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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 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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. 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distinction",[1798,1799,1800],"p",{},"All three fields study ordered random variables. They differ in what makes an analysis credible:",[1802,1803,1804,1823],"table",{},[1805,1806,1807],"thead",{},[1808,1809,1810,1814,1817,1820],"tr",{},[1811,1812,1813],"th",{},"Question",[1811,1815,1816],{},"Classical statistical time series",[1811,1818,1819],{},"Financial time series",[1811,1821,1822],{},"Economic time series",[1824,1825,1826,1841,1855,1945,1959,1973],"tbody",{},[1808,1827,1828,1832,1835,1838],{},[1829,1830,1831],"td",{},"primary object",[1829,1833,1834],{},"stochastic process and dependence structure",[1829,1836,1837],{},"returns, volatility, liquidity, and tail loss",[1829,1839,1840],{},"growth, cycles, long-run relations, and policy transmission",[1808,1842,1843,1846,1849,1852],{},[1829,1844,1845],{},"common clock",[1829,1847,1848],{},"regular, fixed interval",[1829,1850,1851],{},"trading time; daily to tick-by-tick",[1829,1853,1854],{},"release time; monthly\u002Fquarterly, mixed frequency",[1808,1856,1857,1860,1863,1913],{},[1829,1858,1859],{},"usual transformation",[1829,1861,1862],{},"centre, detrend, seasonally adjust",[1829,1864,1865,1866,1912],{},"adjusted price ",[1867,1868,1871,1894],"span",{"className":1869},[1870],"katex",[1867,1872,1875],{"className":1873},[1874],"katex-mathml",[1876,1877,1879],"math",{"xmlns":1878},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[1880,1881,1882,1889],"semantics",{},[1883,1884,1885],"mrow",{},[1886,1887,1888],"mo",{},"→",[1890,1891,1893],"annotation",{"encoding":1892},"application\u002Fx-tex","\\rightarrow",[1867,1895,1899],{"className":1896,"ariaHidden":1898},[1897],"katex-html","true",[1867,1900,1903,1908],{"className":1901},[1902],"base",[1867,1904],{"className":1905,"style":1907},[1906],"strut","height:0.3669em;",[1867,1909,1888],{"className":1910},[1911],"mrel"," log return",[1829,1914,1915,1916,1944],{},"level ",[1867,1917,1919,1932],{"className":1918},[1870],[1867,1920,1922],{"className":1921},[1874],[1876,1923,1924],{"xmlns":1878},[1880,1925,1926,1930],{},[1883,1927,1928],{},[1886,1929,1888],{},[1890,1931,1893],{"encoding":1892},[1867,1933,1935],{"className":1934,"ariaHidden":1898},[1897],[1867,1936,1938,1941],{"className":1937},[1902],[1867,1939],{"className":1940,"style":1907},[1906],[1867,1942,1888],{"className":1943},[1911]," log, difference, growth, gap",[1808,1946,1947,1950,1953,1956],{},[1829,1948,1949],{},"dominant difficulty",[1829,1951,1952],{},"valid covariance and stable dynamics",[1829,1954,1955],{},"weak mean signal, changing variance, heavy tails",[1829,1957,1958],{},"persistence, unit roots, revisions, latent current state",[1808,1960,1961,1964,1967,1970],{},[1829,1962,1963],{},"validation target",[1829,1965,1966],{},"model adequacy and prediction error",[1829,1968,1969],{},"economic value and tail calibration after costs",[1829,1971,1972],{},"real-time forecast or credible structural interpretation",[1808,1974,1975,1978,1981,1984],{},[1829,1976,1977],{},"costly error",[1829,1979,1980],{},"invalid stochastic model",[1829,1982,1983],{},"underestimated loss or false predictability",[1829,1985,1986],{},"bad nowcast or misidentified policy effect",[1798,1988,1989],{},"The classical course asks, “What follows from this stochastic model?”",[1798,1991,1992],{},"The applied course asks, “Is this model aligned with the data available and the decision being made?”",[1793,1994,1996],{"id":1995},"what-remains-unchanged","What remains unchanged",[1798,1998,1999,2000,2252],{},"For the finite vector ",[1867,2001,2003,2061],{"className":2002},[1870],[1867,2004,2006],{"className":2005},[1874],[1876,2007,2008],{"xmlns":1878},[1880,2009,2010,2058],{},[1883,2011,2012,2017,2020,2024,2033,2036,2039,2041,2048],{},[2013,2014,2016],"mi",{"mathvariant":2015},"bold","y",[1886,2018,2019],{},"=",[1886,2021,2023],{"stretchy":2022},"false","(",[2025,2026,2027,2029],"msub",{},[2013,2028,2016],{},[2030,2031,2032],"mn",{},"1",[1886,2034,2035],{"separator":1898},",",[1886,2037,2038],{},"…",[1886,2040,2035],{"separator":1898},[2025,2042,2043,2045],{},[2013,2044,2016],{},[2013,2046,2047],{},"T",[2049,2050,2051,2054],"msup",{},[1886,2052,2053],{"stretchy":2022},")",[2013,2055,2057],{"mathvariant":2056},"normal","⊤",[1890,2059,2060],{"encoding":1892},"\\mathbf y=(y_1,\\ldots,y_T)^\\top",[1867,2062,2064,2088],{"className":2063,"ariaHidden":1898},[1897],[1867,2065,2067,2071,2077,2082,2085],{"className":2066},[1902],[1867,2068],{"className":2069,"style":2070},[1906],"height:0.6389em;vertical-align:-0.1944em;",[1867,2072,2016],{"className":2073,"style":2076},[2074,2075],"mord","mathbf","margin-right:0.016em;",[1867,2078],{"className":2079,"style":2081},[2080],"mspace","margin-right:0.2778em;",[1867,2083,2019],{"className":2084},[1911],[1867,2086],{"className":2087,"style":2081},[2080],[1867,2089,2091,2095,2099,2157,2161,2165,2169,2172,2175,2178,2220],{"className":2090},[1902],[1867,2092],{"className":2093,"style":2094},[1906],"height:1.0991em;vertical-align:-0.25em;",[1867,2096,2023],{"className":2097},[2098],"mopen",[1867,2100,2102,2107],{"className":2101},[2074],[1867,2103,2016],{"className":2104,"style":2106},[2074,2105],"mathnormal","margin-right:0.0359em;",[1867,2108,2111],{"className":2109},[2110],"msupsub",[1867,2112,2116,2148],{"className":2113},[2114,2115],"vlist-t","vlist-t2",[1867,2117,2120,2143],{"className":2118},[2119],"vlist-r",[1867,2121,2125],{"className":2122,"style":2124},[2123],"vlist","height:0.3011em;",[1867,2126,2128,2133],{"style":2127},"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;",[1867,2129],{"className":2130,"style":2132},[2131],"pstrut","height:2.7em;",[1867,2134,2140],{"className":2135},[2136,2137,2138,2139],"sizing","reset-size6","size3","mtight",[1867,2141,2032],{"className":2142},[2074,2139],[1867,2144,2147],{"className":2145},[2146],"vlist-s","​",[1867,2149,2151],{"className":2150},[2119],[1867,2152,2155],{"className":2153,"style":2154},[2123],"height:0.15em;",[1867,2156],{},[1867,2158,2035],{"className":2159},[2160],"mpunct",[1867,2162],{"className":2163,"style":2164},[2080],"margin-right:0.1667em;",[1867,2166,2038],{"className":2167},[2168],"minner",[1867,2170],{"className":2171,"style":2164},[2080],[1867,2173,2035],{"className":2174},[2160],[1867,2176],{"className":2177,"style":2164},[2080],[1867,2179,2181,2184],{"className":2180},[2074],[1867,2182,2016],{"className":2183,"style":2106},[2074,2105],[1867,2185,2187],{"className":2186},[2110],[1867,2188,2190,2212],{"className":2189},[2114,2115],[1867,2191,2193,2209],{"className":2192},[2119],[1867,2194,2197],{"className":2195,"style":2196},[2123],"height:0.3283em;",[1867,2198,2199,2202],{"style":2127},[1867,2200],{"className":2201,"style":2132},[2131],[1867,2203,2205],{"className":2204},[2136,2137,2138,2139],[1867,2206,2047],{"className":2207,"style":2208},[2074,2105,2139],"margin-right:0.1389em;",[1867,2210,2147],{"className":2211},[2146],[1867,2213,2215],{"className":2214},[2119],[1867,2216,2218],{"className":2217,"style":2154},[2123],[1867,2219],{},[1867,2221,2224,2227],{"className":2222},[2223],"mclose",[1867,2225,2053],{"className":2226},[2223],[1867,2228,2230],{"className":2229},[2110],[1867,2231,2233],{"className":2232},[2114],[1867,2234,2236],{"className":2235},[2119],[1867,2237,2240],{"className":2238,"style":2239},[2123],"height:0.8491em;",[1867,2241,2243,2246],{"style":2242},"top:-3.063em;margin-right:0.05em;",[1867,2244],{"className":2245,"style":2132},[2131],[1867,2247,2249],{"className":2248},[2136,2137,2138,2139],[1867,2250,2057],{"className":2251},[2074,2139],", the common language is still:",[1867,2254,2257],{"className":2255},[2256],"katex-display",[1867,2258,2260,2341],{"className":2259},[1870],[1867,2261,2263],{"className":2262},[1874],[1876,2264,2266],{"xmlns":1878,"display":2265},"block",[1880,2267,2268,2338],{},[1883,2269,2270,2272,2274,2277,2280,2283,2286,2288,2291,2294,2296,2298,2301,2303,2305,2307,2310,2312,2314,2317,2320,2322,2324,2326,2328,2330,2332,2335],{},[2013,2271,2016],{"mathvariant":2015},[1886,2273,2019],{},[2013,2275,2276],{},"X",[2013,2278,2279],{},"β",[1886,2281,2282],{},"+",[2013,2284,2285],{"mathvariant":2015},"u",[1886,2287,2035],{"separator":1898},[2080,2289],{"width":2290},"2em",[2013,2292,2293],{},"E",[1886,2295,2023],{"stretchy":2022},[2013,2297,2285],{"mathvariant":2015},[1886,2299,2300],{},"∣",[2013,2302,2276],{},[1886,2304,2053],{"stretchy":2022},[1886,2306,2019],{},[2030,2308,2309],{},"0",[1886,2311,2035],{"separator":1898},[2080,2313],{"width":2290},[2013,2315,2316],{"mathvariant":2056},"Var",[1886,2318,2319],{},"⁡",[1886,2321,2023],{"stretchy":2022},[2013,2323,2285],{"mathvariant":2015},[1886,2325,2300],{},[2013,2327,2276],{},[1886,2329,2053],{"stretchy":2022},[1886,2331,2019],{},[2013,2333,2334],{"mathvariant":2056},"Ω",[2013,2336,2337],{"mathvariant":2056},".",[1890,2339,2340],{"encoding":1892},"\\mathbf y=X\\beta+\\mathbf u,\\qquad\nE(\\mathbf u\\mid X)=0,\\qquad\n\\operatorname{Var}(\\mathbf u\\mid X)=\\Omega.",[1867,2342,2344,2362,2388,2427,2448,2489,2510],{"className":2343,"ariaHidden":1898},[1897],[1867,2345,2347,2350,2353,2356,2359],{"className":2346},[1902],[1867,2348],{"className":2349,"style":2070},[1906],[1867,2351,2016],{"className":2352,"style":2076},[2074,2075],[1867,2354],{"className":2355,"style":2081},[2080],[1867,2357,2019],{"className":2358},[1911],[1867,2360],{"className":2361,"style":2081},[2080],[1867,2363,2365,2369,2373,2377,2381,2385],{"className":2364},[1902],[1867,2366],{"className":2367,"style":2368},[1906],"height:0.8889em;vertical-align:-0.1944em;",[1867,2370,2276],{"className":2371,"style":2372},[2074,2105],"margin-right:0.0785em;",[1867,2374,2279],{"className":2375,"style":2376},[2074,2105],"margin-right:0.0528em;",[1867,2378],{"className":2379,"style":2380},[2080],"margin-right:0.2222em;",[1867,2382,2282],{"className":2383},[2384],"mbin",[1867,2386],{"className":2387,"style":2380},[2080],[1867,2389,2391,2395,2398,2401,2405,2408,2412,2415,2418,2421,2424],{"className":2390},[1902],[1867,2392],{"className":2393,"style":2394},[1906],"height:1em;vertical-align:-0.25em;",[1867,2396,2285],{"className":2397},[2074,2075],[1867,2399,2035],{"className":2400},[2160],[1867,2402],{"className":2403,"style":2404},[2080],"margin-right:2em;",[1867,2406],{"className":2407,"style":2164},[2080],[1867,2409,2293],{"className":2410,"style":2411},[2074,2105],"margin-right:0.0576em;",[1867,2413,2023],{"className":2414},[2098],[1867,2416,2285],{"className":2417},[2074,2075],[1867,2419],{"className":2420,"style":2081},[2080],[1867,2422,2300],{"className":2423},[1911],[1867,2425],{"className":2426,"style":2081},[2080],[1867,2428,2430,2433,2436,2439,2442,2445],{"className":2429},[1902],[1867,2431],{"className":2432,"style":2394},[1906],[1867,2434,2276],{"className":2435,"style":2372},[2074,2105],[1867,2437,2053],{"className":2438},[2223],[1867,2440],{"className":2441,"style":2081},[2080],[1867,2443,2019],{"className":2444},[1911],[1867,2446],{"className":2447,"style":2081},[2080],[1867,2449,2451,2454,2457,2460,2463,2466,2474,2477,2480,2483,2486],{"className":2450},[1902],[1867,2452],{"className":2453,"style":2394},[1906],[1867,2455,2309],{"className":2456},[2074],[1867,2458,2035],{"className":2459},[2160],[1867,2461],{"className":2462,"style":2404},[2080],[1867,2464],{"className":2465,"style":2164},[2080],[1867,2467,2470],{"className":2468},[2469],"mop",[1867,2471,2316],{"className":2472},[2074,2473],"mathrm",[1867,2475,2023],{"className":2476},[2098],[1867,2478,2285],{"className":2479},[2074,2075],[1867,2481],{"className":2482,"style":2081},[2080],[1867,2484,2300],{"className":2485},[1911],[1867,2487],{"className":2488,"style":2081},[2080],[1867,2490,2492,2495,2498,2501,2504,2507],{"className":2491},[1902],[1867,2493],{"className":2494,"style":2394},[1906],[1867,2496,2276],{"className":2497,"style":2372},[2074,2105],[1867,2499,2053],{"className":2500},[2223],[1867,2502],{"className":2503,"style":2081},[2080],[1867,2505,2019],{"className":2506},[1911],[1867,2508],{"className":2509,"style":2081},[2080],[1867,2511,2513,2517],{"className":2512},[1902],[1867,2514],{"className":2515,"style":2516},[1906],"height:0.6833em;",[1867,2518,2520],{"className":2519},[2074],"Ω.",[2522,2523,2524,2558,2590],"ul",{},[2525,2526,2527,2528,2557],"li",{},"Classical analysis studies what structures such as Toeplitz ",[1867,2529,2531,2545],{"className":2530},[1870],[1867,2532,2534],{"className":2533},[1874],[1876,2535,2536],{"xmlns":1878},[1880,2537,2538,2542],{},[1883,2539,2540],{},[2013,2541,2334],{"mathvariant":2056},[1890,2543,2544],{"encoding":1892},"\\Omega",[1867,2546,2548],{"className":2547,"ariaHidden":1898},[1897],[1867,2549,2551,2554],{"className":2550},[1902],[1867,2552],{"className":2553,"style":2516},[1906],[1867,2555,2334],{"className":2556},[2074]," imply.",[2525,2559,2560,2561,2589],{},"Finance often allows diagonal elements of ",[1867,2562,2564,2577],{"className":2563},[1870],[1867,2565,2567],{"className":2566},[1874],[1876,2568,2569],{"xmlns":1878},[1880,2570,2571,2575],{},[1883,2572,2573],{},[2013,2574,2334],{"mathvariant":2056},[1890,2576,2544],{"encoding":1892},[1867,2578,2580],{"className":2579,"ariaHidden":1898},[1897],[1867,2581,2583,2586],{"className":2582},[1902],[1867,2584],{"className":2585,"style":2516},[1906],[1867,2587,2334],{"className":2588},[2074]," to evolve through time and evaluates tail functionals.",[2525,2591,2592],{},"Economics often models persistent means, common trends, simultaneous systems, and imperfectly observed states.",[1798,2594,2595],{},"The algebra transfers. The information set, interpretation, and loss do not transfer automatically.",[1793,2597,2599],{"id":2598},"one-method-three-uses","One method, three uses",[1802,2601,2602,2618],{},[1805,2603,2604],{},[1808,2605,2606,2609,2612,2615],{},[1811,2607,2608],{},"Method",[1811,2610,2611],{},"Classical use",[1811,2613,2614],{},"Finance use",[1811,2616,2617],{},"Economics use",[1824,2619,2620,2634,2648,2662,2676,2690,2704],{},[1808,2621,2622,2625,2628,2631],{},[1829,2623,2624],{},"AR\u002FARMA",[1829,2626,2627],{},"represent stationary dependence",[1829,2629,2630],{},"short-horizon return or spread dynamics",[1829,2632,2633],{},"inflation, growth, or forecast benchmark",[1808,2635,2636,2639,2642,2645],{},[1829,2637,2638],{},"HAC covariance",[1829,2640,2641],{},"inference with serial correlation",[1829,2643,2644],{},"overlapping multi-period returns",[1829,2646,2647],{},"distributed lags and persistent macro regressors",[1808,2649,2650,2653,2656,2659],{},[1829,2651,2652],{},"GARCH",[1829,2654,2655],{},"example of nonlinear conditional variance",[1829,2657,2658],{},"volatility, VaR, derivative\u002Frisk inputs",[1829,2660,2661],{},"inflation or exchange-rate uncertainty when relevant",[1808,2663,2664,2667,2670,2673],{},[1829,2665,2666],{},"cointegration",[1829,2668,2669],{},"reduced-rank long-run system",[1829,2671,2672],{},"spreads, term structure, price discovery",[1829,2674,2675],{},"money–prices, consumption–income, output relations",[1808,2677,2678,2681,2684,2687],{},[1829,2679,2680],{},"VAR",[1829,2682,2683],{},"multivariate forecasting",[1829,2685,2686],{},"return–volatility–liquidity interactions",[1829,2688,2689],{},"policy transmission and macro forecasting",[1808,2691,2692,2695,2698,2701],{},[1829,2693,2694],{},"Kalman filter",[1829,2696,2697],{},"efficient state recursion",[1829,2699,2700],{},"latent volatility, beta, or efficient price",[1829,2702,2703],{},"nowcasting, output gaps, mixed-frequency factors",[1808,2705,2706,2709,2712,2715],{},[1829,2707,2708],{},"spectral methods",[1829,2710,2711],{},"frequency decomposition",[1829,2713,2714],{},"cycles in volatility or market activity",[1829,2716,2717],{},"business-cycle and seasonal frequency separation",[2719,2720,2722],"warning",{"title":2721},"Same equation, different claim","A VAR can forecast without identifying a structural shock. A stationary spread can exist without yielding a profitable trade. A significant return predictor can fail after transaction costs. Never upgrade a statistical relation into an economic claim without the missing assumptions.",[1793,2724,2726],{"id":2725},"matched-example-1-a-persistent-level","Matched example 1: a persistent level",[1798,2728,2729],{},"Suppose",[1867,2731,2733],{"className":2732},[2256],[1867,2734,2736,2782],{"className":2735},[1870],[1867,2737,2739],{"className":2738},[1874],[1876,2740,2741],{"xmlns":1878,"display":2265},[1880,2742,2743,2779],{},[1883,2744,2745,2753,2755,2768,2770,2777],{},[2025,2746,2747,2750],{},[2013,2748,2749],{},"x",[2013,2751,2752],{},"t",[1886,2754,2019],{},[2025,2756,2757,2759],{},[2013,2758,2749],{},[1883,2760,2761,2763,2766],{},[2013,2762,2752],{},[1886,2764,2765],{},"−",[2030,2767,2032],{},[1886,2769,2282],{},[2025,2771,2772,2775],{},[2013,2773,2774],{},"η",[2013,2776,2752],{},[2013,2778,2337],{"mathvariant":2056},[1890,2780,2781],{"encoding":1892},"x_t=x_{t-1}+\\eta_t.",[1867,2783,2785,2843,2909],{"className":2784,"ariaHidden":1898},[1897],[1867,2786,2788,2792,2834,2837,2840],{"className":2787},[1902],[1867,2789],{"className":2790,"style":2791},[1906],"height:0.5806em;vertical-align:-0.15em;",[1867,2793,2795,2798],{"className":2794},[2074],[1867,2796,2749],{"className":2797},[2074,2105],[1867,2799,2801],{"className":2800},[2110],[1867,2802,2804,2826],{"className":2803},[2114,2115],[1867,2805,2807,2823],{"className":2806},[2119],[1867,2808,2811],{"className":2809,"style":2810},[2123],"height:0.2806em;",[1867,2812,2814,2817],{"style":2813},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[1867,2815],{"className":2816,"style":2132},[2131],[1867,2818,2820],{"className":2819},[2136,2137,2138,2139],[1867,2821,2752],{"className":2822},[2074,2105,2139],[1867,2824,2147],{"className":2825},[2146],[1867,2827,2829],{"className":2828},[2119],[1867,2830,2832],{"className":2831,"style":2154},[2123],[1867,2833],{},[1867,2835],{"className":2836,"style":2081},[2080],[1867,2838,2019],{"className":2839},[1911],[1867,2841],{"className":2842,"style":2081},[2080],[1867,2844,2846,2850,2900,2903,2906],{"className":2845},[1902],[1867,2847],{"className":2848,"style":2849},[1906],"height:0.7917em;vertical-align:-0.2083em;",[1867,2851,2853,2856],{"className":2852},[2074],[1867,2854,2749],{"className":2855},[2074,2105],[1867,2857,2859],{"className":2858},[2110],[1867,2860,2862,2891],{"className":2861},[2114,2115],[1867,2863,2865,2888],{"className":2864},[2119],[1867,2866,2868],{"className":2867,"style":2124},[2123],[1867,2869,2870,2873],{"style":2813},[1867,2871],{"className":2872,"style":2132},[2131],[1867,2874,2876],{"className":2875},[2136,2137,2138,2139],[1867,2877,2879,2882,2885],{"className":2878},[2074,2139],[1867,2880,2752],{"className":2881},[2074,2105,2139],[1867,2883,2765],{"className":2884},[2384,2139],[1867,2886,2032],{"className":2887},[2074,2139],[1867,2889,2147],{"className":2890},[2146],[1867,2892,2894],{"className":2893},[2119],[1867,2895,2898],{"className":2896,"style":2897},[2123],"height:0.2083em;",[1867,2899],{},[1867,2901],{"className":2902,"style":2380},[2080],[1867,2904,2282],{"className":2905},[2384],[1867,2907],{"className":2908,"style":2380},[2080],[1867,2910,2912,2916,2956],{"className":2911},[1902],[1867,2913],{"className":2914,"style":2915},[1906],"height:0.625em;vertical-align:-0.1944em;",[1867,2917,2919,2922],{"className":2918},[2074],[1867,2920,2774],{"className":2921,"style":2106},[2074,2105],[1867,2923,2925],{"className":2924},[2110],[1867,2926,2928,2948],{"className":2927},[2114,2115],[1867,2929,2931,2945],{"className":2930},[2119],[1867,2932,2934],{"className":2933,"style":2810},[2123],[1867,2935,2936,2939],{"style":2127},[1867,2937],{"className":2938,"style":2132},[2131],[1867,2940,2942],{"className":2941},[2136,2137,2138,2139],[1867,2943,2752],{"className":2944},[2074,2105,2139],[1867,2946,2147],{"className":2947},[2146],[1867,2949,2951],{"className":2950},[2119],[1867,2952,2954],{"className":2953,"style":2154},[2123],[1867,2955],{},[1867,2957,2337],{"className":2958},[2074],[1798,2960,2961],{},"In the classical course, this is a unit root: shocks have permanent effects and the level is nonstationary.",[1798,2963,2964,2965,3035],{},"In finance, ",[1867,2966,2968,2986],{"className":2967},[1870],[1867,2969,2971],{"className":2970},[1874],[1876,2972,2973],{"xmlns":1878},[1880,2974,2975,2983],{},[1883,2976,2977],{},[2025,2978,2979,2981],{},[2013,2980,2749],{},[2013,2982,2752],{},[1890,2984,2985],{"encoding":1892},"x_t",[1867,2987,2989],{"className":2988,"ariaHidden":1898},[1897],[1867,2990,2992,2995],{"className":2991},[1902],[1867,2993],{"className":2994,"style":2791},[1906],[1867,2996,2998,3001],{"className":2997},[2074],[1867,2999,2749],{"className":3000},[2074,2105],[1867,3002,3004],{"className":3003},[2110],[1867,3005,3007,3027],{"className":3006},[2114,2115],[1867,3008,3010,3024],{"className":3009},[2119],[1867,3011,3013],{"className":3012,"style":2810},[2123],[1867,3014,3015,3018],{"style":2813},[1867,3016],{"className":3017,"style":2132},[2131],[1867,3019,3021],{"className":3020},[2136,2137,2138,2139],[1867,3022,2752],{"className":3023},[2074,2105,2139],[1867,3025,2147],{"className":3026},[2146],[1867,3028,3030],{"className":3029},[2119],[1867,3031,3033],{"className":3032,"style":2154},[2123],[1867,3034],{}," may be a log price. We usually analyse the return",[1867,3037,3039],{"className":3038},[2256],[1867,3040,3042,3082],{"className":3041},[1870],[1867,3043,3045],{"className":3044},[1874],[1876,3046,3047],{"xmlns":1878,"display":2265},[1880,3048,3049,3079],{},[1883,3050,3051,3058,3060,3063,3069,3071,3077],{},[2025,3052,3053,3056],{},[2013,3054,3055],{},"r",[2013,3057,2752],{},[1886,3059,2019],{},[2013,3061,3062],{"mathvariant":2056},"Δ",[2025,3064,3065,3067],{},[2013,3066,2749],{},[2013,3068,2752],{},[1886,3070,2019],{},[2025,3072,3073,3075],{},[2013,3074,2774],{},[2013,3076,2752],{},[1886,3078,2035],{"separator":1898},[1890,3080,3081],{"encoding":1892},"r_t=\\Delta x_t=\\eta_t,",[1867,3083,3085,3142,3201],{"className":3084,"ariaHidden":1898},[1897],[1867,3086,3088,3091,3133,3136,3139],{"className":3087},[1902],[1867,3089],{"className":3090,"style":2791},[1906],[1867,3092,3094,3098],{"className":3093},[2074],[1867,3095,3055],{"className":3096,"style":3097},[2074,2105],"margin-right:0.0278em;",[1867,3099,3101],{"className":3100},[2110],[1867,3102,3104,3125],{"className":3103},[2114,2115],[1867,3105,3107,3122],{"className":3106},[2119],[1867,3108,3110],{"className":3109,"style":2810},[2123],[1867,3111,3113,3116],{"style":3112},"top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;",[1867,3114],{"className":3115,"style":2132},[2131],[1867,3117,3119],{"className":3118},[2136,2137,2138,2139],[1867,3120,2752],{"className":3121},[2074,2105,2139],[1867,3123,2147],{"className":3124},[2146],[1867,3126,3128],{"className":3127},[2119],[1867,3129,3131],{"className":3130,"style":2154},[2123],[1867,3132],{},[1867,3134],{"className":3135,"style":2081},[2080],[1867,3137,2019],{"className":3138},[1911],[1867,3140],{"className":3141,"style":2081},[2080],[1867,3143,3145,3149,3152,3192,3195,3198],{"className":3144},[1902],[1867,3146],{"className":3147,"style":3148},[1906],"height:0.8333em;vertical-align:-0.15em;",[1867,3150,3062],{"className":3151},[2074],[1867,3153,3155,3158],{"className":3154},[2074],[1867,3156,2749],{"className":3157},[2074,2105],[1867,3159,3161],{"className":3160},[2110],[1867,3162,3164,3184],{"className":3163},[2114,2115],[1867,3165,3167,3181],{"className":3166},[2119],[1867,3168,3170],{"className":3169,"style":2810},[2123],[1867,3171,3172,3175],{"style":2813},[1867,3173],{"className":3174,"style":2132},[2131],[1867,3176,3178],{"className":3177},[2136,2137,2138,2139],[1867,3179,2752],{"className":3180},[2074,2105,2139],[1867,3182,2147],{"className":3183},[2146],[1867,3185,3187],{"className":3186},[2119],[1867,3188,3190],{"className":3189,"style":2154},[2123],[1867,3191],{},[1867,3193],{"className":3194,"style":2081},[2080],[1867,3196,2019],{"className":3197},[1911],[1867,3199],{"className":3200,"style":2081},[2080],[1867,3202,3204,3207,3247],{"className":3203},[1902],[1867,3205],{"className":3206,"style":2915},[1906],[1867,3208,3210,3213],{"className":3209},[2074],[1867,3211,2774],{"className":3212,"style":2106},[2074,2105],[1867,3214,3216],{"className":3215},[2110],[1867,3217,3219,3239],{"className":3218},[2114,2115],[1867,3220,3222,3236],{"className":3221},[2119],[1867,3223,3225],{"className":3224,"style":2810},[2123],[1867,3226,3227,3230],{"style":2127},[1867,3228],{"className":3229,"style":2132},[2131],[1867,3231,3233],{"className":3232},[2136,2137,2138,2139],[1867,3234,2752],{"className":3235},[2074,2105,2139],[1867,3237,2147],{"className":3238},[2146],[1867,3240,3242],{"className":3241},[2119],[1867,3243,3245],{"className":3244,"style":2154},[2123],[1867,3246],{},[1867,3248,2035],{"className":3249},[2160],[1798,3251,3252],{},"because it is the investable one-period gain and is closer to stationary.",[1798,3254,3255,3256,3325],{},"In economics, ",[1867,3257,3259,3276],{"className":3258},[1870],[1867,3260,3262],{"className":3261},[1874],[1876,3263,3264],{"xmlns":1878},[1880,3265,3266,3274],{},[1883,3267,3268],{},[2025,3269,3270,3272],{},[2013,3271,2749],{},[2013,3273,2752],{},[1890,3275,2985],{"encoding":1892},[1867,3277,3279],{"className":3278,"ariaHidden":1898},[1897],[1867,3280,3282,3285],{"className":3281},[1902],[1867,3283],{"className":3284,"style":2791},[1906],[1867,3286,3288,3291],{"className":3287},[2074],[1867,3289,2749],{"className":3290},[2074,2105],[1867,3292,3294],{"className":3293},[2110],[1867,3295,3297,3317],{"className":3296},[2114,2115],[1867,3298,3300,3314],{"className":3299},[2119],[1867,3301,3303],{"className":3302,"style":2810},[2123],[1867,3304,3305,3308],{"style":2813},[1867,3306],{"className":3307,"style":2132},[2131],[1867,3309,3311],{"className":3310},[2136,2137,2138,2139],[1867,3312,2752],{"className":3313},[2074,2105,2139],[1867,3315,2147],{"className":3316},[2146],[1867,3318,3320],{"className":3319},[2119],[1867,3321,3323],{"className":3322,"style":2154},[2123],[1867,3324],{}," may be log real GDP. Differencing produces growth, but discards the level relation needed for questions about potential output or cointegration. The transformation must follow the estimand, not a stationarity ritual.",[1793,3327,3329],{"id":3328},"matched-example-2-a-var-innovation","Matched example 2: a VAR innovation",[1798,3331,3332],{},"Write a reduced-form VAR(1):",[1867,3334,3336],{"className":3335},[2256],[1867,3337,3339,3418],{"className":3338},[1870],[1867,3340,3342],{"className":3341},[1874],[1876,3343,3344],{"xmlns":1878,"display":2265},[1880,3345,3346,3415],{},[1883,3347,3348,3354,3356,3359,3371,3373,3379,3381,3383,3385,3387,3393,3402,3404,3406,3413],{},[2025,3349,3350,3352],{},[2013,3351,2016],{"mathvariant":2015},[2013,3353,2752],{},[1886,3355,2019],{},[2013,3357,3358],{},"A",[2025,3360,3361,3363],{},[2013,3362,2016],{"mathvariant":2015},[1883,3364,3365,3367,3369],{},[2013,3366,2752],{},[1886,3368,2765],{},[2030,3370,2032],{},[1886,3372,2282],{},[2025,3374,3375,3377],{},[2013,3376,2285],{"mathvariant":2015},[2013,3378,2752],{},[1886,3380,2035],{"separator":1898},[2080,3382],{"width":2290},[2013,3384,2293],{},[1886,3386,2023],{"stretchy":2022},[2025,3388,3389,3391],{},[2013,3390,2285],{"mathvariant":2015},[2013,3392,2752],{},[3394,3395,3396,3398,3400],"msubsup",{},[2013,3397,2285],{"mathvariant":2015},[2013,3399,2752],{},[2013,3401,2057],{"mathvariant":2056},[1886,3403,2053],{"stretchy":2022},[1886,3405,2019],{},[2025,3407,3408,3411],{},[2013,3409,3410],{"mathvariant":2056},"Σ",[2013,3412,2285],{},[2013,3414,2337],{"mathvariant":2056},[1890,3416,3417],{"encoding":1892},"\\mathbf y_t=A\\mathbf y_{t-1}+\\mathbf u_t,\n\\qquad E(\\mathbf u_t\\mathbf u_t^\\top)=\\Sigma_u.",[1867,3419,3421,3477,3545,3714],{"className":3420,"ariaHidden":1898},[1897],[1867,3422,3424,3427,3468,3471,3474],{"className":3423},[1902],[1867,3425],{"className":3426,"style":2070},[1906],[1867,3428,3430,3433],{"className":3429},[2074],[1867,3431,2016],{"className":3432,"style":2076},[2074,2075],[1867,3434,3436],{"className":3435},[2110],[1867,3437,3439,3460],{"className":3438},[2114,2115],[1867,3440,3442,3457],{"className":3441},[2119],[1867,3443,3445],{"className":3444,"style":2810},[2123],[1867,3446,3448,3451],{"style":3447},"top:-2.55em;margin-left:-0.016em;margin-right:0.05em;",[1867,3449],{"className":3450,"style":2132},[2131],[1867,3452,3454],{"className":3453},[2136,2137,2138,2139],[1867,3455,2752],{"className":3456},[2074,2105,2139],[1867,3458,2147],{"className":3459},[2146],[1867,3461,3463],{"className":3462},[2119],[1867,3464,3466],{"className":3465,"style":2154},[2123],[1867,3467],{},[1867,3469],{"className":3470,"style":2081},[2080],[1867,3472,2019],{"className":3473},[1911],[1867,3475],{"className":3476,"style":2081},[2080],[1867,3478,3480,3484,3487,3536,3539,3542],{"className":3479},[1902],[1867,3481],{"className":3482,"style":3483},[1906],"height:0.8917em;vertical-align:-0.2083em;",[1867,3485,3358],{"className":3486},[2074,2105],[1867,3488,3490,3493],{"className":3489},[2074],[1867,3491,2016],{"className":3492,"style":2076},[2074,2075],[1867,3494,3496],{"className":3495},[2110],[1867,3497,3499,3528],{"className":3498},[2114,2115],[1867,3500,3502,3525],{"className":3501},[2119],[1867,3503,3505],{"className":3504,"style":2124},[2123],[1867,3506,3507,3510],{"style":3447},[1867,3508],{"className":3509,"style":2132},[2131],[1867,3511,3513],{"className":3512},[2136,2137,2138,2139],[1867,3514,3516,3519,3522],{"className":3515},[2074,2139],[1867,3517,2752],{"className":3518},[2074,2105,2139],[1867,3520,2765],{"className":3521},[2384,2139],[1867,3523,2032],{"className":3524},[2074,2139],[1867,3526,2147],{"className":3527},[2146],[1867,3529,3531],{"className":3530},[2119],[1867,3532,3534],{"className":3533,"style":2897},[2123],[1867,3535],{},[1867,3537],{"className":3538,"style":2380},[2080],[1867,3540,2282],{"className":3541},[2384],[1867,3543],{"className":3544,"style":2380},[2080],[1867,3546,3548,3552,3592,3595,3598,3601,3604,3607,3647,3702,3705,3708,3711],{"className":3547},[1902],[1867,3549],{"className":3550,"style":3551},[1906],"height:1.1491em;vertical-align:-0.25em;",[1867,3553,3555,3558],{"className":3554},[2074],[1867,3556,2285],{"className":3557},[2074,2075],[1867,3559,3561],{"className":3560},[2110],[1867,3562,3564,3584],{"className":3563},[2114,2115],[1867,3565,3567,3581],{"className":3566},[2119],[1867,3568,3570],{"className":3569,"style":2810},[2123],[1867,3571,3572,3575],{"style":2813},[1867,3573],{"className":3574,"style":2132},[2131],[1867,3576,3578],{"className":3577},[2136,2137,2138,2139],[1867,3579,2752],{"className":3580},[2074,2105,2139],[1867,3582,2147],{"className":3583},[2146],[1867,3585,3587],{"className":3586},[2119],[1867,3588,3590],{"className":3589,"style":2154},[2123],[1867,3591],{},[1867,3593,2035],{"className":3594},[2160],[1867,3596],{"className":3597,"style":2404},[2080],[1867,3599],{"className":3600,"style":2164},[2080],[1867,3602,2293],{"className":3603,"style":2411},[2074,2105],[1867,3605,2023],{"className":3606},[2098],[1867,3608,3610,3613],{"className":3609},[2074],[1867,3611,2285],{"className":3612},[2074,2075],[1867,3614,3616],{"className":3615},[2110],[1867,3617,3619,3639],{"className":3618},[2114,2115],[1867,3620,3622,3636],{"className":3621},[2119],[1867,3623,3625],{"className":3624,"style":2810},[2123],[1867,3626,3627,3630],{"style":2813},[1867,3628],{"className":3629,"style":2132},[2131],[1867,3631,3633],{"className":3632},[2136,2137,2138,2139],[1867,3634,2752],{"className":3635},[2074,2105,2139],[1867,3637,2147],{"className":3638},[2146],[1867,3640,3642],{"className":3641},[2119],[1867,3643,3645],{"className":3644,"style":2154},[2123],[1867,3646],{},[1867,3648,3650,3653],{"className":3649},[2074],[1867,3651,2285],{"className":3652},[2074,2075],[1867,3654,3656],{"className":3655},[2110],[1867,3657,3659,3693],{"className":3658},[2114,2115],[1867,3660,3662,3690],{"className":3661},[2119],[1867,3663,3666,3678],{"className":3664,"style":3665},[2123],"height:0.8991em;",[1867,3667,3669,3672],{"style":3668},"top:-2.453em;margin-left:0em;margin-right:0.05em;",[1867,3670],{"className":3671,"style":2132},[2131],[1867,3673,3675],{"className":3674},[2136,2137,2138,2139],[1867,3676,2752],{"className":3677},[2074,2105,2139],[1867,3679,3681,3684],{"style":3680},"top:-3.113em;margin-right:0.05em;",[1867,3682],{"className":3683,"style":2132},[2131],[1867,3685,3687],{"className":3686},[2136,2137,2138,2139],[1867,3688,2057],{"className":3689},[2074,2139],[1867,3691,2147],{"className":3692},[2146],[1867,3694,3696],{"className":3695},[2119],[1867,3697,3700],{"className":3698,"style":3699},[2123],"height:0.247em;",[1867,3701],{},[1867,3703,2053],{"className":3704},[2223],[1867,3706],{"className":3707,"style":2081},[2080],[1867,3709,2019],{"className":3710},[1911],[1867,3712],{"className":3713,"style":2081},[2080],[1867,3715,3717,3720,3761],{"className":3716},[1902],[1867,3718],{"className":3719,"style":3148},[1906],[1867,3721,3723,3726],{"className":3722},[2074],[1867,3724,3410],{"className":3725},[2074],[1867,3727,3729],{"className":3728},[2110],[1867,3730,3732,3753],{"className":3731},[2114,2115],[1867,3733,3735,3750],{"className":3734},[2119],[1867,3736,3739],{"className":3737,"style":3738},[2123],"height:0.1514em;",[1867,3740,3741,3744],{"style":2813},[1867,3742],{"className":3743,"style":2132},[2131],[1867,3745,3747],{"className":3746},[2136,2137,2138,2139],[1867,3748,2285],{"className":3749},[2074,2105,2139],[1867,3751,2147],{"className":3752},[2146],[1867,3754,3756],{"className":3755},[2119],[1867,3757,3759],{"className":3758,"style":2154},[2123],[1867,3760],{},[1867,3762,2337],{"className":3763},[2074],[1798,3765,3766,3767,3838],{},"The forecast response to ",[1867,3768,3770,3788],{"className":3769},[1870],[1867,3771,3773],{"className":3772},[1874],[1876,3774,3775],{"xmlns":1878},[1880,3776,3777,3785],{},[1883,3778,3779],{},[2025,3780,3781,3783],{},[2013,3782,2285],{"mathvariant":2015},[2013,3784,2752],{},[1890,3786,3787],{"encoding":1892},"\\mathbf u_t",[1867,3789,3791],{"className":3790,"ariaHidden":1898},[1897],[1867,3792,3794,3798],{"className":3793},[1902],[1867,3795],{"className":3796,"style":3797},[1906],"height:0.5944em;vertical-align:-0.15em;",[1867,3799,3801,3804],{"className":3800},[2074],[1867,3802,2285],{"className":3803},[2074,2075],[1867,3805,3807],{"className":3806},[2110],[1867,3808,3810,3830],{"className":3809},[2114,2115],[1867,3811,3813,3827],{"className":3812},[2119],[1867,3814,3816],{"className":3815,"style":2810},[2123],[1867,3817,3818,3821],{"style":2813},[1867,3819],{"className":3820,"style":2132},[2131],[1867,3822,3824],{"className":3823},[2136,2137,2138,2139],[1867,3825,2752],{"className":3826},[2074,2105,2139],[1867,3828,2147],{"className":3829},[2146],[1867,3831,3833],{"className":3832},[2119],[1867,3834,3836],{"className":3835,"style":2154},[2123],[1867,3837],{}," is well defined. A named shock requires",[1867,3840,3842],{"className":3841},[2256],[1867,3843,3845,3927],{"className":3844},[1870],[1867,3846,3848],{"className":3847},[1874],[1876,3849,3850],{"xmlns":1878,"display":2265},[1880,3851,3852,3924],{},[1883,3853,3854,3860,3862,3865,3873,3875,3877,3879,3881,3887,3895,3897,3899,3902,3904,3906,3908,3914,3916,3922],{},[2025,3855,3856,3858],{},[2013,3857,2285],{"mathvariant":2015},[2013,3859,2752],{},[1886,3861,2019],{},[2013,3863,3864],{},"B",[2025,3866,3867,3871],{},[2013,3868,3870],{"mathvariant":3869},"bold-italic","ε",[2013,3872,2752],{},[1886,3874,2035],{"separator":1898},[2080,3876],{"width":2290},[2013,3878,2293],{},[1886,3880,2023],{"stretchy":2022},[2025,3882,3883,3885],{},[2013,3884,3870],{"mathvariant":3869},[2013,3886,2752],{},[3394,3888,3889,3891,3893],{},[2013,3890,3870],{"mathvariant":3869},[2013,3892,2752],{},[2013,3894,2057],{"mathvariant":2056},[1886,3896,2053],{"stretchy":2022},[1886,3898,2019],{},[2013,3900,3901],{},"I",[1886,3903,2035],{"separator":1898},[2080,3905],{"width":2290},[2013,3907,3864],{},[2049,3909,3910,3912],{},[2013,3911,3864],{},[2013,3913,2057],{"mathvariant":2056},[1886,3915,2019],{},[2025,3917,3918,3920],{},[2013,3919,3410],{"mathvariant":2056},[2013,3921,2285],{},[2013,3923,2337],{"mathvariant":2056},[1890,3925,3926],{"encoding":1892},"\\mathbf u_t=B\\boldsymbol\\varepsilon_t,\\qquad\nE(\\boldsymbol\\varepsilon_t\\boldsymbol\\varepsilon_t^\\top)=I,\\qquad\nBB^\\top=\\Sigma_u.",[1867,3928,3930,3985,4174,4234],{"className":3929,"ariaHidden":1898},[1897],[1867,3931,3933,3936,3976,3979,3982],{"className":3932},[1902],[1867,3934],{"className":3935,"style":3797},[1906],[1867,3937,3939,3942],{"className":3938},[2074],[1867,3940,2285],{"className":3941},[2074,2075],[1867,3943,3945],{"className":3944},[2110],[1867,3946,3948,3968],{"className":3947},[2114,2115],[1867,3949,3951,3965],{"className":3950},[2119],[1867,3952,3954],{"className":3953,"style":2810},[2123],[1867,3955,3956,3959],{"style":2813},[1867,3957],{"className":3958,"style":2132},[2131],[1867,3960,3962],{"className":3961},[2136,2137,2138,2139],[1867,3963,2752],{"className":3964},[2074,2105,2139],[1867,3966,2147],{"className":3967},[2146],[1867,3969,3971],{"className":3970},[2119],[1867,3972,3974],{"className":3973,"style":2154},[2123],[1867,3975],{},[1867,3977],{"className":3978,"style":2081},[2080],[1867,3980,2019],{"className":3981},[1911],[1867,3983],{"className":3984,"style":2081},[2080],[1867,3986,3988,3991,3995,4043,4046,4049,4052,4055,4058,4104,4162,4165,4168,4171],{"className":3987},[1902],[1867,3989],{"className":3990,"style":3551},[1906],[1867,3992,3864],{"className":3993,"style":3994},[2074,2105],"margin-right:0.0502em;",[1867,3996,3998,4008],{"className":3997},[2074],[1867,3999,4001],{"className":4000},[2074],[1867,4002,4004],{"className":4003},[2074],[1867,4005,3870],{"className":4006},[2074,4007],"boldsymbol",[1867,4009,4011],{"className":4010},[2110],[1867,4012,4014,4035],{"className":4013},[2114,2115],[1867,4015,4017,4032],{"className":4016},[2119],[1867,4018,4020],{"className":4019,"style":2810},[2123],[1867,4021,4023,4026],{"style":4022},"top:-2.55em;margin-right:0.05em;",[1867,4024],{"className":4025,"style":2132},[2131],[1867,4027,4029],{"className":4028},[2136,2137,2138,2139],[1867,4030,2752],{"className":4031},[2074,2105,2139],[1867,4033,2147],{"className":4034},[2146],[1867,4036,4038],{"className":4037},[2119],[1867,4039,4041],{"className":4040,"style":2154},[2123],[1867,4042],{},[1867,4044,2035],{"className":4045},[2160],[1867,4047],{"className":4048,"style":2404},[2080],[1867,4050],{"className":4051,"style":2164},[2080],[1867,4053,2293],{"className":4054,"style":2411},[2074,2105],[1867,4056,2023],{"className":4057},[2098],[1867,4059,4061,4070],{"className":4060},[2074],[1867,4062,4064],{"className":4063},[2074],[1867,4065,4067],{"className":4066},[2074],[1867,4068,3870],{"className":4069},[2074,4007],[1867,4071,4073],{"className":4072},[2110],[1867,4074,4076,4096],{"className":4075},[2114,2115],[1867,4077,4079,4093],{"className":4078},[2119],[1867,4080,4082],{"className":4081,"style":2810},[2123],[1867,4083,4084,4087],{"style":4022},[1867,4085],{"className":4086,"style":2132},[2131],[1867,4088,4090],{"className":4089},[2136,2137,2138,2139],[1867,4091,2752],{"className":4092},[2074,2105,2139],[1867,4094,2147],{"className":4095},[2146],[1867,4097,4099],{"className":4098},[2119],[1867,4100,4102],{"className":4101,"style":2154},[2123],[1867,4103],{},[1867,4105,4107,4116],{"className":4106},[2074],[1867,4108,4110],{"className":4109},[2074],[1867,4111,4113],{"className":4112},[2074],[1867,4114,3870],{"className":4115},[2074,4007],[1867,4117,4119],{"className":4118},[2110],[1867,4120,4122,4154],{"className":4121},[2114,2115],[1867,4123,4125,4151],{"className":4124},[2119],[1867,4126,4128,4140],{"className":4127,"style":3665},[2123],[1867,4129,4131,4134],{"style":4130},"top:-2.453em;margin-right:0.05em;",[1867,4132],{"className":4133,"style":2132},[2131],[1867,4135,4137],{"className":4136},[2136,2137,2138,2139],[1867,4138,2752],{"className":4139},[2074,2105,2139],[1867,4141,4142,4145],{"style":3680},[1867,4143],{"className":4144,"style":2132},[2131],[1867,4146,4148],{"className":4147},[2136,2137,2138,2139],[1867,4149,2057],{"className":4150},[2074,2139],[1867,4152,2147],{"className":4153},[2146],[1867,4155,4157],{"className":4156},[2119],[1867,4158,4160],{"className":4159,"style":3699},[2123],[1867,4161],{},[1867,4163,2053],{"className":4164},[2223],[1867,4166],{"className":4167,"style":2081},[2080],[1867,4169,2019],{"className":4170},[1911],[1867,4172],{"className":4173,"style":2081},[2080],[1867,4175,4177,4181,4184,4187,4190,4193,4196,4225,4228,4231],{"className":4176},[1902],[1867,4178],{"className":4179,"style":4180},[1906],"height:1.0935em;vertical-align:-0.1944em;",[1867,4182,3901],{"className":4183,"style":2372},[2074,2105],[1867,4185,2035],{"className":4186},[2160],[1867,4188],{"className":4189,"style":2404},[2080],[1867,4191],{"className":4192,"style":2164},[2080],[1867,4194,3864],{"className":4195,"style":3994},[2074,2105],[1867,4197,4199,4202],{"className":4198},[2074],[1867,4200,3864],{"className":4201,"style":3994},[2074,2105],[1867,4203,4205],{"className":4204},[2110],[1867,4206,4208],{"className":4207},[2114],[1867,4209,4211],{"className":4210},[2119],[1867,4212,4214],{"className":4213,"style":3665},[2123],[1867,4215,4216,4219],{"style":3680},[1867,4217],{"className":4218,"style":2132},[2131],[1867,4220,4222],{"className":4221},[2136,2137,2138,2139],[1867,4223,2057],{"className":4224},[2074,2139],[1867,4226],{"className":4227,"style":2081},[2080],[1867,4229,2019],{"className":4230},[1911],[1867,4232],{"className":4233,"style":2081},[2080],[1867,4235,4237,4240,4280],{"className":4236},[1902],[1867,4238],{"className":4239,"style":3148},[1906],[1867,4241,4243,4246],{"className":4242},[2074],[1867,4244,3410],{"className":4245},[2074],[1867,4247,4249],{"className":4248},[2110],[1867,4250,4252,4272],{"className":4251},[2114,2115],[1867,4253,4255,4269],{"className":4254},[2119],[1867,4256,4258],{"className":4257,"style":3738},[2123],[1867,4259,4260,4263],{"style":2813},[1867,4261],{"className":4262,"style":2132},[2131],[1867,4264,4266],{"className":4265},[2136,2137,2138,2139],[1867,4267,2285],{"className":4268},[2074,2105,2139],[1867,4270,2147],{"className":4271},[2146],[1867,4273,4275],{"className":4274},[2119],[1867,4276,4278],{"className":4277,"style":2154},[2123],[1867,4279],{},[1867,4281,2337],{"className":4282},[2074],[1798,4284,4285,4286,4314],{},"There are many matrices ",[1867,4287,4289,4302],{"className":4288},[1870],[1867,4290,4292],{"className":4291},[1874],[1876,4293,4294],{"xmlns":1878},[1880,4295,4296,4300],{},[1883,4297,4298],{},[2013,4299,3864],{},[1890,4301,3864],{"encoding":1892},[1867,4303,4305],{"className":4304,"ariaHidden":1898},[1897],[1867,4306,4308,4311],{"className":4307},[1902],[1867,4309],{"className":4310,"style":2516},[1906],[1867,4312,3864],{"className":4313,"style":3994},[2074,2105]," satisfying the last equality.",[2522,4316,4317,4320,4323],{},[2525,4318,4319],{},"A finance study may order returns before liquidity and interpret a recursive response cautiously.",[2525,4321,4322],{},"A macro study may use timing restrictions, sign restrictions, or an external instrument to identify a monetary-policy shock.",[2525,4324,4325,4326,4354],{},"The reduced-form fit alone cannot decide which ",[1867,4327,4329,4342],{"className":4328},[1870],[1867,4330,4332],{"className":4331},[1874],[1876,4333,4334],{"xmlns":1878},[1880,4335,4336,4340],{},[1883,4337,4338],{},[2013,4339,3864],{},[1890,4341,3864],{"encoding":1892},[1867,4343,4345],{"className":4344,"ariaHidden":1898},[1897],[1867,4346,4348,4351],{"className":4347},[1902],[1867,4349],{"className":4350,"style":2516},[1906],[1867,4352,3864],{"className":4353,"style":3994},[2074,2105]," is economically correct.",[1798,4356,4357,4364,4365,4370],{},[4358,4359,4363],"a",{"href":4360,"rel":4361},"https:\u002F\u002Fwww.aeaweb.org\u002Farticles?id=10.1257%2F0002828053828518",[4362],"nofollow","Jordà's local projections"," estimate horizon-specific responses directly. ",[4358,4366,4369],{"href":4367,"rel":4368},"https:\u002F\u002Fonlinelibrary.wiley.com\u002Fdoi\u002F10.3982\u002FECTA17813",[4362],"Plagborg-Møller and Wolf"," show that unrestricted local projections and VARs target the same impulse responses; practical differences arise from regularisation, lag choices, and finite samples, not from automatic identification.",[1793,4372,4374],{"id":4373},"matched-example-3-the-forecast-loss","Matched example 3: the forecast loss",[1798,4376,4377,4378,2337],{},"Let ",[1867,4379,4381,4445],{"className":4380},[1870],[1867,4382,4384],{"className":4383},[1874],[1876,4385,4386],{"xmlns":1878},[1880,4387,4388,4442],{},[1883,4389,4390,4404,4406,4418,4420],{},[2025,4391,4392,4395],{},[2013,4393,4394],{},"e",[1883,4396,4397,4399,4401],{},[2013,4398,2752],{},[1886,4400,2282],{},[2013,4402,4403],{},"h",[1886,4405,2019],{},[2025,4407,4408,4410],{},[2013,4409,2016],{},[1883,4411,4412,4414,4416],{},[2013,4413,2752],{},[1886,4415,2282],{},[2013,4417,4403],{},[1886,4419,2765],{},[2025,4421,4422,4430],{},[4423,4424,4425,4427],"mover",{"accent":1898},[2013,4426,2016],{},[1886,4428,4429],{},"^",[1883,4431,4432,4434,4436,4438,4440],{},[2013,4433,2752],{},[1886,4435,2282],{},[2013,4437,4403],{},[1886,4439,2300],{},[2013,4441,2752],{},[1890,4443,4444],{"encoding":1892},"e_{t+h}=y_{t+h}-\\hat y_{t+h\\mid t}",[1867,4446,4448,4514,4578],{"className":4447,"ariaHidden":1898},[1897],[1867,4449,4451,4455,4505,4508,4511],{"className":4450},[1902],[1867,4452],{"className":4453,"style":4454},[1906],"height:0.6389em;vertical-align:-0.2083em;",[1867,4456,4458,4461],{"className":4457},[2074],[1867,4459,4394],{"className":4460},[2074,2105],[1867,4462,4464],{"className":4463},[2110],[1867,4465,4467,4497],{"className":4466},[2114,2115],[1867,4468,4470,4494],{"className":4469},[2119],[1867,4471,4474],{"className":4472,"style":4473},[2123],"height:0.3361em;",[1867,4475,4476,4479],{"style":2813},[1867,4477],{"className":4478,"style":2132},[2131],[1867,4480,4482],{"className":4481},[2136,2137,2138,2139],[1867,4483,4485,4488,4491],{"className":4484},[2074,2139],[1867,4486,2752],{"className":4487},[2074,2105,2139],[1867,4489,2282],{"className":4490},[2384,2139],[1867,4492,4403],{"className":4493},[2074,2105,2139],[1867,4495,2147],{"className":4496},[2146],[1867,4498,4500],{"className":4499},[2119],[1867,4501,4503],{"className":4502,"style":2897},[2123],[1867,4504],{},[1867,4506],{"className":4507,"style":2081},[2080],[1867,4509,2019],{"className":4510},[1911],[1867,4512],{"className":4513,"style":2081},[2080],[1867,4515,4517,4520,4569,4572,4575],{"className":4516},[1902],[1867,4518],{"className":4519,"style":2849},[1906],[1867,4521,4523,4526],{"className":4522},[2074],[1867,4524,2016],{"className":4525,"style":2106},[2074,2105],[1867,4527,4529],{"className":4528},[2110],[1867,4530,4532,4561],{"className":4531},[2114,2115],[1867,4533,4535,4558],{"className":4534},[2119],[1867,4536,4538],{"className":4537,"style":4473},[2123],[1867,4539,4540,4543],{"style":2127},[1867,4541],{"className":4542,"style":2132},[2131],[1867,4544,4546],{"className":4545},[2136,2137,2138,2139],[1867,4547,4549,4552,4555],{"className":4548},[2074,2139],[1867,4550,2752],{"className":4551},[2074,2105,2139],[1867,4553,2282],{"className":4554},[2384,2139],[1867,4556,4403],{"className":4557},[2074,2105,2139],[1867,4559,2147],{"className":4560},[2146],[1867,4562,4564],{"className":4563},[2119],[1867,4565,4567],{"className":4566,"style":2897},[2123],[1867,4568],{},[1867,4570],{"className":4571,"style":2380},[2080],[1867,4573,2765],{"className":4574},[2384],[1867,4576],{"className":4577,"style":2380},[2080],[1867,4579,4581,4585],{"className":4580},[1902],[1867,4582],{"className":4583,"style":4584},[1906],"height:1.0496em;vertical-align:-0.3552em;",[1867,4586,4588,4637],{"className":4587},[2074],[1867,4589,4592],{"className":4590},[2074,4591],"accent",[1867,4593,4595,4628],{"className":4594},[2114,2115],[1867,4596,4598,4625],{"className":4597},[2119],[1867,4599,4602,4612],{"className":4600,"style":4601},[2123],"height:0.6944em;",[1867,4603,4605,4609],{"style":4604},"top:-3em;",[1867,4606],{"className":4607,"style":4608},[2131],"height:3em;",[1867,4610,2016],{"className":4611,"style":2106},[2074,2105],[1867,4613,4614,4617],{"style":4604},[1867,4615],{"className":4616,"style":4608},[2131],[1867,4618,4622],{"className":4619,"style":4621},[4620],"accent-body","left:-0.1944em;",[1867,4623,4429],{"className":4624},[2074],[1867,4626,2147],{"className":4627},[2146],[1867,4629,4631],{"className":4630},[2119],[1867,4632,4635],{"className":4633,"style":4634},[2123],"height:0.1944em;",[1867,4636],{},[1867,4638,4640],{"className":4639},[2110],[1867,4641,4643,4680],{"className":4642},[2114,2115],[1867,4644,4646,4677],{"className":4645},[2119],[1867,4647,4650],{"className":4648,"style":4649},[2123],"height:0.3448em;",[1867,4651,4653,4656],{"style":4652},"top:-2.5198em;margin-left:-0.0359em;margin-right:0.05em;",[1867,4654],{"className":4655,"style":2132},[2131],[1867,4657,4659],{"className":4658},[2136,2137,2138,2139],[1867,4660,4662,4665,4668,4671,4674],{"className":4661},[2074,2139],[1867,4663,2752],{"className":4664},[2074,2105,2139],[1867,4666,2282],{"className":4667},[2384,2139],[1867,4669,4403],{"className":4670},[2074,2105,2139],[1867,4672,2300],{"className":4673},[1911,2139],[1867,4675,2752],{"className":4676},[2074,2105,2139],[1867,4678,2147],{"className":4679},[2146],[1867,4681,4683],{"className":4682},[2119],[1867,4684,4687],{"className":4685,"style":4686},[2123],"height:0.3552em;",[1867,4688],{},[2522,4690,4691,4812,4815],{},[2525,4692,4693,4694,2337],{},"A classical exercise may minimise ",[1867,4695,4697,4730],{"className":4696},[1870],[1867,4698,4700],{"className":4699},[1874],[1876,4701,4702],{"xmlns":1878},[1880,4703,4704,4727],{},[1883,4705,4706,4708,4710,4725],{},[2013,4707,2293],{},[1886,4709,2023],{"stretchy":2022},[3394,4711,4712,4714,4722],{},[2013,4713,4394],{},[1883,4715,4716,4718,4720],{},[2013,4717,2752],{},[1886,4719,2282],{},[2013,4721,4403],{},[2030,4723,4724],{},"2",[1886,4726,2053],{"stretchy":2022},[1890,4728,4729],{"encoding":1892},"E(e_{t+h}^2)",[1867,4731,4733],{"className":4732,"ariaHidden":1898},[1897],[1867,4734,4736,4740,4743,4746,4809],{"className":4735},[1902],[1867,4737],{"className":4738,"style":4739},[1906],"height:1.1555em;vertical-align:-0.3414em;",[1867,4741,2293],{"className":4742,"style":2411},[2074,2105],[1867,4744,2023],{"className":4745},[2098],[1867,4747,4749,4752],{"className":4748},[2074],[1867,4750,4394],{"className":4751},[2074,2105],[1867,4753,4755],{"className":4754},[2110],[1867,4756,4758,4800],{"className":4757},[2114,2115],[1867,4759,4761,4797],{"className":4760},[2119],[1867,4762,4765,4786],{"className":4763,"style":4764},[2123],"height:0.8141em;",[1867,4766,4768,4771],{"style":4767},"top:-2.4169em;margin-left:0em;margin-right:0.05em;",[1867,4769],{"className":4770,"style":2132},[2131],[1867,4772,4774],{"className":4773},[2136,2137,2138,2139],[1867,4775,4777,4780,4783],{"className":4776},[2074,2139],[1867,4778,2752],{"className":4779},[2074,2105,2139],[1867,4781,2282],{"className":4782},[2384,2139],[1867,4784,4403],{"className":4785},[2074,2105,2139],[1867,4787,4788,4791],{"style":2242},[1867,4789],{"className":4790,"style":2132},[2131],[1867,4792,4794],{"className":4793},[2136,2137,2138,2139],[1867,4795,4724],{"className":4796},[2074,2139],[1867,4798,2147],{"className":4799},[2146],[1867,4801,4803],{"className":4802},[2119],[1867,4804,4807],{"className":4805,"style":4806},[2123],"height:0.3414em;",[1867,4808],{},[1867,4810,2053],{"className":4811},[2223],[2525,4813,4814],{},"A portfolio desk may care more about underpredicting the lower tail than a symmetric mean error.",[2525,4816,4817],{},"A policy institution may care about forecast revisions before a meeting, conditional performance during recessions, or a density covering multiple scenarios.",[1798,4819,4820],{},"The correct model comparison is therefore",[1867,4822,4824],{"className":4823},[2256],[1867,4825,4827,4891],{"className":4826},[1870],[1867,4828,4830],{"className":4829},[1874],[1876,4831,4832],{"xmlns":1878,"display":2265},[1880,4833,4834,4888],{},[1883,4835,4836,4838,4841,4844,4846,4858,4860,4881,4883,4886],{},[2013,4837,2293],{},[1886,4839,4840],{"stretchy":2022},"[",[2013,4842,4843],{},"L",[1886,4845,2023],{"stretchy":2022},[2025,4847,4848,4850],{},[2013,4849,2016],{},[1883,4851,4852,4854,4856],{},[2013,4853,2752],{},[1886,4855,2282],{},[2013,4857,4403],{},[1886,4859,2035],{"separator":1898},[2025,4861,4862,4869],{},[4423,4863,4864,4867],{"accent":1898},[2013,4865,4866],{},"f",[1886,4868,4429],{},[1883,4870,4871,4873,4875,4877,4879],{},[2013,4872,2752],{},[1886,4874,2282],{},[2013,4876,4403],{},[1886,4878,2300],{},[2013,4880,2752],{},[1886,4882,2053],{"stretchy":2022},[1886,4884,4885],{"stretchy":2022},"]",[1886,4887,2035],{"separator":1898},[1890,4889,4890],{"encoding":1892},"E[L(y_{t+h},\\hat f_{t+h\\mid t})],",[1867,4892,4894],{"className":4893,"ariaHidden":1898},[1897],[1867,4895,4897,4901,4904,4907,4910,4913,4962,4965,4968,5067,5071],{"className":4896},[1902],[1867,4898],{"className":4899,"style":4900},[1906],"height:1.3131em;vertical-align:-0.3552em;",[1867,4902,2293],{"className":4903,"style":2411},[2074,2105],[1867,4905,4840],{"className":4906},[2098],[1867,4908,4843],{"className":4909},[2074,2105],[1867,4911,2023],{"className":4912},[2098],[1867,4914,4916,4919],{"className":4915},[2074],[1867,4917,2016],{"className":4918,"style":2106},[2074,2105],[1867,4920,4922],{"className":4921},[2110],[1867,4923,4925,4954],{"className":4924},[2114,2115],[1867,4926,4928,4951],{"className":4927},[2119],[1867,4929,4931],{"className":4930,"style":4473},[2123],[1867,4932,4933,4936],{"style":2127},[1867,4934],{"className":4935,"style":2132},[2131],[1867,4937,4939],{"className":4938},[2136,2137,2138,2139],[1867,4940,4942,4945,4948],{"className":4941},[2074,2139],[1867,4943,2752],{"className":4944},[2074,2105,2139],[1867,4946,2282],{"className":4947},[2384,2139],[1867,4949,4403],{"className":4950},[2074,2105,2139],[1867,4952,2147],{"className":4953},[2146],[1867,4955,4957],{"className":4956},[2119],[1867,4958,4960],{"className":4959,"style":2897},[2123],[1867,4961],{},[1867,4963,2035],{"className":4964},[2160],[1867,4966],{"className":4967,"style":2164},[2080],[1867,4969,4971,5017],{"className":4970},[2074],[1867,4972,4974],{"className":4973},[2074,4591],[1867,4975,4977,5009],{"className":4976},[2114,2115],[1867,4978,4980,5006],{"className":4979},[2119],[1867,4981,4984,4993],{"className":4982,"style":4983},[2123],"height:0.9579em;",[1867,4985,4986,4989],{"style":4604},[1867,4987],{"className":4988,"style":4608},[2131],[1867,4990,4866],{"className":4991,"style":4992},[2074,2105],"margin-right:0.1076em;",[1867,4994,4996,4999],{"style":4995},"top:-3.2634em;",[1867,4997],{"className":4998,"style":4608},[2131],[1867,5000,5003],{"className":5001,"style":5002},[4620],"left:-0.0833em;",[1867,5004,4429],{"className":5005},[2074],[1867,5007,2147],{"className":5008},[2146],[1867,5010,5012],{"className":5011},[2119],[1867,5013,5015],{"className":5014,"style":4634},[2123],[1867,5016],{},[1867,5018,5020],{"className":5019},[2110],[1867,5021,5023,5059],{"className":5022},[2114,2115],[1867,5024,5026,5056],{"className":5025},[2119],[1867,5027,5029],{"className":5028,"style":4649},[2123],[1867,5030,5032,5035],{"style":5031},"top:-2.5198em;margin-left:-0.1076em;margin-right:0.05em;",[1867,5033],{"className":5034,"style":2132},[2131],[1867,5036,5038],{"className":5037},[2136,2137,2138,2139],[1867,5039,5041,5044,5047,5050,5053],{"className":5040},[2074,2139],[1867,5042,2752],{"className":5043},[2074,2105,2139],[1867,5045,2282],{"className":5046},[2384,2139],[1867,5048,4403],{"className":5049},[2074,2105,2139],[1867,5051,2300],{"className":5052},[1911,2139],[1867,5054,2752],{"className":5055},[2074,2105,2139],[1867,5057,2147],{"className":5058},[2146],[1867,5060,5062],{"className":5061},[2119],[1867,5063,5065],{"className":5064,"style":4686},[2123],[1867,5066],{},[1867,5068,5070],{"className":5069},[2223],")]",[1867,5072,2035],{"className":5073},[2160],[1798,5075,5076,5077,5105,5106,5110],{},"where ",[1867,5078,5080,5093],{"className":5079},[1870],[1867,5081,5083],{"className":5082},[1874],[1876,5084,5085],{"xmlns":1878},[1880,5086,5087,5091],{},[1883,5088,5089],{},[2013,5090,4843],{},[1890,5092,4843],{"encoding":1892},[1867,5094,5096],{"className":5095,"ariaHidden":1898},[1897],[1867,5097,5099,5102],{"className":5098},[1902],[1867,5100],{"className":5101,"style":2516},[1906],[1867,5103,4843],{"className":5104},[2074,2105]," is chosen ",[5107,5108,5109],"strong",{},"before"," seeing the winning model.",[1793,5112,5114],{"id":5113},"the-usage-decision","The usage decision",[1798,5116,5117],{},"Use this sequence before fitting anything:",[1802,5119,5120,5133],{},[1805,5121,5122],{},[1808,5123,5124,5127,5130],{},[1811,5125,5126],{},"Decision",[1811,5128,5129],{},"If yes",[1811,5131,5132],{},"Consequence",[1824,5134,5135,5146,5157,5168,5179,5190],{},[1808,5136,5137,5140,5143],{},[1829,5138,5139],{},"Is the object a traded price?",[1829,5141,5142],{},"transform to an adjusted return unless the level relation is itself the target",[1829,5144,5145],{},"inspect market calendar, corporate actions, costs, and tails",[1808,5147,5148,5151,5154],{},[1829,5149,5150],{},"Is the target a macroeconomic level?",[1829,5152,5153],{},"test whether trends and long-run relations are substantively meaningful",[1829,5155,5156],{},"compare difference, cointegration, and state-space specifications",[1808,5158,5159,5162,5165],{},[1829,5160,5161],{},"Was the value revised after release?",[1829,5163,5164],{},"preserve vintage and release timestamps",[1829,5166,5167],{},"evaluate against information available at each forecast origin",[1808,5169,5170,5173,5176],{},[1829,5171,5172],{},"Is the claim causal or structural?",[1829,5174,5175],{},"forecasting fit is insufficient",[1829,5177,5178],{},"state and defend an identification design",[1808,5180,5181,5184,5187],{},[1829,5182,5183],{},"Is the loss asymmetric or tail-focused?",[1829,5185,5186],{},"RMSE is insufficient",[1829,5188,5189],{},"evaluate quantiles, VaR\u002FES, or decision-specific utility",[1808,5191,5192,5195,5198],{},[1829,5193,5194],{},"Do horizons overlap?",[1829,5196,5197],{},"residuals share observations",[1829,5199,5200],{},"use an appropriate long-run covariance and honest split",[1793,5202,5204],{"id":5203},"three-common-category-errors","Three common category errors",[5206,5207,5208,5214,5220],"ol",{},[2525,5209,5210,5213],{},[5107,5211,5212],{},"Stationary therefore useful:"," a spread may be stationary but too slow, costly, or unstable to trade.",[2525,5215,5216,5219],{},[5107,5217,5218],{},"Predictive therefore causal:"," a yield spread may forecast activity without representing an intervention.",[2525,5221,5222,5225],{},[5107,5223,5224],{},"Revised therefore known:"," a final macro series can make a historical nowcast look better than information available in real time.",[1793,5227,5229],{"id":5228},"practice","Practice",[1798,5231,5232],{},"For each case, choose the track and the missing safeguard.",[5206,5234,5235,5238,5241,5244],{},[2525,5236,5237],{},"Daily close-to-close equity returns are used to estimate tomorrow's 1% loss quantile.",[2525,5239,5240],{},"Quarterly consumption and income levels are modelled jointly to study long-run adjustment.",[2525,5242,5243],{},"Monthly inflation and policy rates are used to report the response to a monetary-policy shock.",[2525,5245,5246],{},"An ARMA simulation is used to verify a Yule–Walker identity.",[5248,5249,5251],"legacy-details",{"title":5250},"Answers",[5206,5252,5253,5256,5259,5262],{},[2525,5254,5255],{},"Finance: adjusted prices, tail loss, changing volatility, and out-of-sample VaR calibration.",[2525,5257,5258],{},"Economics with cointegration: test rank and interpret the error-correction relation.",[2525,5260,5261],{},"Economics with structural identification: define why the innovation is a policy shock.",[2525,5263,5264],{},"Classical statistics: covariance validity and algebra are the main objects.",[1793,5266,5268],{"id":5267},"working-rule","Working rule",[1798,5270,5271],{},"Use the classical course to justify the stochastic machinery. Use this course to justify the transformation, information set, identification, and decision. A strong analysis needs both.",[1798,5273,5274,5275,2337],{},"Next: ",[4358,5276,424],{"href":5277},"..\u002F02-data-transformations\u002F",{"title":10,"searchDepth":5279,"depth":5279,"links":5280},2,[5281,5282,5283,5284,5285,5286,5287,5288,5289,5290],{"id":1795,"depth":5279,"text":1796},{"id":1995,"depth":5279,"text":1996},{"id":2598,"depth":5279,"text":2599},{"id":2725,"depth":5279,"text":2726},{"id":3328,"depth":5279,"text":3329},{"id":4373,"depth":5279,"text":4374},{"id":5113,"depth":5279,"text":5114},{"id":5203,"depth":5279,"text":5204},{"id":5228,"depth":5279,"text":5229},{"id":5267,"depth":5279,"text":5268},"A decision guide to classical statistical, financial, and economic time series, with matched examples and method-selection rules.","md",{"sidebar":5294},{"order":5295},1,true,{"title":418,"description":5291},"yGYL8bXUlZvdJnGaZNRmbPvQ9sIqgSLZSECJy0xgdvg",[5300,5302],{"title":412,"path":413,"stem":414,"description":5301,"children":-1},"A matrix-based course in returns, volatility, persistent predictors, cointegration, structural dynamics, nowcasting, and forecast evaluation.",{"title":424,"path":425,"stem":426,"description":5303,"children":-1},"Transform prices and macroeconomic releases with explicit differencing, aggregation, timing, and vintage operators.",1785754723647]