to-economics","zh\u002Fintro-to-economics",[1369,1373,1377,1381,1385,1389,1393,1397,1401,1405,1409,1413,1417],{"title":1370,"path":1371,"stem":1372},"经济学导论 (微观与宏观)","\u002Fzh\u002Fintro-to-economics\u002F00-intro","zh\u002Fintro-to-economics\u002F00-intro",{"title":1374,"path":1375,"stem":1376},"第1章：经济学基础原理","\u002Fzh\u002Fintro-to-economics\u002F01-foundations","zh\u002Fintro-to-economics\u002F01-foundations",{"title":1378,"path":1379,"stem":1380},"第2章：需求与供给","\u002Fzh\u002Fintro-to-economics\u002F02-demand-and-supply","zh\u002Fintro-to-economics\u002F02-demand-and-supply",{"title":1382,"path":1383,"stem":1384},"第3章：弹性","\u002Fzh\u002Fintro-to-economics\u002F03-elasticity","zh\u002Fintro-to-economics\u002F03-elasticity",{"title":1386,"path":1387,"stem":1388},"第4章：市场结构","\u002Fzh\u002Fintro-to-economics\u002F04-market-structures","zh\u002Fintro-to-economics\u002F04-market-structures",{"title":1390,"path":1391,"stem":1392},"第5章：GDP 与财富","\u002Fzh\u002Fintro-to-economics\u002F05-gdp-and-wealth","zh\u002Fintro-to-economics\u002F05-gdp-and-wealth",{"title":1394,"path":1395,"stem":1396},"第6章：通货膨胀与失业","\u002Fzh\u002Fintro-to-economics\u002F06-inflation-and-unemployment","zh\u002Fintro-to-economics\u002F06-inflation-and-unemployment",{"title":1398,"path":1399,"stem":1400},"第7章：经济增长","\u002Fzh\u002Fintro-to-economics\u002F07-economic-growth","zh\u002Fintro-to-economics\u002F07-economic-growth",{"title":1402,"path":1403,"stem":1404},"第8章：货币与银行","\u002Fzh\u002Fintro-to-economics\u002F08-money-and-banking","zh\u002Fintro-to-economics\u002F08-money-and-banking",{"title":1406,"path":1407,"stem":1408},"第9章：货币政策与 AD-AS 模型","\u002Fzh\u002Fintro-to-economics\u002F09-monetary-policy-and-ad-as","zh\u002Fintro-to-economics\u002F09-monetary-policy-and-ad-as",{"title":1410,"path":1411,"stem":1412},"第10章：财政政策","\u002Fzh\u002Fintro-to-economics\u002F10-fiscal-policy","zh\u002Fintro-to-economics\u002F10-fiscal-policy",{"title":1414,"path":1415,"stem":1416},"第11章：开放经济与汇率","\u002Fzh\u002Fintro-to-economics\u002F11-open-economy-and-exchange-rates","zh\u002Fintro-to-economics\u002F11-open-economy-and-exchange-rates",{"title":1418,"path":1419,"stem":1420},"第12章：综合复习与案例分析","\u002Fzh\u002Fintro-to-economics\u002F12-review-and-case-studies","zh\u002Fintro-to-economics\u002F12-review-and-case-studies",{"title":1422,"path":1423,"stem":1424,"children":1425},"宏观经济学","\u002Fzh\u002Fmacroeconomics","zh\u002Fmacroeconomics\u002Findex",[1426,1427,1431,1435,1439,1443,1447,1451,1455,1459,1463],{"title":1422,"path":1423,"stem":1424},{"title":1428,"path":1429,"stem":1430},"第一章：国民账户与宏观指标","\u002Fzh\u002Fmacroeconomics\u002F01-national-accounts","zh\u002Fmacroeconomics\u002F01-national-accounts",{"title":1432,"path":1433,"stem":1434},"第二章：消费、投资与凯恩斯交叉","\u002Fzh\u002Fmacroeconomics\u002F02-consumption-investment","zh\u002Fmacroeconomics\u002F02-consumption-investment",{"title":1436,"path":1437,"stem":1438},"第三章：货币、银行与货币政策","\u002Fzh\u002Fmacroeconomics\u002F03-money-and-monetary-policy","zh\u002Fmacroeconomics\u002F03-money-and-monetary-policy",{"title":1440,"path":1441,"stem":1442},"第四章：AD–AS、通货膨胀与失业","\u002Fzh\u002Fmacroeconomics\u002F04-ad-as-inflation-unemployment","zh\u002Fmacroeconomics\u002F04-ad-as-inflation-unemployment",{"title":1444,"path":1445,"stem":1446},"第五章：财政政策、债务与稳定化","\u002Fzh\u002Fmacroeconomics\u002F05-fiscal-policy-and-debt","zh\u002Fmacroeconomics\u002F05-fiscal-policy-and-debt",{"title":1448,"path":1449,"stem":1450},"第六章：经济增长、生产率与发展","\u002Fzh\u002Fmacroeconomics\u002F06-growth-productivity","zh\u002Fmacroeconomics\u002F06-growth-productivity",{"title":1452,"path":1453,"stem":1454},"第七章：开放经济、汇率与国际收支","\u002Fzh\u002Fmacroeconomics\u002F07-open-economy","zh\u002Fmacroeconomics\u002F07-open-economy",{"title":1456,"path":1457,"stem":1458},"第八章：宏观研究项目与政策分析","\u002Fzh\u002Fmacroeconomics\u002F08-macro-research-project","zh\u002Fmacroeconomics\u002F08-macro-research-project",{"title":1460,"path":1461,"stem":1462},"第九章：宏观经济学浏览器交互实验","\u002Fzh\u002Fmacroeconomics\u002F09-interactive-policy-labs","zh\u002Fmacroeconomics\u002F09-interactive-policy-labs",{"title":1464,"path":1465,"stem":1466},"第十章：前沿文献与当代宏观案例（2023—2026）","\u002Fzh\u002Fmacroeconomics\u002F10-frontier-literature-2026","zh\u002Fmacroeconomics\u002F10-frontier-literature-2026",{"title":1468,"path":1469,"stem":1470,"children":1471},"微观计量经济学","\u002Fzh\u002Fmicroeconometrics","zh\u002Fmicroeconometrics\u002Findex",[1472,1473,1479,1485,1491,1497,1503,1509,1515,1521,1527,1533,1539],{"title":1468,"path":1469,"stem":1470},{"title":1474,"path":1475,"stem":1476,"children":1477},"第一章：微观计量与因果推断导论","\u002Fzh\u002Fmicroeconometrics\u002F01-intro","zh\u002Fmicroeconometrics\u002F01-intro\u002Findex",[1478],{"title":1474,"path":1475,"stem":1476},{"title":1480,"path":1481,"stem":1482,"children":1483},"第二章：线性回归与 OLS","\u002Fzh\u002Fmicroeconometrics\u002F02-ols","zh\u002Fmicroeconometrics\u002F02-ols\u002Findex",[1484],{"title":1480,"path":1481,"stem":1482},{"title":1486,"path":1487,"stem":1488,"children":1489},"第三章：工具变量法","\u002Fzh\u002Fmicroeconometrics\u002F03-iv","zh\u002Fmicroeconometrics\u002F03-iv\u002Findex",[1490],{"title":1486,"path":1487,"stem":1488},{"title":1492,"path":1493,"stem":1494,"children":1495},"第四章：面板数据方法","\u002Fzh\u002Fmicroeconometrics\u002F04-panel","zh\u002Fmicroeconometrics\u002F04-panel\u002Findex",[1496],{"title":1492,"path":1493,"stem":1494},{"title":1498,"path":1499,"stem":1500,"children":1501},"第五章：双重差分法","\u002Fzh\u002Fmicroeconometrics\u002F05-did","zh\u002Fmicroeconometrics\u002F05-did\u002Findex",[1502],{"title":1498,"path":1499,"stem":1500},{"title":1504,"path":1505,"stem":1506,"children":1507},"第六章：断点回归设计","\u002Fzh\u002Fmicroeconometrics\u002F06-rdd","zh\u002Fmicroeconometrics\u002F06-rdd\u002Findex",[1508],{"title":1504,"path":1505,"stem":1506},{"title":1510,"path":1511,"stem":1512,"children":1513},"第七章：匹配、倾向得分与加权","\u002Fzh\u002Fmicroeconometrics\u002F07-matching","zh\u002Fmicroeconometrics\u002F07-matching\u002Findex",[1514],{"title":1510,"path":1511,"stem":1512},{"title":1516,"path":1517,"stem":1518,"children":1519},"第八章：离散选择模型","\u002Fzh\u002Fmicroeconometrics\u002F08-discrete-choice","zh\u002Fmicroeconometrics\u002F08-discrete-choice\u002Findex",[1520],{"title":1516,"path":1517,"stem":1518},{"title":1522,"path":1523,"stem":1524,"children":1525},"第九章：计数数据与受限因变量","\u002Fzh\u002Fmicroeconometrics\u002F09-count-limited","zh\u002Fmicroeconometrics\u002F09-count-limited\u002Findex",[1526],{"title":1522,"path":1523,"stem":1524},{"title":1528,"path":1529,"stem":1530,"children":1531},"第十章：合成控制法","\u002Fzh\u002Fmicroeconometrics\u002F10-synthetic-control","zh\u002Fmicroeconometrics\u002F10-synthetic-control\u002Findex",[1532],{"title":1528,"path":1529,"stem":1530},{"title":1534,"path":1535,"stem":1536,"children":1537},"第十一章：机器学习与因果推断","\u002Fzh\u002Fmicroeconometrics\u002F11-ml-causal","zh\u002Fmicroeconometrics\u002F11-ml-causal\u002Findex",[1538],{"title":1534,"path":1535,"stem":1536},{"title":1540,"path":1541,"stem":1542},"第十二章：前沿文献与现代微观案例（2024—2026）","\u002Fzh\u002Fmicroeconometrics\u002F12-frontier-literature-2026","zh\u002Fmicroeconometrics\u002F12-frontier-literature-2026",{"title":716,"path":1544,"stem":1545,"children":1546,"page":249},"\u002Fzh\u002Fmicroeconomics","zh\u002Fmicroeconomics",[1547,1553,1559,1565,1571,1577,1583,1589,1595,1601,1607,1613,1619],{"title":1548,"path":1549,"stem":1550,"children":1551},"微观经济学 III","\u002Fzh\u002Fmicroeconomics\u002F00-intro","zh\u002Fmicroeconomics\u002F00-intro\u002Findex",[1552],{"title":1548,"path":1549,"stem":1550},{"title":1554,"path":1555,"stem":1556,"children":1557},"消费者理论与分析基础","\u002Fzh\u002Fmicroeconomics\u002F01-fundations","zh\u002Fmicroeconomics\u002F01-fundations\u002Findex",[1558],{"title":1554,"path":1555,"stem":1556},{"title":1560,"path":1561,"stem":1562,"children":1563},"比较静态分析与福利测度","\u002Fzh\u002Fmicroeconomics\u002F02-comparative-statics","zh\u002Fmicroeconomics\u002F02-comparative-statics\u002Findex",[1564],{"title":1560,"path":1561,"stem":1562},{"title":1566,"path":1567,"stem":1568,"children":1569},"不确定性下的决策","\u002Fzh\u002Fmicroeconomics\u002F03-uncertainty","zh\u002Fmicroeconomics\u002F03-uncertainty\u002Findex",[1570],{"title":1566,"path":1567,"stem":1568},{"title":1572,"path":1573,"stem":1574,"children":1575},"一般均衡与福利经济学","\u002Fzh\u002Fmicroeconomics\u002F04-general-equilibrium","zh\u002Fmicroeconomics\u002F04-general-equilibrium\u002Findex",[1576],{"title":1572,"path":1573,"stem":1574},{"title":1578,"path":1579,"stem":1580,"children":1581},"博弈论：静态与动态博弈","\u002Fzh\u002Fmicroeconomics\u002F05-game-theory","zh\u002Fmicroeconomics\u002F05-game-theory\u002Findex",[1582],{"title":1578,"path":1579,"stem":1580},{"title":1584,"path":1585,"stem":1586,"children":1587},"寡头垄断与策略性市场行为","\u002Fzh\u002Fmicroeconomics\u002F06-oligopoly","zh\u002Fmicroeconomics\u002F06-oligopoly\u002Findex",[1588],{"title":1584,"path":1585,"stem":1586},{"title":1590,"path":1591,"stem":1592,"children":1593},"信息经济学：逆向选择与道德风险","\u002Fzh\u002Fmicroeconomics\u002F07-information-economics","zh\u002Fmicroeconomics\u002F07-information-economics\u002Findex",[1594],{"title":1590,"path":1591,"stem":1592},{"title":1596,"path":1597,"stem":1598,"children":1599},"机制设计与拍卖理论","\u002Fzh\u002Fmicroeconomics\u002F08-mechanism-design","zh\u002Fmicroeconomics\u002F08-mechanism-design\u002Findex",[1600],{"title":1596,"path":1597,"stem":1598},{"title":1602,"path":1603,"stem":1604,"children":1605},"行为与实验微观经济学","\u002Fzh\u002Fmicroeconomics\u002F09-behavioural-economics","zh\u002Fmicroeconomics\u002F09-behavioural-economics\u002Findex",[1606],{"title":1602,"path":1603,"stem":1604},{"title":1608,"path":1609,"stem":1610,"children":1611},"外部性、公共物品与机制","\u002Fzh\u002Fmicroeconomics\u002F10-externalities-public-goods","zh\u002Fmicroeconomics\u002F10-externalities-public-goods\u002Findex",[1612],{"title":1608,"path":1609,"stem":1610},{"title":1614,"path":1615,"stem":1616,"children":1617},"市场设计与匹配理论","\u002Fzh\u002Fmicroeconomics\u002F11-market-design","zh\u002Fmicroeconomics\u002F11-market-design\u002Findex",[1618],{"title":1614,"path":1615,"stem":1616},{"title":1620,"path":1621,"stem":1622,"children":1623},"第十二章：微观经济学：回顾与前沿应用","\u002Fzh\u002Fmicroeconomics\u002F12-review","zh\u002Fmicroeconomics\u002F12-review\u002Findex",[1624],{"title":1620,"path":1621,"stem":1622},{"title":799,"path":1626,"stem":1627,"children":1628,"page":249},"\u002Fzh\u002Fplayground","zh\u002Fplayground",[1629],{"title":1630,"path":1631,"stem":1632},"Chart.js 可视化","\u002Fzh\u002Fplayground\u002F05-chartjs","zh\u002Fplayground\u002F05-chartjs",{"title":1634,"path":1635,"stem":1636,"children":1637},"概率论与数理统计","\u002Fzh\u002Fprob-and-stats","zh\u002Fprob-and-stats\u002Findex",[1638,1639,1645,1680,1727],{"title":1634,"path":1635,"stem":1636},{"title":1640,"path":1641,"stem":1642,"children":1643},"第零章：概率统计的对象与学习方法","\u002Fzh\u002Fprob-and-stats\u002F00-intro","zh\u002Fprob-and-stats\u002F00-intro\u002Findex",[1644],{"title":1640,"path":1641,"stem":1642},{"title":1646,"path":1647,"stem":1648,"children":1649,"page":249},"01 Probability","\u002Fzh\u002Fprob-and-stats\u002F01-probability","zh\u002Fprob-and-stats\u002F01-probability",[1650,1656,1662,1668,1674],{"title":1651,"path":1652,"stem":1653,"children":1654},"第一章：概率论基础","\u002Fzh\u002Fprob-and-stats\u002F01-probability\u002F01-prob-theory","zh\u002Fprob-and-stats\u002F01-probability\u002F01-prob-theory\u002Findex",[1655],{"title":1651,"path":1652,"stem":1653},{"title":1657,"path":1658,"stem":1659,"children":1660},"第二章：随机变量与分布","\u002Fzh\u002Fprob-and-stats\u002F01-probability\u002F02-random-variables","zh\u002Fprob-and-stats\u002F01-probability\u002F02-random-variables\u002Findex",[1661],{"title":1657,"path":1658,"stem":1659},{"title":1663,"path":1664,"stem":1665,"children":1666},"第三章：期望、方差与条件矩","\u002Fzh\u002Fprob-and-stats\u002F01-probability\u002F03-moment","zh\u002Fprob-and-stats\u002F01-probability\u002F03-moment\u002Findex",[1667],{"title":1663,"path":1664,"stem":1665},{"title":1669,"path":1670,"stem":1671,"children":1672},"第四章：常见分布族与建模机制","\u002Fzh\u002Fprob-and-stats\u002F01-probability\u002F04-families","zh\u002Fprob-and-stats\u002F01-probability\u002F04-families\u002Findex",[1673],{"title":1669,"path":1670,"stem":1671},{"title":1675,"path":1676,"stem":1677,"children":1678},"第五章：收敛与渐近理论","\u002Fzh\u002Fprob-and-stats\u002F01-probability\u002F05-asymptotics","zh\u002Fprob-and-stats\u002F01-probability\u002F05-asymptotics\u002Findex",[1679],{"title":1675,"path":1676,"stem":1677},{"title":1681,"path":1682,"stem":1683,"children":1684,"page":249},"02 Statistics","\u002Fzh\u002Fprob-and-stats\u002F02-statistics","zh\u002Fprob-and-stats\u002F02-statistics",[1685,1691,1697,1703,1709,1715,1721],{"title":1686,"path":1687,"stem":1688,"children":1689},"第六章：抽样分布","\u002Fzh\u002Fprob-and-stats\u002F02-statistics\u002F01-sampling","zh\u002Fprob-and-stats\u002F02-statistics\u002F01-sampling\u002Findex",[1690],{"title":1686,"path":1687,"stem":1688},{"title":1692,"path":1693,"stem":1694,"children":1695},"第七章：区间估计","\u002Fzh\u002Fprob-and-stats\u002F02-statistics\u002F02-interval-estimation","zh\u002Fprob-and-stats\u002F02-statistics\u002F02-interval-estimation\u002Findex",[1696],{"title":1692,"path":1693,"stem":1694},{"title":1698,"path":1699,"stem":1700,"children":1701},"第八章：点估计理论","\u002Fzh\u002Fprob-and-stats\u002F02-statistics\u002F03-point-estimation","zh\u002Fprob-and-stats\u002F02-statistics\u002F03-point-estimation\u002Findex",[1702],{"title":1698,"path":1699,"stem":1700},{"title":1704,"path":1705,"stem":1706,"children":1707},"第九章：点估计方法","\u002Fzh\u002Fprob-and-stats\u002F02-statistics\u002F04-pe-method","zh\u002Fprob-and-stats\u002F02-statistics\u002F04-pe-method\u002Findex",[1708],{"title":1704,"path":1705,"stem":1706},{"title":1710,"path":1711,"stem":1712,"children":1713},"第十章：假设检验原理","\u002Fzh\u002Fprob-and-stats\u002F02-statistics\u002F05-hypothesis","zh\u002Fprob-and-stats\u002F02-statistics\u002F05-hypothesis\u002Findex",[1714],{"title":1710,"path":1711,"stem":1712},{"title":1716,"path":1717,"stem":1718,"children":1719},"第十一章：常用检验方法与选择","\u002Fzh\u002Fprob-and-stats\u002F02-statistics\u002F06-hypothesis-method","zh\u002Fprob-and-stats\u002F02-statistics\u002F06-hypothesis-method\u002Findex",[1720],{"title":1716,"path":1717,"stem":1718},{"title":1722,"path":1723,"stem":1724,"children":1725},"第十二章：Bootstrap 与重抽样","\u002Fzh\u002Fprob-and-stats\u002F02-statistics\u002F07-bootstrap","zh\u002Fprob-and-stats\u002F02-statistics\u002F07-bootstrap\u002Findex",[1726],{"title":1722,"path":1723,"stem":1724},{"title":1728,"path":1729,"stem":1730},"第十三章：前沿文献与现代统计案例（2023—2026）","\u002Fzh\u002Fprob-and-stats\u002F03-frontier-literature-2026","zh\u002Fprob-and-stats\u002F03-frontier-literature-2026",{"title":1732,"path":1733,"stem":1734,"children":1735,"page":249},"Quant","\u002Fzh\u002Fquant","zh\u002Fquant",[1736,1742,1746,1750,1754,1758,1762,1766,1770,1774,1778],{"title":1737,"path":1738,"stem":1739,"children":1740},"量化投资——从可检验信号到可执行组合","\u002Fzh\u002Fquant\u002F00-index","zh\u002Fquant\u002F00-index",[1741],{"title":1737,"path":1738,"stem":1739},{"title":1743,"path":1744,"stem":1745},"数据获取与预处理","\u002Fzh\u002Fquant\u002F01-research-data","zh\u002Fquant\u002F01-research-data",{"title":1747,"path":1748,"stem":1749},"因子与交易信号","\u002Fzh\u002Fquant\u002F02-factor-and-signals","zh\u002Fquant\u002F02-factor-and-signals",{"title":1751,"path":1752,"stem":1753},"策略建模与回测","\u002Fzh\u002Fquant\u002F03-modeling-and-backtest","zh\u002Fquant\u002F03-modeling-and-backtest",{"title":1755,"path":1756,"stem":1757},"组合构建与风险建模（资产定价视角）","\u002Fzh\u002Fquant\u002F04-portfolio-and-risk","zh\u002Fquant\u002F04-portfolio-and-risk",{"title":1759,"path":1760,"stem":1761},"执行策略与市场微结构概览","\u002Fzh\u002Fquant\u002F05-execution-and-microstructure","zh\u002Fquant\u002F05-execution-and-microstructure",{"title":1763,"path":1764,"stem":1765},"策略上线、监控与迭代","\u002Fzh\u002Fquant\u002F06-production-and-monitoring","zh\u002Fquant\u002F06-production-and-monitoring",{"title":1767,"path":1768,"stem":1769},"量化工程与工具链概览","\u002Fzh\u002Fquant\u002F07-engineering-stack","zh\u002Fquant\u002F07-engineering-stack",{"title":1771,"path":1772,"stem":1773},"计量方法与实证检验","\u002Fzh\u002Fquant\u002F08-econometric-methods","zh\u002Fquant\u002F08-econometric-methods",{"title":1775,"path":1776,"stem":1777},"案例研究：多因子股票 Alpha 策略全流程","\u002Fzh\u002Fquant\u002F09-case-study","zh\u002Fquant\u002F09-case-study",{"title":1779,"path":1780,"stem":1781},"量化投资文献与软件图谱","\u002Fzh\u002Fquant\u002F10-reading-software-map","zh\u002Fquant\u002F10-reading-software-map",null,{"id":1784,"title":442,"body":1785,"description":6647,"extension":6648,"features":1782,"hero":1782,"layout":1782,"locale":1782,"meta":6649,"navigation":1782,"path":443,"published":6652,"seo":6653,"stem":444,"__hash__":6654},"docs\u002Fen\u002Ffinancial-economic-time-series\u002F05-unit-roots-cointegration\u002Findex.md",{"type":1786,"value":1787,"toc":6635},"minimark",[1788,1792,1797,1801,2081,2453,2456,2460,2463,2891,3101,3104,3115,3119,3425,3537,3569,3572,4046,4168,4265,4268,4500,4510,4514,4517,4987,5307,5734,5956,5960,5966,6036,6040,6043,6057,6060,6080,6083,6087,6148,6151,6223,6227,6279,6283,6557,6629],[1789,1790,442],"h1",{"id":1791},"unit-roots-cointegration-and-error-correction",[1793,1794,1796],"h2",{"id":1795},"persistence-is-not-one-phenomenon","Persistence is not one phenomenon",[1798,1799,1800],"p",{},"Compare:",[1802,1803,1806],"span",{"className":1804},[1805],"katex-display",[1802,1807,1810,1876],{"className":1808},[1809],"katex",[1802,1811,1814],{"className":1812},[1813],"katex-mathml",[1815,1816,1819],"math",{"xmlns":1817,"display":1818},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML","block",[1820,1821,1822,1871],"semantics",{},[1823,1824,1825,1835,1839,1842,1857,1860,1867],"mrow",{},[1826,1827,1828,1832],"msub",{},[1829,1830,1831],"mi",{},"x",[1829,1833,1834],{},"t",[1836,1837,1838],"mo",{},"=",[1829,1840,1841],{},"ρ",[1826,1843,1844,1846],{},[1829,1845,1831],{},[1823,1847,1848,1850,1853],{},[1829,1849,1834],{},[1836,1851,1852],{},"−",[1854,1855,1856],"mn",{},"1",[1836,1858,1859],{},"+",[1826,1861,1862,1865],{},[1829,1863,1864],{},"u",[1829,1866,1834],{},[1829,1868,1870],{"mathvariant":1869},"normal",".",[1872,1873,1875],"annotation",{"encoding":1874},"application\u002Fx-tex","x_t=\\rho x_{t-1}+u_t.",[1802,1877,1881,1960,2032],{"className":1878,"ariaHidden":1880},[1879],"katex-html","true",[1802,1882,1885,1890,1948,1953,1957],{"className":1883},[1884],"base",[1802,1886],{"className":1887,"style":1889},[1888],"strut","height:0.5806em;vertical-align:-0.15em;",[1802,1891,1894,1898],{"className":1892},[1893],"mord",[1802,1895,1831],{"className":1896},[1893,1897],"mathnormal",[1802,1899,1902],{"className":1900},[1901],"msupsub",[1802,1903,1907,1939],{"className":1904},[1905,1906],"vlist-t","vlist-t2",[1802,1908,1911,1934],{"className":1909},[1910],"vlist-r",[1802,1912,1916],{"className":1913,"style":1915},[1914],"vlist","height:0.2806em;",[1802,1917,1919,1924],{"style":1918},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[1802,1920],{"className":1921,"style":1923},[1922],"pstrut","height:2.7em;",[1802,1925,1931],{"className":1926},[1927,1928,1929,1930],"sizing","reset-size6","size3","mtight",[1802,1932,1834],{"className":1933},[1893,1897,1930],[1802,1935,1938],{"className":1936},[1937],"vlist-s","​",[1802,1940,1942],{"className":1941},[1910],[1802,1943,1946],{"className":1944,"style":1945},[1914],"height:0.15em;",[1802,1947],{},[1802,1949],{"className":1950,"style":1952},[1951],"mspace","margin-right:0.2778em;",[1802,1954,1838],{"className":1955},[1956],"mrel",[1802,1958],{"className":1959,"style":1952},[1951],[1802,1961,1963,1967,1970,2022,2026,2029],{"className":1962},[1884],[1802,1964],{"className":1965,"style":1966},[1888],"height:0.7917em;vertical-align:-0.2083em;",[1802,1968,1841],{"className":1969},[1893,1897],[1802,1971,1973,1976],{"className":1972},[1893],[1802,1974,1831],{"className":1975},[1893,1897],[1802,1977,1979],{"className":1978},[1901],[1802,1980,1982,2013],{"className":1981},[1905,1906],[1802,1983,1985,2010],{"className":1984},[1910],[1802,1986,1989],{"className":1987,"style":1988},[1914],"height:0.3011em;",[1802,1990,1991,1994],{"style":1918},[1802,1992],{"className":1993,"style":1923},[1922],[1802,1995,1997],{"className":1996},[1927,1928,1929,1930],[1802,1998,2000,2003,2007],{"className":1999},[1893,1930],[1802,2001,1834],{"className":2002},[1893,1897,1930],[1802,2004,1852],{"className":2005},[2006,1930],"mbin",[1802,2008,1856],{"className":2009},[1893,1930],[1802,2011,1938],{"className":2012},[1937],[1802,2014,2016],{"className":2015},[1910],[1802,2017,2020],{"className":2018,"style":2019},[1914],"height:0.2083em;",[1802,2021],{},[1802,2023],{"className":2024,"style":2025},[1951],"margin-right:0.2222em;",[1802,2027,1859],{"className":2028},[2006],[1802,2030],{"className":2031,"style":2025},[1951],[1802,2033,2035,2038,2078],{"className":2034},[1884],[1802,2036],{"className":2037,"style":1889},[1888],[1802,2039,2041,2044],{"className":2040},[1893],[1802,2042,1864],{"className":2043},[1893,1897],[1802,2045,2047],{"className":2046},[1901],[1802,2048,2050,2070],{"className":2049},[1905,1906],[1802,2051,2053,2067],{"className":2052},[1910],[1802,2054,2056],{"className":2055,"style":1915},[1914],[1802,2057,2058,2061],{"style":1918},[1802,2059],{"className":2060,"style":1923},[1922],[1802,2062,2064],{"className":2063},[1927,1928,1929,1930],[1802,2065,1834],{"className":2066},[1893,1897,1930],[1802,2068,1938],{"className":2069},[1937],[1802,2071,2073],{"className":2072},[1910],[1802,2074,2076],{"className":2075,"style":1945},[1914],[1802,2077],{},[1802,2079,1870],{"className":2080},[1893],[2082,2083,2084,2225,2421],"ul",{},[2085,2086,2087,2088,2153,2154,2224],"li",{},"If ",[1802,2089,2091,2115],{"className":2090},[1809],[1802,2092,2094],{"className":2093},[1813],[1815,2095,2096],{"xmlns":1817},[1820,2097,2098,2112],{},[1823,2099,2100,2103,2105,2107,2110],{},[1829,2101,2102],{"mathvariant":1869},"∣",[1829,2104,1841],{},[1829,2106,2102],{"mathvariant":1869},[1836,2108,2109],{},"\u003C",[1854,2111,1856],{},[1872,2113,2114],{"encoding":1874},"|\\rho|\u003C1",[1802,2116,2118,2143],{"className":2117,"ariaHidden":1880},[1879],[1802,2119,2121,2125,2128,2131,2134,2137,2140],{"className":2120},[1884],[1802,2122],{"className":2123,"style":2124},[1888],"height:1em;vertical-align:-0.25em;",[1802,2126,2102],{"className":2127},[1893],[1802,2129,1841],{"className":2130},[1893,1897],[1802,2132,2102],{"className":2133},[1893],[1802,2135],{"className":2136,"style":1952},[1951],[1802,2138,2109],{"className":2139},[1956],[1802,2141],{"className":2142,"style":1952},[1951],[1802,2144,2146,2150],{"className":2145},[1884],[1802,2147],{"className":2148,"style":2149},[1888],"height:0.6444em;",[1802,2151,1856],{"className":2152},[1893],", shocks decay and ",[1802,2155,2157,2175],{"className":2156},[1809],[1802,2158,2160],{"className":2159},[1813],[1815,2161,2162],{"xmlns":1817},[1820,2163,2164,2172],{},[1823,2165,2166],{},[1826,2167,2168,2170],{},[1829,2169,1831],{},[1829,2171,1834],{},[1872,2173,2174],{"encoding":1874},"x_t",[1802,2176,2178],{"className":2177,"ariaHidden":1880},[1879],[1802,2179,2181,2184],{"className":2180},[1884],[1802,2182],{"className":2183,"style":1889},[1888],[1802,2185,2187,2190],{"className":2186},[1893],[1802,2188,1831],{"className":2189},[1893,1897],[1802,2191,2193],{"className":2192},[1901],[1802,2194,2196,2216],{"className":2195},[1905,1906],[1802,2197,2199,2213],{"className":2198},[1910],[1802,2200,2202],{"className":2201,"style":1915},[1914],[1802,2203,2204,2207],{"style":1918},[1802,2205],{"className":2206,"style":1923},[1922],[1802,2208,2210],{"className":2209},[1927,1928,1929,1930],[1802,2211,1834],{"className":2212},[1893,1897,1930],[1802,2214,1938],{"className":2215},[1937],[1802,2217,2219],{"className":2218},[1910],[1802,2220,2222],{"className":2221,"style":1945},[1914],[1802,2223],{}," is stationary under stable conditions.",[2085,2226,2087,2227,2279,2280,2420],{},[1802,2228,2230,2248],{"className":2229},[1809],[1802,2231,2233],{"className":2232},[1813],[1815,2234,2235],{"xmlns":1817},[1820,2236,2237,2245],{},[1823,2238,2239,2241,2243],{},[1829,2240,1841],{},[1836,2242,1838],{},[1854,2244,1856],{},[1872,2246,2247],{"encoding":1874},"\\rho=1",[1802,2249,2251,2270],{"className":2250,"ariaHidden":1880},[1879],[1802,2252,2254,2258,2261,2264,2267],{"className":2253},[1884],[1802,2255],{"className":2256,"style":2257},[1888],"height:0.625em;vertical-align:-0.1944em;",[1802,2259,1841],{"className":2260},[1893,1897],[1802,2262],{"className":2263,"style":1952},[1951],[1802,2265,1838],{"className":2266},[1956],[1802,2268],{"className":2269,"style":1952},[1951],[1802,2271,2273,2276],{"className":2272},[1884],[1802,2274],{"className":2275,"style":2149},[1888],[1802,2277,1856],{"className":2278},[1893],", ",[1802,2281,2283,2312],{"className":2282},[1809],[1802,2284,2286],{"className":2285},[1813],[1815,2287,2288],{"xmlns":1817},[1820,2289,2290,2309],{},[1823,2291,2292,2295,2301,2303],{},[1829,2293,2294],{"mathvariant":1869},"Δ",[1826,2296,2297,2299],{},[1829,2298,1831],{},[1829,2300,1834],{},[1836,2302,1838],{},[1826,2304,2305,2307],{},[1829,2306,1864],{},[1829,2308,1834],{},[1872,2310,2311],{"encoding":1874},"\\Delta x_t=u_t",[1802,2313,2315,2374],{"className":2314,"ariaHidden":1880},[1879],[1802,2316,2318,2322,2325,2365,2368,2371],{"className":2317},[1884],[1802,2319],{"className":2320,"style":2321},[1888],"height:0.8333em;vertical-align:-0.15em;",[1802,2323,2294],{"className":2324},[1893],[1802,2326,2328,2331],{"className":2327},[1893],[1802,2329,1831],{"className":2330},[1893,1897],[1802,2332,2334],{"className":2333},[1901],[1802,2335,2337,2357],{"className":2336},[1905,1906],[1802,2338,2340,2354],{"className":2339},[1910],[1802,2341,2343],{"className":2342,"style":1915},[1914],[1802,2344,2345,2348],{"style":1918},[1802,2346],{"className":2347,"style":1923},[1922],[1802,2349,2351],{"className":2350},[1927,1928,1929,1930],[1802,2352,1834],{"className":2353},[1893,1897,1930],[1802,2355,1938],{"className":2356},[1937],[1802,2358,2360],{"className":2359},[1910],[1802,2361,2363],{"className":2362,"style":1945},[1914],[1802,2364],{},[1802,2366],{"className":2367,"style":1952},[1951],[1802,2369,1838],{"className":2370},[1956],[1802,2372],{"className":2373,"style":1952},[1951],[1802,2375,2377,2380],{"className":2376},[1884],[1802,2378],{"className":2379,"style":1889},[1888],[1802,2381,2383,2386],{"className":2382},[1893],[1802,2384,1864],{"className":2385},[1893,1897],[1802,2387,2389],{"className":2388},[1901],[1802,2390,2392,2412],{"className":2391},[1905,1906],[1802,2393,2395,2409],{"className":2394},[1910],[1802,2396,2398],{"className":2397,"style":1915},[1914],[1802,2399,2400,2403],{"style":1918},[1802,2401],{"className":2402,"style":1923},[1922],[1802,2404,2406],{"className":2405},[1927,1928,1929,1930],[1802,2407,1834],{"className":2408},[1893,1897,1930],[1802,2410,1938],{"className":2411},[1937],[1802,2413,2415],{"className":2414},[1910],[1802,2416,2418],{"className":2417,"style":1945},[1914],[1802,2419],{}," and shocks permanently change the level.",[2085,2422,2087,2423,2452],{},[1802,2424,2426,2440],{"className":2425},[1809],[1802,2427,2429],{"className":2428},[1813],[1815,2430,2431],{"xmlns":1817},[1820,2432,2433,2437],{},[1823,2434,2435],{},[1829,2436,1841],{},[1872,2438,2439],{"encoding":1874},"\\rho",[1802,2441,2443],{"className":2442,"ariaHidden":1880},[1879],[1802,2444,2446,2449],{"className":2445},[1884],[1802,2447],{"className":2448,"style":2257},[1888],[1802,2450,1841],{"className":2451},[1893,1897]," is close to one, finite samples may not reliably distinguish the two.",[1798,2454,2455],{},"This distinction affects forecasts, standard errors, and the meaning of a level regression. A unit-root test is evidence about a maintained model, not a mechanical permission slip to difference every series.",[1793,2457,2459],{"id":2458},"why-unrelated-trends-can-look-convincing","Why unrelated trends can look convincing",[1798,2461,2462],{},"Let",[1802,2464,2466],{"className":2465},[1805],[1802,2467,2469,2547],{"className":2468},[1809],[1802,2470,2472],{"className":2471},[1813],[1815,2473,2474],{"xmlns":1817,"display":1818},[1820,2475,2476,2544],{},[1823,2477,2478,2484,2486,2498,2500,2506,2509,2512,2519,2521,2533,2535,2542],{},[1826,2479,2480,2482],{},[1829,2481,1831],{},[1829,2483,1834],{},[1836,2485,1838],{},[1826,2487,2488,2490],{},[1829,2489,1831],{},[1823,2491,2492,2494,2496],{},[1829,2493,1834],{},[1836,2495,1852],{},[1854,2497,1856],{},[1836,2499,1859],{},[1826,2501,2502,2504],{},[1829,2503,1864],{},[1829,2505,1834],{},[1836,2507,2508],{"separator":1880},",",[1951,2510],{"width":2511},"2em",[1826,2513,2514,2517],{},[1829,2515,2516],{},"y",[1829,2518,1834],{},[1836,2520,1838],{},[1826,2522,2523,2525],{},[1829,2524,2516],{},[1823,2526,2527,2529,2531],{},[1829,2528,1834],{},[1836,2530,1852],{},[1854,2532,1856],{},[1836,2534,1859],{},[1826,2536,2537,2540],{},[1829,2538,2539],{},"v",[1829,2541,1834],{},[1836,2543,2508],{"separator":1880},[1872,2545,2546],{"encoding":1874},"x_t=x_{t-1}+u_t,\\qquad\ny_t=y_{t-1}+v_t,",[1802,2548,2550,2605,2669,2778,2842],{"className":2549,"ariaHidden":1880},[1879],[1802,2551,2553,2556,2596,2599,2602],{"className":2552},[1884],[1802,2554],{"className":2555,"style":1889},[1888],[1802,2557,2559,2562],{"className":2558},[1893],[1802,2560,1831],{"className":2561},[1893,1897],[1802,2563,2565],{"className":2564},[1901],[1802,2566,2568,2588],{"className":2567},[1905,1906],[1802,2569,2571,2585],{"className":2570},[1910],[1802,2572,2574],{"className":2573,"style":1915},[1914],[1802,2575,2576,2579],{"style":1918},[1802,2577],{"className":2578,"style":1923},[1922],[1802,2580,2582],{"className":2581},[1927,1928,1929,1930],[1802,2583,1834],{"className":2584},[1893,1897,1930],[1802,2586,1938],{"className":2587},[1937],[1802,2589,2591],{"className":2590},[1910],[1802,2592,2594],{"className":2593,"style":1945},[1914],[1802,2595],{},[1802,2597],{"className":2598,"style":1952},[1951],[1802,2600,1838],{"className":2601},[1956],[1802,2603],{"className":2604,"style":1952},[1951],[1802,2606,2608,2611,2660,2663,2666],{"className":2607},[1884],[1802,2609],{"className":2610,"style":1966},[1888],[1802,2612,2614,2617],{"className":2613},[1893],[1802,2615,1831],{"className":2616},[1893,1897],[1802,2618,2620],{"className":2619},[1901],[1802,2621,2623,2652],{"className":2622},[1905,1906],[1802,2624,2626,2649],{"className":2625},[1910],[1802,2627,2629],{"className":2628,"style":1988},[1914],[1802,2630,2631,2634],{"style":1918},[1802,2632],{"className":2633,"style":1923},[1922],[1802,2635,2637],{"className":2636},[1927,1928,1929,1930],[1802,2638,2640,2643,2646],{"className":2639},[1893,1930],[1802,2641,1834],{"className":2642},[1893,1897,1930],[1802,2644,1852],{"className":2645},[2006,1930],[1802,2647,1856],{"className":2648},[1893,1930],[1802,2650,1938],{"className":2651},[1937],[1802,2653,2655],{"className":2654},[1910],[1802,2656,2658],{"className":2657,"style":2019},[1914],[1802,2659],{},[1802,2661],{"className":2662,"style":2025},[1951],[1802,2664,1859],{"className":2665},[2006],[1802,2667],{"className":2668,"style":2025},[1951],[1802,2670,2672,2675,2715,2719,2723,2727,2769,2772,2775],{"className":2671},[1884],[1802,2673],{"className":2674,"style":2257},[1888],[1802,2676,2678,2681],{"className":2677},[1893],[1802,2679,1864],{"className":2680},[1893,1897],[1802,2682,2684],{"className":2683},[1901],[1802,2685,2687,2707],{"className":2686},[1905,1906],[1802,2688,2690,2704],{"className":2689},[1910],[1802,2691,2693],{"className":2692,"style":1915},[1914],[1802,2694,2695,2698],{"style":1918},[1802,2696],{"className":2697,"style":1923},[1922],[1802,2699,2701],{"className":2700},[1927,1928,1929,1930],[1802,2702,1834],{"className":2703},[1893,1897,1930],[1802,2705,1938],{"className":2706},[1937],[1802,2708,2710],{"className":2709},[1910],[1802,2711,2713],{"className":2712,"style":1945},[1914],[1802,2714],{},[1802,2716,2508],{"className":2717},[2718],"mpunct",[1802,2720],{"className":2721,"style":2722},[1951],"margin-right:2em;",[1802,2724],{"className":2725,"style":2726},[1951],"margin-right:0.1667em;",[1802,2728,2730,2734],{"className":2729},[1893],[1802,2731,2516],{"className":2732,"style":2733},[1893,1897],"margin-right:0.0359em;",[1802,2735,2737],{"className":2736},[1901],[1802,2738,2740,2761],{"className":2739},[1905,1906],[1802,2741,2743,2758],{"className":2742},[1910],[1802,2744,2746],{"className":2745,"style":1915},[1914],[1802,2747,2749,2752],{"style":2748},"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;",[1802,2750],{"className":2751,"style":1923},[1922],[1802,2753,2755],{"className":2754},[1927,1928,1929,1930],[1802,2756,1834],{"className":2757},[1893,1897,1930],[1802,2759,1938],{"className":2760},[1937],[1802,2762,2764],{"className":2763},[1910],[1802,2765,2767],{"className":2766,"style":1945},[1914],[1802,2768],{},[1802,2770],{"className":2771,"style":1952},[1951],[1802,2773,1838],{"className":2774},[1956],[1802,2776],{"className":2777,"style":1952},[1951],[1802,2779,2781,2784,2833,2836,2839],{"className":2780},[1884],[1802,2782],{"className":2783,"style":1966},[1888],[1802,2785,2787,2790],{"className":2786},[1893],[1802,2788,2516],{"className":2789,"style":2733},[1893,1897],[1802,2791,2793],{"className":2792},[1901],[1802,2794,2796,2825],{"className":2795},[1905,1906],[1802,2797,2799,2822],{"className":2798},[1910],[1802,2800,2802],{"className":2801,"style":1988},[1914],[1802,2803,2804,2807],{"style":2748},[1802,2805],{"className":2806,"style":1923},[1922],[1802,2808,2810],{"className":2809},[1927,1928,1929,1930],[1802,2811,2813,2816,2819],{"className":2812},[1893,1930],[1802,2814,1834],{"className":2815},[1893,1897,1930],[1802,2817,1852],{"className":2818},[2006,1930],[1802,2820,1856],{"className":2821},[1893,1930],[1802,2823,1938],{"className":2824},[1937],[1802,2826,2828],{"className":2827},[1910],[1802,2829,2831],{"className":2830,"style":2019},[1914],[1802,2832],{},[1802,2834],{"className":2835,"style":2025},[1951],[1802,2837,1859],{"className":2838},[2006],[1802,2840],{"className":2841,"style":2025},[1951],[1802,2843,2845,2848,2888],{"className":2844},[1884],[1802,2846],{"className":2847,"style":2257},[1888],[1802,2849,2851,2854],{"className":2850},[1893],[1802,2852,2539],{"className":2853,"style":2733},[1893,1897],[1802,2855,2857],{"className":2856},[1901],[1802,2858,2860,2880],{"className":2859},[1905,1906],[1802,2861,2863,2877],{"className":2862},[1910],[1802,2864,2866],{"className":2865,"style":1915},[1914],[1802,2867,2868,2871],{"style":2748},[1802,2869],{"className":2870,"style":1923},[1922],[1802,2872,2874],{"className":2873},[1927,1928,1929,1930],[1802,2875,1834],{"className":2876},[1893,1897,1930],[1802,2878,1938],{"className":2879},[1937],[1802,2881,2883],{"className":2882},[1910],[1802,2884,2886],{"className":2885,"style":1945},[1914],[1802,2887],{},[1802,2889,2508],{"className":2890},[2718],[1798,2892,2893,2894,2964,2965,3034,3035,3100],{},"with independent innovations. Regressing ",[1802,2895,2897,2915],{"className":2896},[1809],[1802,2898,2900],{"className":2899},[1813],[1815,2901,2902],{"xmlns":1817},[1820,2903,2904,2912],{},[1823,2905,2906],{},[1826,2907,2908,2910],{},[1829,2909,2516],{},[1829,2911,1834],{},[1872,2913,2914],{"encoding":1874},"y_t",[1802,2916,2918],{"className":2917,"ariaHidden":1880},[1879],[1802,2919,2921,2924],{"className":2920},[1884],[1802,2922],{"className":2923,"style":2257},[1888],[1802,2925,2927,2930],{"className":2926},[1893],[1802,2928,2516],{"className":2929,"style":2733},[1893,1897],[1802,2931,2933],{"className":2932},[1901],[1802,2934,2936,2956],{"className":2935},[1905,1906],[1802,2937,2939,2953],{"className":2938},[1910],[1802,2940,2942],{"className":2941,"style":1915},[1914],[1802,2943,2944,2947],{"style":2748},[1802,2945],{"className":2946,"style":1923},[1922],[1802,2948,2950],{"className":2949},[1927,1928,1929,1930],[1802,2951,1834],{"className":2952},[1893,1897,1930],[1802,2954,1938],{"className":2955},[1937],[1802,2957,2959],{"className":2958},[1910],[1802,2960,2962],{"className":2961,"style":1945},[1914],[1802,2963],{}," on ",[1802,2966,2968,2985],{"className":2967},[1809],[1802,2969,2971],{"className":2970},[1813],[1815,2972,2973],{"xmlns":1817},[1820,2974,2975,2983],{},[1823,2976,2977],{},[1826,2978,2979,2981],{},[1829,2980,1831],{},[1829,2982,1834],{},[1872,2984,2174],{"encoding":1874},[1802,2986,2988],{"className":2987,"ariaHidden":1880},[1879],[1802,2989,2991,2994],{"className":2990},[1884],[1802,2992],{"className":2993,"style":1889},[1888],[1802,2995,2997,3000],{"className":2996},[1893],[1802,2998,1831],{"className":2999},[1893,1897],[1802,3001,3003],{"className":3002},[1901],[1802,3004,3006,3026],{"className":3005},[1905,1906],[1802,3007,3009,3023],{"className":3008},[1910],[1802,3010,3012],{"className":3011,"style":1915},[1914],[1802,3013,3014,3017],{"style":1918},[1802,3015],{"className":3016,"style":1923},[1922],[1802,3018,3020],{"className":3019},[1927,1928,1929,1930],[1802,3021,1834],{"className":3022},[1893,1897,1930],[1802,3024,1938],{"className":3025},[1937],[1802,3027,3029],{"className":3028},[1910],[1802,3030,3032],{"className":3031,"style":1945},[1914],[1802,3033],{}," can produce a high ",[1802,3036,3038,3059],{"className":3037},[1809],[1802,3039,3041],{"className":3040},[1813],[1815,3042,3043],{"xmlns":1817},[1820,3044,3045,3056],{},[1823,3046,3047],{},[3048,3049,3050,3053],"msup",{},[1829,3051,3052],{},"R",[1854,3054,3055],{},"2",[1872,3057,3058],{"encoding":1874},"R^2",[1802,3060,3062],{"className":3061,"ariaHidden":1880},[1879],[1802,3063,3065,3069],{"className":3064},[1884],[1802,3066],{"className":3067,"style":3068},[1888],"height:0.8141em;",[1802,3070,3072,3076],{"className":3071},[1893],[1802,3073,3052],{"className":3074,"style":3075},[1893,1897],"margin-right:0.0077em;",[1802,3077,3079],{"className":3078},[1901],[1802,3080,3082],{"className":3081},[1905],[1802,3083,3085],{"className":3084},[1910],[1802,3086,3088],{"className":3087,"style":3068},[1914],[1802,3089,3091,3094],{"style":3090},"top:-3.063em;margin-right:0.05em;",[1802,3092],{"className":3093,"style":1923},[1922],[1802,3095,3097],{"className":3096},[1927,1928,1929,1930],[1802,3098,3055],{"className":3099},[1893,1930]," and a conventional-looking t-statistic even though the innovations are unrelated. The regression treats persistent excursions as repeated independent evidence.",[1798,3102,3103],{},"Reasonable responses are:",[2082,3105,3106,3109,3112],{},[2085,3107,3108],{},"difference the variables if the question concerns short-run changes;",[2085,3110,3111],{},"model deterministic trends if theory specifies them;",[2085,3113,3114],{},"use cointegration if theory concerns a stable linear combination of nonstationary levels.",[1793,3116,3118],{"id":3117},"cointegration","Cointegration",[1798,3120,3121,3122,3152,3153,3228,3229,3280,3281,3337,3338,3391,3392,3424],{},"For an ",[1802,3123,3125,3139],{"className":3124},[1809],[1802,3126,3128],{"className":3127},[1813],[1815,3129,3130],{"xmlns":1817},[1820,3131,3132,3137],{},[1823,3133,3134],{},[1829,3135,3136],{},"n",[1872,3138,3136],{"encoding":1874},[1802,3140,3142],{"className":3141,"ariaHidden":1880},[1879],[1802,3143,3145,3149],{"className":3144},[1884],[1802,3146],{"className":3147,"style":3148},[1888],"height:0.4306em;",[1802,3150,3136],{"className":3151},[1893,1897],"-vector ",[1802,3154,3156,3175],{"className":3155},[1809],[1802,3157,3159],{"className":3158},[1813],[1815,3160,3161],{"xmlns":1817},[1820,3162,3163,3172],{},[1823,3164,3165],{},[1826,3166,3167,3170],{},[1829,3168,2516],{"mathvariant":3169},"bold",[1829,3171,1834],{},[1872,3173,3174],{"encoding":1874},"\\mathbf y_t",[1802,3176,3178],{"className":3177,"ariaHidden":1880},[1879],[1802,3179,3181,3185],{"className":3180},[1884],[1802,3182],{"className":3183,"style":3184},[1888],"height:0.6389em;vertical-align:-0.1944em;",[1802,3186,3188,3193],{"className":3187},[1893],[1802,3189,2516],{"className":3190,"style":3192},[1893,3191],"mathbf","margin-right:0.016em;",[1802,3194,3196],{"className":3195},[1901],[1802,3197,3199,3220],{"className":3198},[1905,1906],[1802,3200,3202,3217],{"className":3201},[1910],[1802,3203,3205],{"className":3204,"style":1915},[1914],[1802,3206,3208,3211],{"style":3207},"top:-2.55em;margin-left:-0.016em;margin-right:0.05em;",[1802,3209],{"className":3210,"style":1923},[1922],[1802,3212,3214],{"className":3213},[1927,1928,1929,1930],[1802,3215,1834],{"className":3216},[1893,1897,1930],[1802,3218,1938],{"className":3219},[1937],[1802,3221,3223],{"className":3222},[1910],[1802,3224,3226],{"className":3225,"style":1945},[1914],[1802,3227],{}," whose components are ",[1802,3230,3232,3256],{"className":3231},[1809],[1802,3233,3235],{"className":3234},[1813],[1815,3236,3237],{"xmlns":1817},[1820,3238,3239,3253],{},[1823,3240,3241,3244,3248,3250],{},[1829,3242,3243],{},"I",[1836,3245,3247],{"stretchy":3246},"false","(",[1854,3249,1856],{},[1836,3251,3252],{"stretchy":3246},")",[1872,3254,3255],{"encoding":1874},"I(1)",[1802,3257,3259],{"className":3258,"ariaHidden":1880},[1879],[1802,3260,3262,3265,3269,3273,3276],{"className":3261},[1884],[1802,3263],{"className":3264,"style":2124},[1888],[1802,3266,3243],{"className":3267,"style":3268},[1893,1897],"margin-right:0.0785em;",[1802,3270,3247],{"className":3271},[3272],"mopen",[1802,3274,1856],{"className":3275},[1893],[1802,3277,3252],{"className":3278},[3279],"mclose",", cointegration rank ",[1802,3282,3284,3305],{"className":3283},[1809],[1802,3285,3287],{"className":3286},[1813],[1815,3288,3289],{"xmlns":1817},[1820,3290,3291,3302],{},[1823,3292,3293,3296,3299],{},[1829,3294,3295],{},"r",[1836,3297,3298],{},">",[1854,3300,3301],{},"0",[1872,3303,3304],{"encoding":1874},"r>0",[1802,3306,3308,3328],{"className":3307,"ariaHidden":1880},[1879],[1802,3309,3311,3315,3319,3322,3325],{"className":3310},[1884],[1802,3312],{"className":3313,"style":3314},[1888],"height:0.5782em;vertical-align:-0.0391em;",[1802,3316,3295],{"className":3317,"style":3318},[1893,1897],"margin-right:0.0278em;",[1802,3320],{"className":3321,"style":1952},[1951],[1802,3323,3298],{"className":3324},[1956],[1802,3326],{"className":3327,"style":1952},[1951],[1802,3329,3331,3334],{"className":3330},[1884],[1802,3332],{"className":3333,"style":2149},[1888],[1802,3335,3301],{"className":3336},[1893]," means that an ",[1802,3339,3341,3360],{"className":3340},[1809],[1802,3342,3344],{"className":3343},[1813],[1815,3345,3346],{"xmlns":1817},[1820,3347,3348,3357],{},[1823,3349,3350,3352,3355],{},[1829,3351,3136],{},[1836,3353,3354],{},"×",[1829,3356,3295],{},[1872,3358,3359],{"encoding":1874},"n\\times r",[1802,3361,3363,3382],{"className":3362,"ariaHidden":1880},[1879],[1802,3364,3366,3370,3373,3376,3379],{"className":3365},[1884],[1802,3367],{"className":3368,"style":3369},[1888],"height:0.6667em;vertical-align:-0.0833em;",[1802,3371,3136],{"className":3372},[1893,1897],[1802,3374],{"className":3375,"style":2025},[1951],[1802,3377,3354],{"className":3378},[2006],[1802,3380],{"className":3381,"style":2025},[1951],[1802,3383,3385,3388],{"className":3384},[1884],[1802,3386],{"className":3387,"style":3148},[1888],[1802,3389,3295],{"className":3390,"style":3318},[1893,1897]," matrix ",[1802,3393,3395,3410],{"className":3394},[1809],[1802,3396,3398],{"className":3397},[1813],[1815,3399,3400],{"xmlns":1817},[1820,3401,3402,3407],{},[1823,3403,3404],{},[1829,3405,3406],{},"β",[1872,3408,3409],{"encoding":1874},"\\beta",[1802,3411,3413],{"className":3412,"ariaHidden":1880},[1879],[1802,3414,3416,3420],{"className":3415},[1884],[1802,3417],{"className":3418,"style":3419},[1888],"height:0.8889em;vertical-align:-0.1944em;",[1802,3421,3406],{"className":3422,"style":3423},[1893,1897],"margin-right:0.0528em;"," exists such that",[1802,3426,3428],{"className":3427},[1805],[1802,3429,3431,3456],{"className":3430},[1809],[1802,3432,3434],{"className":3433},[1813],[1815,3435,3436],{"xmlns":1817,"display":1818},[1820,3437,3438,3453],{},[1823,3439,3440,3447],{},[3048,3441,3442,3444],{},[1829,3443,3406],{},[1829,3445,3446],{"mathvariant":1869},"⊤",[1826,3448,3449,3451],{},[1829,3450,2516],{"mathvariant":3169},[1829,3452,1834],{},[1872,3454,3455],{"encoding":1874},"\\beta^\\top\\mathbf y_t",[1802,3457,3459],{"className":3458,"ariaHidden":1880},[1879],[1802,3460,3462,3466,3497],{"className":3461},[1884],[1802,3463],{"className":3464,"style":3465},[1888],"height:1.0935em;vertical-align:-0.1944em;",[1802,3467,3469,3472],{"className":3468},[1893],[1802,3470,3406],{"className":3471,"style":3423},[1893,1897],[1802,3473,3475],{"className":3474},[1901],[1802,3476,3478],{"className":3477},[1905],[1802,3479,3481],{"className":3480},[1910],[1802,3482,3485],{"className":3483,"style":3484},[1914],"height:0.8991em;",[1802,3486,3488,3491],{"style":3487},"top:-3.113em;margin-right:0.05em;",[1802,3489],{"className":3490,"style":1923},[1922],[1802,3492,3494],{"className":3493},[1927,1928,1929,1930],[1802,3495,3446],{"className":3496},[1893,1930],[1802,3498,3500,3503],{"className":3499},[1893],[1802,3501,2516],{"className":3502,"style":3192},[1893,3191],[1802,3504,3506],{"className":3505},[1901],[1802,3507,3509,3529],{"className":3508},[1905,1906],[1802,3510,3512,3526],{"className":3511},[1910],[1802,3513,3515],{"className":3514,"style":1915},[1914],[1802,3516,3517,3520],{"style":3207},[1802,3518],{"className":3519,"style":1923},[1922],[1802,3521,3523],{"className":3522},[1927,1928,1929,1930],[1802,3524,1834],{"className":3525},[1893,1897,1930],[1802,3527,1938],{"className":3528},[1937],[1802,3530,3532],{"className":3531},[1910],[1802,3533,3535],{"className":3534,"style":1945},[1914],[1802,3536],{},[1798,3538,3539,3540,3568],{},"is stationary. The columns of ",[1802,3541,3543,3556],{"className":3542},[1809],[1802,3544,3546],{"className":3545},[1813],[1815,3547,3548],{"xmlns":1817},[1820,3549,3550,3554],{},[1823,3551,3552],{},[1829,3553,3406],{},[1872,3555,3409],{"encoding":1874},[1802,3557,3559],{"className":3558,"ariaHidden":1880},[1879],[1802,3560,3562,3565],{"className":3561},[1884],[1802,3563],{"className":3564,"style":3419},[1888],[1802,3566,3406],{"className":3567,"style":3423},[1893,1897]," define long-run relations; they are not automatically causal parameters.",[1798,3570,3571],{},"A VAR in levels can be rewritten as a vector error-correction model:",[1802,3573,3575],{"className":3574},[1805],[1802,3576,3578,3671],{"className":3577},[1809],[1802,3579,3581],{"className":3580},[1813],[1815,3582,3583],{"xmlns":1817,"display":1818},[1820,3584,3585,3668],{},[1823,3586,3587,3589,3595,3597,3600,3612,3614,3637,3644,3646,3658,3660,3666],{},[1829,3588,2294],{"mathvariant":1869},[1826,3590,3591,3593],{},[1829,3592,2516],{"mathvariant":3169},[1829,3594,1834],{},[1836,3596,1838],{},[1829,3598,3599],{"mathvariant":1869},"Π",[1826,3601,3602,3604],{},[1829,3603,2516],{"mathvariant":3169},[1823,3605,3606,3608,3610],{},[1829,3607,1834],{},[1836,3609,1852],{},[1854,3611,1856],{},[1836,3613,1859],{},[3615,3616,3617,3620,3629],"munderover",{},[1836,3618,3619],{},"∑",[1823,3621,3622,3625,3627],{},[1829,3623,3624],{},"i",[1836,3626,1838],{},[1854,3628,1856],{},[1823,3630,3631,3633,3635],{},[1829,3632,1798],{},[1836,3634,1852],{},[1854,3636,1856],{},[1826,3638,3639,3642],{},[1829,3640,3641],{"mathvariant":1869},"Γ",[1829,3643,3624],{},[1829,3645,2294],{"mathvariant":1869},[1826,3647,3648,3650],{},[1829,3649,2516],{"mathvariant":3169},[1823,3651,3652,3654,3656],{},[1829,3653,1834],{},[1836,3655,1852],{},[1829,3657,3624],{},[1836,3659,1859],{},[1826,3661,3662,3664],{},[1829,3663,1864],{"mathvariant":3169},[1829,3665,1834],{},[1829,3667,1870],{"mathvariant":1869},[1872,3669,3670],{"encoding":1874},"\\Delta\\mathbf y_t\n=\\Pi\\mathbf y_{t-1}\n+\\sum_{i=1}^{p-1}\\Gamma_i\\Delta\\mathbf y_{t-i}\n+\\mathbf u_t.",[1802,3672,3674,3733,3801,3996],{"className":3673,"ariaHidden":1880},[1879],[1802,3675,3677,3681,3684,3724,3727,3730],{"className":3676},[1884],[1802,3678],{"className":3679,"style":3680},[1888],"height:0.8778em;vertical-align:-0.1944em;",[1802,3682,2294],{"className":3683},[1893],[1802,3685,3687,3690],{"className":3686},[1893],[1802,3688,2516],{"className":3689,"style":3192},[1893,3191],[1802,3691,3693],{"className":3692},[1901],[1802,3694,3696,3716],{"className":3695},[1905,1906],[1802,3697,3699,3713],{"className":3698},[1910],[1802,3700,3702],{"className":3701,"style":1915},[1914],[1802,3703,3704,3707],{"style":3207},[1802,3705],{"className":3706,"style":1923},[1922],[1802,3708,3710],{"className":3709},[1927,1928,1929,1930],[1802,3711,1834],{"className":3712},[1893,1897,1930],[1802,3714,1938],{"className":3715},[1937],[1802,3717,3719],{"className":3718},[1910],[1802,3720,3722],{"className":3721,"style":1945},[1914],[1802,3723],{},[1802,3725],{"className":3726,"style":1952},[1951],[1802,3728,1838],{"className":3729},[1956],[1802,3731],{"className":3732,"style":1952},[1951],[1802,3734,3736,3740,3743,3792,3795,3798],{"className":3735},[1884],[1802,3737],{"className":3738,"style":3739},[1888],"height:0.8917em;vertical-align:-0.2083em;",[1802,3741,3599],{"className":3742},[1893],[1802,3744,3746,3749],{"className":3745},[1893],[1802,3747,2516],{"className":3748,"style":3192},[1893,3191],[1802,3750,3752],{"className":3751},[1901],[1802,3753,3755,3784],{"className":3754},[1905,1906],[1802,3756,3758,3781],{"className":3757},[1910],[1802,3759,3761],{"className":3760,"style":1988},[1914],[1802,3762,3763,3766],{"style":3207},[1802,3764],{"className":3765,"style":1923},[1922],[1802,3767,3769],{"className":3768},[1927,1928,1929,1930],[1802,3770,3772,3775,3778],{"className":3771},[1893,1930],[1802,3773,1834],{"className":3774},[1893,1897,1930],[1802,3776,1852],{"className":3777},[2006,1930],[1802,3779,1856],{"className":3780},[1893,1930],[1802,3782,1938],{"className":3783},[1937],[1802,3785,3787],{"className":3786},[1910],[1802,3788,3790],{"className":3789,"style":2019},[1914],[1802,3791],{},[1802,3793],{"className":3794,"style":2025},[1951],[1802,3796,1859],{"className":3797},[2006],[1802,3799],{"className":3800,"style":2025},[1951],[1802,3802,3804,3808,3891,3894,3935,3938,3987,3990,3993],{"className":3803},[1884],[1802,3805],{"className":3806,"style":3807},[1888],"height:3.1259em;vertical-align:-1.2777em;",[1802,3809,3813],{"className":3810},[3811,3812],"mop","op-limits",[1802,3814,3816,3882],{"className":3815},[1905,1906],[1802,3817,3819,3879],{"className":3818},[1910],[1802,3820,3823,3845,3858],{"className":3821,"style":3822},[1914],"height:1.8482em;",[1802,3824,3826,3830],{"style":3825},"top:-1.8723em;margin-left:0em;",[1802,3827],{"className":3828,"style":3829},[1922],"height:3.05em;",[1802,3831,3833],{"className":3832},[1927,1928,1929,1930],[1802,3834,3836,3839,3842],{"className":3835},[1893,1930],[1802,3837,3624],{"className":3838},[1893,1897,1930],[1802,3840,1838],{"className":3841},[1956,1930],[1802,3843,1856],{"className":3844},[1893,1930],[1802,3846,3848,3851],{"style":3847},"top:-3.05em;",[1802,3849],{"className":3850,"style":3829},[1922],[1802,3852,3853],{},[1802,3854,3619],{"className":3855},[3811,3856,3857],"op-symbol","large-op",[1802,3859,3861,3864],{"style":3860},"top:-4.3471em;margin-left:0em;",[1802,3862],{"className":3863,"style":3829},[1922],[1802,3865,3867],{"className":3866},[1927,1928,1929,1930],[1802,3868,3870,3873,3876],{"className":3869},[1893,1930],[1802,3871,1798],{"className":3872},[1893,1897,1930],[1802,3874,1852],{"className":3875},[2006,1930],[1802,3877,1856],{"className":3878},[1893,1930],[1802,3880,1938],{"className":3881},[1937],[1802,3883,3885],{"className":3884},[1910],[1802,3886,3889],{"className":3887,"style":3888},[1914],"height:1.2777em;",[1802,3890],{},[1802,3892],{"className":3893,"style":2726},[1951],[1802,3895,3897,3900],{"className":3896},[1893],[1802,3898,3641],{"className":3899},[1893],[1802,3901,3903],{"className":3902},[1901],[1802,3904,3906,3927],{"className":3905},[1905,1906],[1802,3907,3909,3924],{"className":3908},[1910],[1802,3910,3913],{"className":3911,"style":3912},[1914],"height:0.3117em;",[1802,3914,3915,3918],{"style":1918},[1802,3916],{"className":3917,"style":1923},[1922],[1802,3919,3921],{"className":3920},[1927,1928,1929,1930],[1802,3922,3624],{"className":3923},[1893,1897,1930],[1802,3925,1938],{"className":3926},[1937],[1802,3928,3930],{"className":3929},[1910],[1802,3931,3933],{"className":3932,"style":1945},[1914],[1802,3934],{},[1802,3936,2294],{"className":3937},[1893],[1802,3939,3941,3944],{"className":3940},[1893],[1802,3942,2516],{"className":3943,"style":3192},[1893,3191],[1802,3945,3947],{"className":3946},[1901],[1802,3948,3950,3979],{"className":3949},[1905,1906],[1802,3951,3953,3976],{"className":3952},[1910],[1802,3954,3956],{"className":3955,"style":3912},[1914],[1802,3957,3958,3961],{"style":3207},[1802,3959],{"className":3960,"style":1923},[1922],[1802,3962,3964],{"className":3963},[1927,1928,1929,1930],[1802,3965,3967,3970,3973],{"className":3966},[1893,1930],[1802,3968,1834],{"className":3969},[1893,1897,1930],[1802,3971,1852],{"className":3972},[2006,1930],[1802,3974,3624],{"className":3975},[1893,1897,1930],[1802,3977,1938],{"className":3978},[1937],[1802,3980,3982],{"className":3981},[1910],[1802,3983,3985],{"className":3984,"style":2019},[1914],[1802,3986],{},[1802,3988],{"className":3989,"style":2025},[1951],[1802,3991,1859],{"className":3992},[2006],[1802,3994],{"className":3995,"style":2025},[1951],[1802,3997,3999,4003,4043],{"className":3998},[1884],[1802,4000],{"className":4001,"style":4002},[1888],"height:0.5944em;vertical-align:-0.15em;",[1802,4004,4006,4009],{"className":4005},[1893],[1802,4007,1864],{"className":4008},[1893,3191],[1802,4010,4012],{"className":4011},[1901],[1802,4013,4015,4035],{"className":4014},[1905,1906],[1802,4016,4018,4032],{"className":4017},[1910],[1802,4019,4021],{"className":4020,"style":1915},[1914],[1802,4022,4023,4026],{"style":1918},[1802,4024],{"className":4025,"style":1923},[1922],[1802,4027,4029],{"className":4028},[1927,1928,1929,1930],[1802,4030,1834],{"className":4031},[1893,1897,1930],[1802,4033,1938],{"className":4034},[1937],[1802,4036,4038],{"className":4037},[1910],[1802,4039,4041],{"className":4040,"style":1945},[1914],[1802,4042],{},[1802,4044,1870],{"className":4045},[1893],[1798,4047,2087,4048,4167],{},[1802,4049,4051,4087],{"className":4050},[1809],[1802,4052,4054],{"className":4053},[1813],[1815,4055,4056],{"xmlns":1817},[1820,4057,4058,4084],{},[1823,4059,4060,4062,4064,4067,4070,4072,4074,4076,4078,4080,4082],{},[1854,4061,3301],{},[1836,4063,2109],{},[1829,4065,4066],{"mathvariant":1869},"rank",[1836,4068,4069],{},"⁡",[1836,4071,3247],{"stretchy":3246},[1829,4073,3599],{"mathvariant":1869},[1836,4075,3252],{"stretchy":3246},[1836,4077,1838],{},[1829,4079,3295],{},[1836,4081,2109],{},[1829,4083,3136],{},[1872,4085,4086],{"encoding":1874},"0\u003C\\operatorname{rank}(\\Pi)=r\u003Cn",[1802,4088,4090,4109,4140,4158],{"className":4089,"ariaHidden":1880},[1879],[1802,4091,4093,4097,4100,4103,4106],{"className":4092},[1884],[1802,4094],{"className":4095,"style":4096},[1888],"height:0.6835em;vertical-align:-0.0391em;",[1802,4098,3301],{"className":4099},[1893],[1802,4101],{"className":4102,"style":1952},[1951],[1802,4104,2109],{"className":4105},[1956],[1802,4107],{"className":4108,"style":1952},[1951],[1802,4110,4112,4115,4122,4125,4128,4131,4134,4137],{"className":4111},[1884],[1802,4113],{"className":4114,"style":2124},[1888],[1802,4116,4118],{"className":4117},[3811],[1802,4119,4066],{"className":4120},[1893,4121],"mathrm",[1802,4123,3247],{"className":4124},[3272],[1802,4126,3599],{"className":4127},[1893],[1802,4129,3252],{"className":4130},[3279],[1802,4132],{"className":4133,"style":1952},[1951],[1802,4135,1838],{"className":4136},[1956],[1802,4138],{"className":4139,"style":1952},[1951],[1802,4141,4143,4146,4149,4152,4155],{"className":4142},[1884],[1802,4144],{"className":4145,"style":3314},[1888],[1802,4147,3295],{"className":4148,"style":3318},[1893,1897],[1802,4150],{"className":4151,"style":1952},[1951],[1802,4153,2109],{"className":4154},[1956],[1802,4156],{"className":4157,"style":1952},[1951],[1802,4159,4161,4164],{"className":4160},[1884],[1802,4162],{"className":4163,"style":3148},[1888],[1802,4165,3136],{"className":4166},[1893,1897],", factor",[1802,4169,4171],{"className":4170},[1805],[1802,4172,4174,4201],{"className":4173},[1809],[1802,4175,4177],{"className":4176},[1813],[1815,4178,4179],{"xmlns":1817,"display":1818},[1820,4180,4181,4198],{},[1823,4182,4183,4185,4187,4190,4196],{},[1829,4184,3599],{"mathvariant":1869},[1836,4186,1838],{},[1829,4188,4189],{},"α",[3048,4191,4192,4194],{},[1829,4193,3406],{},[1829,4195,3446],{"mathvariant":1869},[1836,4197,2508],{"separator":1880},[1872,4199,4200],{"encoding":1874},"\\Pi=\\alpha\\beta^\\top,",[1802,4202,4204,4223],{"className":4203,"ariaHidden":1880},[1879],[1802,4205,4207,4211,4214,4217,4220],{"className":4206},[1884],[1802,4208],{"className":4209,"style":4210},[1888],"height:0.6833em;",[1802,4212,3599],{"className":4213},[1893],[1802,4215],{"className":4216,"style":1952},[1951],[1802,4218,1838],{"className":4219},[1956],[1802,4221],{"className":4222,"style":1952},[1951],[1802,4224,4226,4229,4233,4262],{"className":4225},[1884],[1802,4227],{"className":4228,"style":3465},[1888],[1802,4230,4189],{"className":4231,"style":4232},[1893,1897],"margin-right:0.0037em;",[1802,4234,4236,4239],{"className":4235},[1893],[1802,4237,3406],{"className":4238,"style":3423},[1893,1897],[1802,4240,4242],{"className":4241},[1901],[1802,4243,4245],{"className":4244},[1905],[1802,4246,4248],{"className":4247},[1910],[1802,4249,4251],{"className":4250,"style":3484},[1914],[1802,4252,4253,4256],{"style":3487},[1802,4254],{"className":4255,"style":1923},[1922],[1802,4257,4259],{"className":4258},[1927,1928,1929,1930],[1802,4260,3446],{"className":4261},[1893,1930],[1802,4263,2508],{"className":4264},[2718],[1798,4266,4267],{},"where:",[2082,4269,4270,4395,4427],{},[2085,4271,4272,4394],{},[1802,4273,4275,4305],{"className":4274},[1809],[1802,4276,4278],{"className":4277},[1813],[1815,4279,4280],{"xmlns":1817},[1820,4281,4282,4302],{},[1823,4283,4284,4290],{},[3048,4285,4286,4288],{},[1829,4287,3406],{},[1829,4289,3446],{"mathvariant":1869},[1826,4291,4292,4294],{},[1829,4293,2516],{"mathvariant":3169},[1823,4295,4296,4298,4300],{},[1829,4297,1834],{},[1836,4299,1852],{},[1854,4301,1856],{},[1872,4303,4304],{"encoding":1874},"\\beta^\\top\\mathbf y_{t-1}",[1802,4306,4308],{"className":4307,"ariaHidden":1880},[1879],[1802,4309,4311,4315,4345],{"className":4310},[1884],[1802,4312],{"className":4313,"style":4314},[1888],"height:1.0574em;vertical-align:-0.2083em;",[1802,4316,4318,4321],{"className":4317},[1893],[1802,4319,3406],{"className":4320,"style":3423},[1893,1897],[1802,4322,4324],{"className":4323},[1901],[1802,4325,4327],{"className":4326},[1905],[1802,4328,4330],{"className":4329},[1910],[1802,4331,4334],{"className":4332,"style":4333},[1914],"height:0.8491em;",[1802,4335,4336,4339],{"style":3090},[1802,4337],{"className":4338,"style":1923},[1922],[1802,4340,4342],{"className":4341},[1927,1928,1929,1930],[1802,4343,3446],{"className":4344},[1893,1930],[1802,4346,4348,4351],{"className":4347},[1893],[1802,4349,2516],{"className":4350,"style":3192},[1893,3191],[1802,4352,4354],{"className":4353},[1901],[1802,4355,4357,4386],{"className":4356},[1905,1906],[1802,4358,4360,4383],{"className":4359},[1910],[1802,4361,4363],{"className":4362,"style":1988},[1914],[1802,4364,4365,4368],{"style":3207},[1802,4366],{"className":4367,"style":1923},[1922],[1802,4369,4371],{"className":4370},[1927,1928,1929,1930],[1802,4372,4374,4377,4380],{"className":4373},[1893,1930],[1802,4375,1834],{"className":4376},[1893,1897,1930],[1802,4378,1852],{"className":4379},[2006,1930],[1802,4381,1856],{"className":4382},[1893,1930],[1802,4384,1938],{"className":4385},[1937],[1802,4387,4389],{"className":4388},[1910],[1802,4390,4392],{"className":4391,"style":2019},[1914],[1802,4393],{}," contains the long-run disequilibria;",[2085,4396,4397,4426],{},[1802,4398,4400,4414],{"className":4399},[1809],[1802,4401,4403],{"className":4402},[1813],[1815,4404,4405],{"xmlns":1817},[1820,4406,4407,4411],{},[1823,4408,4409],{},[1829,4410,4189],{},[1872,4412,4413],{"encoding":1874},"\\alpha",[1802,4415,4417],{"className":4416,"ariaHidden":1880},[1879],[1802,4418,4420,4423],{"className":4419},[1884],[1802,4421],{"className":4422,"style":3148},[1888],[1802,4424,4189],{"className":4425,"style":4232},[1893,1897]," contains the adjustment speeds;",[2085,4428,4429,4499],{},[1802,4430,4432,4450],{"className":4431},[1809],[1802,4433,4435],{"className":4434},[1813],[1815,4436,4437],{"xmlns":1817},[1820,4438,4439,4447],{},[1823,4440,4441],{},[1826,4442,4443,4445],{},[1829,4444,3641],{"mathvariant":1869},[1829,4446,3624],{},[1872,4448,4449],{"encoding":1874},"\\Gamma_i",[1802,4451,4453],{"className":4452,"ariaHidden":1880},[1879],[1802,4454,4456,4459],{"className":4455},[1884],[1802,4457],{"className":4458,"style":2321},[1888],[1802,4460,4462,4465],{"className":4461},[1893],[1802,4463,3641],{"className":4464},[1893],[1802,4466,4468],{"className":4467},[1901],[1802,4469,4471,4491],{"className":4470},[1905,1906],[1802,4472,4474,4488],{"className":4473},[1910],[1802,4475,4477],{"className":4476,"style":3912},[1914],[1802,4478,4479,4482],{"style":1918},[1802,4480],{"className":4481,"style":1923},[1922],[1802,4483,4485],{"className":4484},[1927,1928,1929,1930],[1802,4486,3624],{"className":4487},[1893,1897,1930],[1802,4489,1938],{"className":4490},[1937],[1802,4492,4494],{"className":4493},[1910],[1802,4495,4497],{"className":4496,"style":1945},[1914],[1802,4498],{}," describe short-run dynamics.",[1798,4501,4502,4509],{},[4503,4504,4508],"a",{"href":4505,"rel":4506},"https:\u002F\u002Fwww.econometricsociety.org\u002Fpublications\u002Feconometrica\u002Fbrowse\u002F1991\u002F11\u002F01\u002Festimation-and-hypothesis-testing-cointegration-vectors",[4507],"nofollow","Johansen's likelihood framework"," turns the rank question into a reduced-rank multivariate estimation problem.",[1793,4511,4513],{"id":4512},"bivariate-derivation","Bivariate derivation",[1798,4515,4516],{},"Suppose",[1802,4518,4520],{"className":4519},[1805],[1802,4521,4523,4612],{"className":4522},[1809],[1802,4524,4526],{"className":4525},[1813],[1815,4527,4528],{"xmlns":1817,"display":1818},[1820,4529,4530,4609],{},[1823,4531,4532,4538,4540,4543,4549,4551,4557,4559,4561,4567,4569,4571,4583,4585,4592,4594,4597,4599,4601,4603,4605,4607],{},[1826,4533,4534,4536],{},[1829,4535,2516],{},[1829,4537,1834],{},[1836,4539,1838],{},[1829,4541,4542],{},"θ",[1826,4544,4545,4547],{},[1829,4546,1831],{},[1829,4548,1834],{},[1836,4550,1859],{},[1826,4552,4553,4555],{},[1829,4554,1864],{},[1829,4556,1834],{},[1836,4558,2508],{"separator":1880},[1951,4560],{"width":2511},[1826,4562,4563,4565],{},[1829,4564,1864],{},[1829,4566,1834],{},[1836,4568,1838],{},[1829,4570,1841],{},[1826,4572,4573,4575],{},[1829,4574,1864],{},[1823,4576,4577,4579,4581],{},[1829,4578,1834],{},[1836,4580,1852],{},[1854,4582,1856],{},[1836,4584,1859],{},[1826,4586,4587,4590],{},[1829,4588,4589],{},"e",[1829,4591,1834],{},[1836,4593,2508],{"separator":1880},[1951,4595],{"width":4596},"1em",[1829,4598,2102],{"mathvariant":1869},[1829,4600,1841],{},[1829,4602,2102],{"mathvariant":1869},[1836,4604,2109],{},[1854,4606,1856],{},[1836,4608,2508],{"separator":1880},[1872,4610,4611],{"encoding":1874},"y_t=\\theta x_t+u_t,\\qquad\nu_t=\\rho u_{t-1}+e_t,\\quad |\\rho|\u003C1,",[1802,4613,4615,4670,4729,4833,4900,4974],{"className":4614,"ariaHidden":1880},[1879],[1802,4616,4618,4621,4661,4664,4667],{"className":4617},[1884],[1802,4619],{"className":4620,"style":2257},[1888],[1802,4622,4624,4627],{"className":4623},[1893],[1802,4625,2516],{"className":4626,"style":2733},[1893,1897],[1802,4628,4630],{"className":4629},[1901],[1802,4631,4633,4653],{"className":4632},[1905,1906],[1802,4634,4636,4650],{"className":4635},[1910],[1802,4637,4639],{"className":4638,"style":1915},[1914],[1802,4640,4641,4644],{"style":2748},[1802,4642],{"className":4643,"style":1923},[1922],[1802,4645,4647],{"className":4646},[1927,1928,1929,1930],[1802,4648,1834],{"className":4649},[1893,1897,1930],[1802,4651,1938],{"className":4652},[1937],[1802,4654,4656],{"className":4655},[1910],[1802,4657,4659],{"className":4658,"style":1945},[1914],[1802,4660],{},[1802,4662],{"className":4663,"style":1952},[1951],[1802,4665,1838],{"className":4666},[1956],[1802,4668],{"className":4669,"style":1952},[1951],[1802,4671,4673,4677,4680,4720,4723,4726],{"className":4672},[1884],[1802,4674],{"className":4675,"style":4676},[1888],"height:0.8444em;vertical-align:-0.15em;",[1802,4678,4542],{"className":4679,"style":3318},[1893,1897],[1802,4681,4683,4686],{"className":4682},[1893],[1802,4684,1831],{"className":4685},[1893,1897],[1802,4687,4689],{"className":4688},[1901],[1802,4690,4692,4712],{"className":4691},[1905,1906],[1802,4693,4695,4709],{"className":4694},[1910],[1802,4696,4698],{"className":4697,"style":1915},[1914],[1802,4699,4700,4703],{"style":1918},[1802,4701],{"className":4702,"style":1923},[1922],[1802,4704,4706],{"className":4705},[1927,1928,1929,1930],[1802,4707,1834],{"className":4708},[1893,1897,1930],[1802,4710,1938],{"className":4711},[1937],[1802,4713,4715],{"className":4714},[1910],[1802,4716,4718],{"className":4717,"style":1945},[1914],[1802,4719],{},[1802,4721],{"className":4722,"style":2025},[1951],[1802,4724,1859],{"className":4725},[2006],[1802,4727],{"className":4728,"style":2025},[1951],[1802,4730,4732,4735,4775,4778,4781,4784,4824,4827,4830],{"className":4731},[1884],[1802,4733],{"className":4734,"style":2257},[1888],[1802,4736,4738,4741],{"className":4737},[1893],[1802,4739,1864],{"className":4740},[1893,1897],[1802,4742,4744],{"className":4743},[1901],[1802,4745,4747,4767],{"className":4746},[1905,1906],[1802,4748,4750,4764],{"className":4749},[1910],[1802,4751,4753],{"className":4752,"style":1915},[1914],[1802,4754,4755,4758],{"style":1918},[1802,4756],{"className":4757,"style":1923},[1922],[1802,4759,4761],{"className":4760},[1927,1928,1929,1930],[1802,4762,1834],{"className":4763},[1893,1897,1930],[1802,4765,1938],{"className":4766},[1937],[1802,4768,4770],{"className":4769},[1910],[1802,4771,4773],{"className":4772,"style":1945},[1914],[1802,4774],{},[1802,4776,2508],{"className":4777},[2718],[1802,4779],{"className":4780,"style":2722},[1951],[1802,4782],{"className":4783,"style":2726},[1951],[1802,4785,4787,4790],{"className":4786},[1893],[1802,4788,1864],{"className":4789},[1893,1897],[1802,4791,4793],{"className":4792},[1901],[1802,4794,4796,4816],{"className":4795},[1905,1906],[1802,4797,4799,4813],{"className":4798},[1910],[1802,4800,4802],{"className":4801,"style":1915},[1914],[1802,4803,4804,4807],{"style":1918},[1802,4805],{"className":4806,"style":1923},[1922],[1802,4808,4810],{"className":4809},[1927,1928,1929,1930],[1802,4811,1834],{"className":4812},[1893,1897,1930],[1802,4814,1938],{"className":4815},[1937],[1802,4817,4819],{"className":4818},[1910],[1802,4820,4822],{"className":4821,"style":1945},[1914],[1802,4823],{},[1802,4825],{"className":4826,"style":1952},[1951],[1802,4828,1838],{"className":4829},[1956],[1802,4831],{"className":4832,"style":1952},[1951],[1802,4834,4836,4839,4842,4891,4894,4897],{"className":4835},[1884],[1802,4837],{"className":4838,"style":1966},[1888],[1802,4840,1841],{"className":4841},[1893,1897],[1802,4843,4845,4848],{"className":4844},[1893],[1802,4846,1864],{"className":4847},[1893,1897],[1802,4849,4851],{"className":4850},[1901],[1802,4852,4854,4883],{"className":4853},[1905,1906],[1802,4855,4857,4880],{"className":4856},[1910],[1802,4858,4860],{"className":4859,"style":1988},[1914],[1802,4861,4862,4865],{"style":1918},[1802,4863],{"className":4864,"style":1923},[1922],[1802,4866,4868],{"className":4867},[1927,1928,1929,1930],[1802,4869,4871,4874,4877],{"className":4870},[1893,1930],[1802,4872,1834],{"className":4873},[1893,1897,1930],[1802,4875,1852],{"className":4876},[2006,1930],[1802,4878,1856],{"className":4879},[1893,1930],[1802,4881,1938],{"className":4882},[1937],[1802,4884,4886],{"className":4885},[1910],[1802,4887,4889],{"className":4888,"style":2019},[1914],[1802,4890],{},[1802,4892],{"className":4893,"style":2025},[1951],[1802,4895,1859],{"className":4896},[2006],[1802,4898],{"className":4899,"style":2025},[1951],[1802,4901,4903,4906,4946,4949,4953,4956,4959,4962,4965,4968,4971],{"className":4902},[1884],[1802,4904],{"className":4905,"style":2124},[1888],[1802,4907,4909,4912],{"className":4908},[1893],[1802,4910,4589],{"className":4911},[1893,1897],[1802,4913,4915],{"className":4914},[1901],[1802,4916,4918,4938],{"className":4917},[1905,1906],[1802,4919,4921,4935],{"className":4920},[1910],[1802,4922,4924],{"className":4923,"style":1915},[1914],[1802,4925,4926,4929],{"style":1918},[1802,4927],{"className":4928,"style":1923},[1922],[1802,4930,4932],{"className":4931},[1927,1928,1929,1930],[1802,4933,1834],{"className":4934},[1893,1897,1930],[1802,4936,1938],{"className":4937},[1937],[1802,4939,4941],{"className":4940},[1910],[1802,4942,4944],{"className":4943,"style":1945},[1914],[1802,4945],{},[1802,4947,2508],{"className":4948},[2718],[1802,4950],{"className":4951,"style":4952},[1951],"margin-right:1em;",[1802,4954],{"className":4955,"style":2726},[1951],[1802,4957,2102],{"className":4958},[1893],[1802,4960,1841],{"className":4961},[1893,1897],[1802,4963,2102],{"className":4964},[1893],[1802,4966],{"className":4967,"style":1952},[1951],[1802,4969,2109],{"className":4970},[1956],[1802,4972],{"className":4973,"style":1952},[1951],[1802,4975,4977,4981,4984],{"className":4976},[1884],[1802,4978],{"className":4979,"style":4980},[1888],"height:0.8389em;vertical-align:-0.1944em;",[1802,4982,1856],{"className":4983},[1893],[1802,4985,2508],{"className":4986},[2718],[1798,4988,4989,4990,5059,5060,5103,5104,5306],{},"while ",[1802,4991,4993,5010],{"className":4992},[1809],[1802,4994,4996],{"className":4995},[1813],[1815,4997,4998],{"xmlns":1817},[1820,4999,5000,5008],{},[1823,5001,5002],{},[1826,5003,5004,5006],{},[1829,5005,1831],{},[1829,5007,1834],{},[1872,5009,2174],{"encoding":1874},[1802,5011,5013],{"className":5012,"ariaHidden":1880},[1879],[1802,5014,5016,5019],{"className":5015},[1884],[1802,5017],{"className":5018,"style":1889},[1888],[1802,5020,5022,5025],{"className":5021},[1893],[1802,5023,1831],{"className":5024},[1893,1897],[1802,5026,5028],{"className":5027},[1901],[1802,5029,5031,5051],{"className":5030},[1905,1906],[1802,5032,5034,5048],{"className":5033},[1910],[1802,5035,5037],{"className":5036,"style":1915},[1914],[1802,5038,5039,5042],{"style":1918},[1802,5040],{"className":5041,"style":1923},[1922],[1802,5043,5045],{"className":5044},[1927,1928,1929,1930],[1802,5046,1834],{"className":5047},[1893,1897,1930],[1802,5049,1938],{"className":5050},[1937],[1802,5052,5054],{"className":5053},[1910],[1802,5055,5057],{"className":5056,"style":1945},[1914],[1802,5058],{}," is ",[1802,5061,5063,5082],{"className":5062},[1809],[1802,5064,5066],{"className":5065},[1813],[1815,5067,5068],{"xmlns":1817},[1820,5069,5070,5080],{},[1823,5071,5072,5074,5076,5078],{},[1829,5073,3243],{},[1836,5075,3247],{"stretchy":3246},[1854,5077,1856],{},[1836,5079,3252],{"stretchy":3246},[1872,5081,3255],{"encoding":1874},[1802,5083,5085],{"className":5084,"ariaHidden":1880},[1879],[1802,5086,5088,5091,5094,5097,5100],{"className":5087},[1884],[1802,5089],{"className":5090,"style":2124},[1888],[1802,5092,3243],{"className":5093,"style":3268},[1893,1897],[1802,5095,3247],{"className":5096},[3272],[1802,5098,1856],{"className":5099},[1893],[1802,5101,3252],{"className":5102},[3279],". Then the spread ",[1802,5105,5107,5143],{"className":5106},[1809],[1802,5108,5110],{"className":5109},[1813],[1815,5111,5112],{"xmlns":1817},[1820,5113,5114,5140],{},[1823,5115,5116,5122,5124,5130,5132,5134],{},[1826,5117,5118,5120],{},[1829,5119,1864],{},[1829,5121,1834],{},[1836,5123,1838],{},[1826,5125,5126,5128],{},[1829,5127,2516],{},[1829,5129,1834],{},[1836,5131,1852],{},[1829,5133,4542],{},[1826,5135,5136,5138],{},[1829,5137,1831],{},[1829,5139,1834],{},[1872,5141,5142],{"encoding":1874},"u_t=y_t-\\theta x_t",[1802,5144,5146,5201,5257],{"className":5145,"ariaHidden":1880},[1879],[1802,5147,5149,5152,5192,5195,5198],{"className":5148},[1884],[1802,5150],{"className":5151,"style":1889},[1888],[1802,5153,5155,5158],{"className":5154},[1893],[1802,5156,1864],{"className":5157},[1893,1897],[1802,5159,5161],{"className":5160},[1901],[1802,5162,5164,5184],{"className":5163},[1905,1906],[1802,5165,5167,5181],{"className":5166},[1910],[1802,5168,5170],{"className":5169,"style":1915},[1914],[1802,5171,5172,5175],{"style":1918},[1802,5173],{"className":5174,"style":1923},[1922],[1802,5176,5178],{"className":5177},[1927,1928,1929,1930],[1802,5179,1834],{"className":5180},[1893,1897,1930],[1802,5182,1938],{"className":5183},[1937],[1802,5185,5187],{"className":5186},[1910],[1802,5188,5190],{"className":5189,"style":1945},[1914],[1802,5191],{},[1802,5193],{"className":5194,"style":1952},[1951],[1802,5196,1838],{"className":5197},[1956],[1802,5199],{"className":5200,"style":1952},[1951],[1802,5202,5204,5208,5248,5251,5254],{"className":5203},[1884],[1802,5205],{"className":5206,"style":5207},[1888],"height:0.7778em;vertical-align:-0.1944em;",[1802,5209,5211,5214],{"className":5210},[1893],[1802,5212,2516],{"className":5213,"style":2733},[1893,1897],[1802,5215,5217],{"className":5216},[1901],[1802,5218,5220,5240],{"className":5219},[1905,1906],[1802,5221,5223,5237],{"className":5222},[1910],[1802,5224,5226],{"className":5225,"style":1915},[1914],[1802,5227,5228,5231],{"style":2748},[1802,5229],{"className":5230,"style":1923},[1922],[1802,5232,5234],{"className":5233},[1927,1928,1929,1930],[1802,5235,1834],{"className":5236},[1893,1897,1930],[1802,5238,1938],{"className":5239},[1937],[1802,5241,5243],{"className":5242},[1910],[1802,5244,5246],{"className":5245,"style":1945},[1914],[1802,5247],{},[1802,5249],{"className":5250,"style":2025},[1951],[1802,5252,1852],{"className":5253},[2006],[1802,5255],{"className":5256,"style":2025},[1951],[1802,5258,5260,5263,5266],{"className":5259},[1884],[1802,5261],{"className":5262,"style":4676},[1888],[1802,5264,4542],{"className":5265,"style":3318},[1893,1897],[1802,5267,5269,5272],{"className":5268},[1893],[1802,5270,1831],{"className":5271},[1893,1897],[1802,5273,5275],{"className":5274},[1901],[1802,5276,5278,5298],{"className":5277},[1905,1906],[1802,5279,5281,5295],{"className":5280},[1910],[1802,5282,5284],{"className":5283,"style":1915},[1914],[1802,5285,5286,5289],{"style":1918},[1802,5287],{"className":5288,"style":1923},[1922],[1802,5290,5292],{"className":5291},[1927,1928,1929,1930],[1802,5293,1834],{"className":5294},[1893,1897,1930],[1802,5296,1938],{"className":5297},[1937],[1802,5299,5301],{"className":5300},[1910],[1802,5302,5304],{"className":5303,"style":1945},[1914],[1802,5305],{}," is stationary. Differencing gives",[1802,5308,5310],{"className":5309},[1805],[1802,5311,5313,5399],{"className":5312},[1809],[1802,5314,5316],{"className":5315},[1813],[1815,5317,5318],{"xmlns":1817,"display":1818},[1820,5319,5320,5396],{},[1823,5321,5322,5324,5330,5332,5334,5336,5342,5344,5346,5348,5350,5352,5354,5356,5368,5370,5372,5384,5386,5388,5394],{},[1829,5323,2294],{"mathvariant":1869},[1826,5325,5326,5328],{},[1829,5327,2516],{},[1829,5329,1834],{},[1836,5331,1838],{},[1829,5333,4542],{},[1829,5335,2294],{"mathvariant":1869},[1826,5337,5338,5340],{},[1829,5339,1831],{},[1829,5341,1834],{},[1836,5343,1859],{},[1836,5345,3247],{"stretchy":3246},[1829,5347,1841],{},[1836,5349,1852],{},[1854,5351,1856],{},[1836,5353,3252],{"stretchy":3246},[1836,5355,3247],{"stretchy":3246},[1826,5357,5358,5360],{},[1829,5359,2516],{},[1823,5361,5362,5364,5366],{},[1829,5363,1834],{},[1836,5365,1852],{},[1854,5367,1856],{},[1836,5369,1852],{},[1829,5371,4542],{},[1826,5373,5374,5376],{},[1829,5375,1831],{},[1823,5377,5378,5380,5382],{},[1829,5379,1834],{},[1836,5381,1852],{},[1854,5383,1856],{},[1836,5385,3252],{"stretchy":3246},[1836,5387,1859],{},[1826,5389,5390,5392],{},[1829,5391,4589],{},[1829,5393,1834],{},[1829,5395,1870],{"mathvariant":1869},[1872,5397,5398],{"encoding":1874},"\\Delta y_t\n=\\theta\\Delta x_t\n+(\\rho-1)(y_{t-1}-\\theta x_{t-1})\n+e_t.",[1802,5400,5402,5460,5521,5542,5615,5685],{"className":5401,"ariaHidden":1880},[1879],[1802,5403,5405,5408,5411,5451,5454,5457],{"className":5404},[1884],[1802,5406],{"className":5407,"style":3680},[1888],[1802,5409,2294],{"className":5410},[1893],[1802,5412,5414,5417],{"className":5413},[1893],[1802,5415,2516],{"className":5416,"style":2733},[1893,1897],[1802,5418,5420],{"className":5419},[1901],[1802,5421,5423,5443],{"className":5422},[1905,1906],[1802,5424,5426,5440],{"className":5425},[1910],[1802,5427,5429],{"className":5428,"style":1915},[1914],[1802,5430,5431,5434],{"style":2748},[1802,5432],{"className":5433,"style":1923},[1922],[1802,5435,5437],{"className":5436},[1927,1928,1929,1930],[1802,5438,1834],{"className":5439},[1893,1897,1930],[1802,5441,1938],{"className":5442},[1937],[1802,5444,5446],{"className":5445},[1910],[1802,5447,5449],{"className":5448,"style":1945},[1914],[1802,5450],{},[1802,5452],{"className":5453,"style":1952},[1951],[1802,5455,1838],{"className":5456},[1956],[1802,5458],{"className":5459,"style":1952},[1951],[1802,5461,5463,5466,5469,5472,5512,5515,5518],{"className":5462},[1884],[1802,5464],{"className":5465,"style":4676},[1888],[1802,5467,4542],{"className":5468,"style":3318},[1893,1897],[1802,5470,2294],{"className":5471},[1893],[1802,5473,5475,5478],{"className":5474},[1893],[1802,5476,1831],{"className":5477},[1893,1897],[1802,5479,5481],{"className":5480},[1901],[1802,5482,5484,5504],{"className":5483},[1905,1906],[1802,5485,5487,5501],{"className":5486},[1910],[1802,5488,5490],{"className":5489,"style":1915},[1914],[1802,5491,5492,5495],{"style":1918},[1802,5493],{"className":5494,"style":1923},[1922],[1802,5496,5498],{"className":5497},[1927,1928,1929,1930],[1802,5499,1834],{"className":5500},[1893,1897,1930],[1802,5502,1938],{"className":5503},[1937],[1802,5505,5507],{"className":5506},[1910],[1802,5508,5510],{"className":5509,"style":1945},[1914],[1802,5511],{},[1802,5513],{"className":5514,"style":2025},[1951],[1802,5516,1859],{"className":5517},[2006],[1802,5519],{"className":5520,"style":2025},[1951],[1802,5522,5524,5527,5530,5533,5536,5539],{"className":5523},[1884],[1802,5525],{"className":5526,"style":2124},[1888],[1802,5528,3247],{"className":5529},[3272],[1802,5531,1841],{"className":5532},[1893,1897],[1802,5534],{"className":5535,"style":2025},[1951],[1802,5537,1852],{"className":5538},[2006],[1802,5540],{"className":5541,"style":2025},[1951],[1802,5543,5545,5548,5551,5554,5557,5606,5609,5612],{"className":5544},[1884],[1802,5546],{"className":5547,"style":2124},[1888],[1802,5549,1856],{"className":5550},[1893],[1802,5552,3252],{"className":5553},[3279],[1802,5555,3247],{"className":5556},[3272],[1802,5558,5560,5563],{"className":5559},[1893],[1802,5561,2516],{"className":5562,"style":2733},[1893,1897],[1802,5564,5566],{"className":5565},[1901],[1802,5567,5569,5598],{"className":5568},[1905,1906],[1802,5570,5572,5595],{"className":5571},[1910],[1802,5573,5575],{"className":5574,"style":1988},[1914],[1802,5576,5577,5580],{"style":2748},[1802,5578],{"className":5579,"style":1923},[1922],[1802,5581,5583],{"className":5582},[1927,1928,1929,1930],[1802,5584,5586,5589,5592],{"className":5585},[1893,1930],[1802,5587,1834],{"className":5588},[1893,1897,1930],[1802,5590,1852],{"className":5591},[2006,1930],[1802,5593,1856],{"className":5594},[1893,1930],[1802,5596,1938],{"className":5597},[1937],[1802,5599,5601],{"className":5600},[1910],[1802,5602,5604],{"className":5603,"style":2019},[1914],[1802,5605],{},[1802,5607],{"className":5608,"style":2025},[1951],[1802,5610,1852],{"className":5611},[2006],[1802,5613],{"className":5614,"style":2025},[1951],[1802,5616,5618,5621,5624,5673,5676,5679,5682],{"className":5617},[1884],[1802,5619],{"className":5620,"style":2124},[1888],[1802,5622,4542],{"className":5623,"style":3318},[1893,1897],[1802,5625,5627,5630],{"className":5626},[1893],[1802,5628,1831],{"className":5629},[1893,1897],[1802,5631,5633],{"className":5632},[1901],[1802,5634,5636,5665],{"className":5635},[1905,1906],[1802,5637,5639,5662],{"className":5638},[1910],[1802,5640,5642],{"className":5641,"style":1988},[1914],[1802,5643,5644,5647],{"style":1918},[1802,5645],{"className":5646,"style":1923},[1922],[1802,5648,5650],{"className":5649},[1927,1928,1929,1930],[1802,5651,5653,5656,5659],{"className":5652},[1893,1930],[1802,5654,1834],{"className":5655},[1893,1897,1930],[1802,5657,1852],{"className":5658},[2006,1930],[1802,5660,1856],{"className":5661},[1893,1930],[1802,5663,1938],{"className":5664},[1937],[1802,5666,5668],{"className":5667},[1910],[1802,5669,5671],{"className":5670,"style":2019},[1914],[1802,5672],{},[1802,5674,3252],{"className":5675},[3279],[1802,5677],{"className":5678,"style":2025},[1951],[1802,5680,1859],{"className":5681},[2006],[1802,5683],{"className":5684,"style":2025},[1951],[1802,5686,5688,5691,5731],{"className":5687},[1884],[1802,5689],{"className":5690,"style":1889},[1888],[1802,5692,5694,5697],{"className":5693},[1893],[1802,5695,4589],{"className":5696},[1893,1897],[1802,5698,5700],{"className":5699},[1901],[1802,5701,5703,5723],{"className":5702},[1905,1906],[1802,5704,5706,5720],{"className":5705},[1910],[1802,5707,5709],{"className":5708,"style":1915},[1914],[1802,5710,5711,5714],{"style":1918},[1802,5712],{"className":5713,"style":1923},[1922],[1802,5715,5717],{"className":5716},[1927,1928,1929,1930],[1802,5718,1834],{"className":5719},[1893,1897,1930],[1802,5721,1938],{"className":5722},[1937],[1802,5724,5726],{"className":5725},[1910],[1802,5727,5729],{"className":5728,"style":1945},[1914],[1802,5730],{},[1802,5732,1870],{"className":5733},[1893],[1798,5735,5736,5737,5810,5811,5880,5881,1870],{},"The coefficient ",[1802,5738,5740,5762],{"className":5739},[1809],[1802,5741,5743],{"className":5742},[1813],[1815,5744,5745],{"xmlns":1817},[1820,5746,5747,5759],{},[1823,5748,5749,5751,5753,5755,5757],{},[1829,5750,1841],{},[1836,5752,1852],{},[1854,5754,1856],{},[1836,5756,2109],{},[1854,5758,3301],{},[1872,5760,5761],{"encoding":1874},"\\rho-1\u003C0",[1802,5763,5765,5783,5801],{"className":5764,"ariaHidden":1880},[1879],[1802,5766,5768,5771,5774,5777,5780],{"className":5767},[1884],[1802,5769],{"className":5770,"style":5207},[1888],[1802,5772,1841],{"className":5773},[1893,1897],[1802,5775],{"className":5776,"style":2025},[1951],[1802,5778,1852],{"className":5779},[2006],[1802,5781],{"className":5782,"style":2025},[1951],[1802,5784,5786,5789,5792,5795,5798],{"className":5785},[1884],[1802,5787],{"className":5788,"style":4096},[1888],[1802,5790,1856],{"className":5791},[1893],[1802,5793],{"className":5794,"style":1952},[1951],[1802,5796,2109],{"className":5797},[1956],[1802,5799],{"className":5800,"style":1952},[1951],[1802,5802,5804,5807],{"className":5803},[1884],[1802,5805],{"className":5806,"style":2149},[1888],[1802,5808,3301],{"className":5809},[1893]," is error correction: a positive deviation in the previous period predicts downward adjustment in ",[1802,5812,5814,5831],{"className":5813},[1809],[1802,5815,5817],{"className":5816},[1813],[1815,5818,5819],{"xmlns":1817},[1820,5820,5821,5829],{},[1823,5822,5823],{},[1826,5824,5825,5827],{},[1829,5826,2516],{},[1829,5828,1834],{},[1872,5830,2914],{"encoding":1874},[1802,5832,5834],{"className":5833,"ariaHidden":1880},[1879],[1802,5835,5837,5840],{"className":5836},[1884],[1802,5838],{"className":5839,"style":2257},[1888],[1802,5841,5843,5846],{"className":5842},[1893],[1802,5844,2516],{"className":5845,"style":2733},[1893,1897],[1802,5847,5849],{"className":5848},[1901],[1802,5850,5852,5872],{"className":5851},[1905,1906],[1802,5853,5855,5869],{"className":5854},[1910],[1802,5856,5858],{"className":5857,"style":1915},[1914],[1802,5859,5860,5863],{"style":2748},[1802,5861],{"className":5862,"style":1923},[1922],[1802,5864,5866],{"className":5865},[1927,1928,1929,1930],[1802,5867,1834],{"className":5868},[1893,1897,1930],[1802,5870,1938],{"className":5871},[1937],[1802,5873,5875],{"className":5874},[1910],[1802,5876,5878],{"className":5877,"style":1945},[1914],[1802,5879],{},", conditional on ",[1802,5882,5884,5904],{"className":5883},[1809],[1802,5885,5887],{"className":5886},[1813],[1815,5888,5889],{"xmlns":1817},[1820,5890,5891,5901],{},[1823,5892,5893,5895],{},[1829,5894,2294],{"mathvariant":1869},[1826,5896,5897,5899],{},[1829,5898,1831],{},[1829,5900,1834],{},[1872,5902,5903],{"encoding":1874},"\\Delta x_t",[1802,5905,5907],{"className":5906,"ariaHidden":1880},[1879],[1802,5908,5910,5913,5916],{"className":5909},[1884],[1802,5911],{"className":5912,"style":2321},[1888],[1802,5914,2294],{"className":5915},[1893],[1802,5917,5919,5922],{"className":5918},[1893],[1802,5920,1831],{"className":5921},[1893,1897],[1802,5923,5925],{"className":5924},[1901],[1802,5926,5928,5948],{"className":5927},[1905,1906],[1802,5929,5931,5945],{"className":5930},[1910],[1802,5932,5934],{"className":5933,"style":1915},[1914],[1802,5935,5936,5939],{"style":1918},[1802,5937],{"className":5938,"style":1923},[1922],[1802,5940,5942],{"className":5941},[1927,1928,1929,1930],[1802,5943,1834],{"className":5944},[1893,1897,1930],[1802,5946,1938],{"className":5947},[1937],[1802,5949,5951],{"className":5950},[1910],[1802,5952,5954],{"className":5953,"style":1945},[1914],[1802,5955],{},[1793,5957,5959],{"id":5958},"r-laboratory-recover-equilibrium-and-adjustment","R laboratory: recover equilibrium and adjustment",[5961,5962],"web-r",{"code64":5963,"layout":5964,"locale":7,"title":5965},"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","vertical","Cointegrated random walks and an error-correction model",[1798,5967,5968,5969,5998,5999,6035],{},"The estimated long-run slope should be near ",[1802,5970,5972,5986],{"className":5971},[1809],[1802,5973,5975],{"className":5974},[1813],[1815,5976,5977],{"xmlns":1817},[1820,5978,5979,5984],{},[1823,5980,5981],{},[1854,5982,5983],{},"1.5",[1872,5985,5983],{"encoding":1874},[1802,5987,5989],{"className":5988,"ariaHidden":1880},[1879],[1802,5990,5992,5995],{"className":5991},[1884],[1802,5993],{"className":5994,"style":2149},[1888],[1802,5996,5983],{"className":5997},[1893],", and the error-correction coefficient near ",[1802,6000,6002,6019],{"className":6001},[1809],[1802,6003,6005],{"className":6004},[1813],[1815,6006,6007],{"xmlns":1817},[1820,6008,6009,6016],{},[1823,6010,6011,6013],{},[1836,6012,1852],{},[1854,6014,6015],{},"0.35",[1872,6017,6018],{"encoding":1874},"-0.35",[1802,6020,6022],{"className":6021,"ariaHidden":1880},[1879],[1802,6023,6025,6029,6032],{"className":6024},[1884],[1802,6026],{"className":6027,"style":6028},[1888],"height:0.7278em;vertical-align:-0.0833em;",[1802,6030,1852],{"className":6031},[1893],[1802,6033,6015],{"className":6034},[1893],". The test statistic is included only as a persistence contrast; valid unit-root inference uses nonstandard critical values and a carefully specified deterministic component.",[1793,6037,6039],{"id":6038},"finance-use-spread-price-discovery-or-trading","Finance use: spread, price discovery, or trading?",[1798,6041,6042],{},"Examples include:",[2082,6044,6045,6048,6051,6054],{},[2085,6046,6047],{},"spot and futures prices linked by carry;",[2085,6049,6050],{},"yields at different maturities under a term-structure relation;",[2085,6052,6053],{},"prices of economically linked securities;",[2085,6055,6056],{},"multiple venues contributing to price discovery.",[1798,6058,6059],{},"Cointegration supports a statistical long-run relation. A trading claim additionally needs:",[2082,6061,6062,6065,6068,6071,6074,6077],{},[2085,6063,6064],{},"stability after the formation sample;",[2085,6066,6067],{},"adjustment fast enough relative to the horizon;",[2085,6069,6070],{},"tradability of both legs;",[2085,6072,6073],{},"transaction costs, funding, shorting, and execution;",[2085,6075,6076],{},"a rule fixed before the test sample;",[2085,6078,6079],{},"tail exposure when the historical relation breaks.",[1798,6081,6082],{},"“Stationary spread” is not synonymous with “arbitrage.”",[1793,6084,6086],{"id":6085},"economics-use-equilibrium-and-adjustment","Economics use: equilibrium and adjustment",[1798,6088,6089,6090,6118,6119,6147],{},"Examples include consumption and income, prices and monetary aggregates, or related output measures. Here ",[1802,6091,6093,6106],{"className":6092},[1809],[1802,6094,6096],{"className":6095},[1813],[1815,6097,6098],{"xmlns":1817},[1820,6099,6100,6104],{},[1823,6101,6102],{},[1829,6103,3406],{},[1872,6105,3409],{"encoding":1874},[1802,6107,6109],{"className":6108,"ariaHidden":1880},[1879],[1802,6110,6112,6115],{"className":6111},[1884],[1802,6113],{"className":6114,"style":3419},[1888],[1802,6116,3406],{"className":6117,"style":3423},[1893,1897]," is usually interpreted through economic theory, and ",[1802,6120,6122,6135],{"className":6121},[1809],[1802,6123,6125],{"className":6124},[1813],[1815,6126,6127],{"xmlns":1817},[1820,6128,6129,6133],{},[1823,6130,6131],{},[1829,6132,4189],{},[1872,6134,4413],{"encoding":1874},[1802,6136,6138],{"className":6137,"ariaHidden":1880},[1879],[1802,6139,6141,6144],{"className":6140},[1884],[1802,6142],{"className":6143,"style":3148},[1888],[1802,6145,4189],{"className":6146,"style":4232},[1893,1897]," asks which variables respond when the system departs from the long-run relation.",[1798,6149,6150],{},"That interpretation requires care:",[2082,6152,6153,6156,6159,6220],{},[2085,6154,6155],{},"normalising one coefficient to one does not make that variable exogenous;",[2085,6157,6158],{},"rank can be sensitive to lag length, deterministic terms, breaks, and sample span;",[2085,6160,6161,6162,6190,6191,6219],{},"a policy regime change can alter both ",[1802,6163,6165,6178],{"className":6164},[1809],[1802,6166,6168],{"className":6167},[1813],[1815,6169,6170],{"xmlns":1817},[1820,6171,6172,6176],{},[1823,6173,6174],{},[1829,6175,4189],{},[1872,6177,4413],{"encoding":1874},[1802,6179,6181],{"className":6180,"ariaHidden":1880},[1879],[1802,6182,6184,6187],{"className":6183},[1884],[1802,6185],{"className":6186,"style":3148},[1888],[1802,6188,4189],{"className":6189,"style":4232},[1893,1897]," and ",[1802,6192,6194,6207],{"className":6193},[1809],[1802,6195,6197],{"className":6196},[1813],[1815,6198,6199],{"xmlns":1817},[1820,6200,6201,6205],{},[1823,6202,6203],{},[1829,6204,3406],{},[1872,6206,3409],{"encoding":1874},[1802,6208,6210],{"className":6209,"ariaHidden":1880},[1879],[1802,6211,6213,6216],{"className":6212},[1884],[1802,6214],{"className":6215,"style":3419},[1888],[1802,6217,3406],{"className":6218,"style":3423},[1893,1897],";",[2085,6221,6222],{},"cointegration does not by itself identify a structural mechanism.",[1793,6224,6226],{"id":6225},"levels-var-vecm-or-differences","Levels VAR, VECM, or differences?",[6228,6229,6230,6243],"table",{},[6231,6232,6233],"thead",{},[6234,6235,6236,6240],"tr",{},[6237,6238,6239],"th",{},"Goal",[6237,6241,6242],{},"Defensible starting point",[6244,6245,6246,6255,6263,6271],"tbody",{},[6234,6247,6248,6252],{},[6249,6250,6251],"td",{},"short-run forecast with no long-run claim",[6249,6253,6254],{},"compare differences, levels, and robust benchmarks out-of-sample",[6234,6256,6257,6260],{},[6249,6258,6259],{},"preserve a theorised stable level relation",[6249,6261,6262],{},"VECM with rank and stability analysis",[6234,6264,6265,6268],{},[6249,6266,6267],{},"structural impulse responses",[6249,6269,6270],{},"levels\u002FVECM plus explicit shock identification",[6234,6272,6273,6276],{},[6249,6274,6275],{},"trade a spread",[6249,6277,6278],{},"cointegration plus execution, costs, stability, and risk design",[1793,6280,6282],{"id":6281},"practice","Practice",[6284,6285,6286,6464,6554],"ol",{},[2085,6287,2087,6288,6393,6394,6463],{},[1802,6289,6291,6314],{"className":6290},[1809],[1802,6292,6294],{"className":6293},[1813],[1815,6295,6296],{"xmlns":1817},[1820,6297,6298,6312],{},[1823,6299,6300,6306],{},[3048,6301,6302,6304],{},[1829,6303,3406],{},[1829,6305,3446],{"mathvariant":1869},[1826,6307,6308,6310],{},[1829,6309,2516],{"mathvariant":3169},[1829,6311,1834],{},[1872,6313,3455],{"encoding":1874},[1802,6315,6317],{"className":6316,"ariaHidden":1880},[1879],[1802,6318,6320,6324,6353],{"className":6319},[1884],[1802,6321],{"className":6322,"style":6323},[1888],"height:1.0435em;vertical-align:-0.1944em;",[1802,6325,6327,6330],{"className":6326},[1893],[1802,6328,3406],{"className":6329,"style":3423},[1893,1897],[1802,6331,6333],{"className":6332},[1901],[1802,6334,6336],{"className":6335},[1905],[1802,6337,6339],{"className":6338},[1910],[1802,6340,6342],{"className":6341,"style":4333},[1914],[1802,6343,6344,6347],{"style":3090},[1802,6345],{"className":6346,"style":1923},[1922],[1802,6348,6350],{"className":6349},[1927,1928,1929,1930],[1802,6351,3446],{"className":6352},[1893,1930],[1802,6354,6356,6359],{"className":6355},[1893],[1802,6357,2516],{"className":6358,"style":3192},[1893,3191],[1802,6360,6362],{"className":6361},[1901],[1802,6363,6365,6385],{"className":6364},[1905,1906],[1802,6366,6368,6382],{"className":6367},[1910],[1802,6369,6371],{"className":6370,"style":1915},[1914],[1802,6372,6373,6376],{"style":3207},[1802,6374],{"className":6375,"style":1923},[1922],[1802,6377,6379],{"className":6378},[1927,1928,1929,1930],[1802,6380,1834],{"className":6381},[1893,1897,1930],[1802,6383,1938],{"className":6384},[1937],[1802,6386,6388],{"className":6387},[1910],[1802,6389,6391],{"className":6390,"style":1945},[1914],[1802,6392],{}," is stationary, must every element of ",[1802,6395,6397,6414],{"className":6396},[1809],[1802,6398,6400],{"className":6399},[1813],[1815,6401,6402],{"xmlns":1817},[1820,6403,6404,6412],{},[1823,6405,6406],{},[1826,6407,6408,6410],{},[1829,6409,2516],{"mathvariant":3169},[1829,6411,1834],{},[1872,6413,3174],{"encoding":1874},[1802,6415,6417],{"className":6416,"ariaHidden":1880},[1879],[1802,6418,6420,6423],{"className":6419},[1884],[1802,6421],{"className":6422,"style":3184},[1888],[1802,6424,6426,6429],{"className":6425},[1893],[1802,6427,2516],{"className":6428,"style":3192},[1893,3191],[1802,6430,6432],{"className":6431},[1901],[1802,6433,6435,6455],{"className":6434},[1905,1906],[1802,6436,6438,6452],{"className":6437},[1910],[1802,6439,6441],{"className":6440,"style":1915},[1914],[1802,6442,6443,6446],{"style":3207},[1802,6444],{"className":6445,"style":1923},[1922],[1802,6447,6449],{"className":6448},[1927,1928,1929,1930],[1802,6450,1834],{"className":6451},[1893,1897,1930],[1802,6453,1938],{"className":6454},[1937],[1802,6456,6458],{"className":6457},[1910],[1802,6459,6461],{"className":6460,"style":1945},[1914],[1802,6462],{}," be stationary?",[2085,6465,6466,6467,6553],{},"In ",[1802,6468,6470,6494],{"className":6469},[1809],[1802,6471,6473],{"className":6472},[1813],[1815,6474,6475],{"xmlns":1817},[1820,6476,6477,6491],{},[1823,6478,6479,6481,6483,6485],{},[1829,6480,3599],{"mathvariant":1869},[1836,6482,1838],{},[1829,6484,4189],{},[3048,6486,6487,6489],{},[1829,6488,3406],{},[1829,6490,3446],{"mathvariant":1869},[1872,6492,6493],{"encoding":1874},"\\Pi=\\alpha\\beta^\\top",[1802,6495,6497,6515],{"className":6496,"ariaHidden":1880},[1879],[1802,6498,6500,6503,6506,6509,6512],{"className":6499},[1884],[1802,6501],{"className":6502,"style":4210},[1888],[1802,6504,3599],{"className":6505},[1893],[1802,6507],{"className":6508,"style":1952},[1951],[1802,6510,1838],{"className":6511},[1956],[1802,6513],{"className":6514,"style":1952},[1951],[1802,6516,6518,6521,6524],{"className":6517},[1884],[1802,6519],{"className":6520,"style":6323},[1888],[1802,6522,4189],{"className":6523,"style":4232},[1893,1897],[1802,6525,6527,6530],{"className":6526},[1893],[1802,6528,3406],{"className":6529,"style":3423},[1893,1897],[1802,6531,6533],{"className":6532},[1901],[1802,6534,6536],{"className":6535},[1905],[1802,6537,6539],{"className":6538},[1910],[1802,6540,6542],{"className":6541,"style":4333},[1914],[1802,6543,6544,6547],{"style":3090},[1802,6545],{"className":6546,"style":1923},[1922],[1802,6548,6550],{"className":6549},[1927,1928,1929,1930],[1802,6551,3446],{"className":6552},[1893,1930],", which matrix describes disequilibrium and which describes response?",[2085,6555,6556],{},"Why can a structural break resemble failure of cointegration?",[6558,6559,6561],"legacy-details",{"title":6560},"Answers",[6284,6562,6563,6566,6626],{},[2085,6564,6565],{},"No. Cointegration is precisely a stationary combination of individually nonstationary variables.",[2085,6567,6568,6596,6597,6625],{},[1802,6569,6571,6584],{"className":6570},[1809],[1802,6572,6574],{"className":6573},[1813],[1815,6575,6576],{"xmlns":1817},[1820,6577,6578,6582],{},[1823,6579,6580],{},[1829,6581,3406],{},[1872,6583,3409],{"encoding":1874},[1802,6585,6587],{"className":6586,"ariaHidden":1880},[1879],[1802,6588,6590,6593],{"className":6589},[1884],[1802,6591],{"className":6592,"style":3419},[1888],[1802,6594,3406],{"className":6595,"style":3423},[1893,1897]," defines long-run relations; ",[1802,6598,6600,6613],{"className":6599},[1809],[1802,6601,6603],{"className":6602},[1813],[1815,6604,6605],{"xmlns":1817},[1820,6606,6607,6611],{},[1823,6608,6609],{},[1829,6610,4189],{},[1872,6612,4413],{"encoding":1874},[1802,6614,6616],{"className":6615,"ariaHidden":1880},[1879],[1802,6617,6619,6622],{"className":6618},[1884],[1802,6620],{"className":6621,"style":3148},[1888],[1802,6623,4189],{"className":6624,"style":4232},[1893,1897]," gives adjustment loading.",[2085,6627,6628],{},"A relation that changes once is not stationary around one constant parameter over the full sample.",[1798,6630,6631,6632,1870],{},"Next: ",[4503,6633,448],{"href":6634},"..\u002F06-var-identification\u002F",{"title":10,"searchDepth":6636,"depth":6636,"links":6637},2,[6638,6639,6640,6641,6642,6643,6644,6645,6646],{"id":1795,"depth":6636,"text":1796},{"id":2458,"depth":6636,"text":2459},{"id":3117,"depth":6636,"text":3118},{"id":4512,"depth":6636,"text":4513},{"id":5958,"depth":6636,"text":5959},{"id":6038,"depth":6636,"text":6039},{"id":6085,"depth":6636,"text":6086},{"id":6225,"depth":6636,"text":6226},{"id":6281,"depth":6636,"text":6282},"Diagnose spurious levels, derive reduced-rank error correction, and distinguish financial spreads from economic equilibria.","md",{"sidebar":6650},{"order":6651},5,true,{"title":442,"description":6647},"x_lg-R7sqSSWjHdO-YMTApUAod1BpGsj4ojXSQux7-Y",[6656,6658],{"title":436,"path":437,"stem":438,"description":6657,"children":-1},"Conditional variance, GARCH quasi-likelihood, leverage, heavy tails, and translation into VaR and expected shortfall.",{"title":448,"path":449,"stem":450,"description":6659,"children":-1},"Separate multivariate forecasting from structural shocks using companion matrices, impact restrictions, and impulse responses.",1785754724121]