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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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Statistics","\u002Fzh\u002Fprob-and-stats\u002F02-statistics","zh\u002Fprob-and-stats\u002F02-statistics",[1685,1691,1697,1703,1709,1715,1721],{"title":1686,"path":1687,"stem":1688,"children":1689},"第六章：抽样分布","\u002Fzh\u002Fprob-and-stats\u002F02-statistics\u002F01-sampling","zh\u002Fprob-and-stats\u002F02-statistics\u002F01-sampling\u002Findex",[1690],{"title":1686,"path":1687,"stem":1688},{"title":1692,"path":1693,"stem":1694,"children":1695},"第七章：区间估计","\u002Fzh\u002Fprob-and-stats\u002F02-statistics\u002F02-interval-estimation","zh\u002Fprob-and-stats\u002F02-statistics\u002F02-interval-estimation\u002Findex",[1696],{"title":1692,"path":1693,"stem":1694},{"title":1698,"path":1699,"stem":1700,"children":1701},"第八章：点估计理论","\u002Fzh\u002Fprob-and-stats\u002F02-statistics\u002F03-point-estimation","zh\u002Fprob-and-stats\u002F02-statistics\u002F03-point-estimation\u002Findex",[1702],{"title":1698,"path":1699,"stem":1700},{"title":1704,"path":1705,"stem":1706,"children":1707},"第九章：点估计方法","\u002Fzh\u002Fprob-and-stats\u002F02-statistics\u002F04-pe-method","zh\u002Fprob-and-stats\u002F02-statistics\u002F04-pe-method\u002Findex",[1708],{"title":1704,"path":1705,"stem":1706},{"title":1710,"path":1711,"stem":1712,"children":1713},"第十章：假设检验原理","\u002Fzh\u002Fprob-and-stats\u002F02-statistics\u002F05-hypothesis","zh\u002Fprob-and-stats\u002F02-statistics\u002F05-hypothesis\u002Findex",[1714],{"title":1710,"path":1711,"stem":1712},{"title":1716,"path":1717,"stem":1718,"children":1719},"第十一章：常用检验方法与选择","\u002Fzh\u002Fprob-and-stats\u002F02-statistics\u002F06-hypothesis-method","zh\u002Fprob-and-stats\u002F02-statistics\u002F06-hypothesis-method\u002Findex",[1720],{"title":1716,"path":1717,"stem":1718},{"title":1722,"path":1723,"stem":1724,"children":1725},"第十二章：Bootstrap 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X_{t-1}+\\varepsilon_t,",[1841,3678,3680,3735,3753,3821],{"className":3679,"ariaHidden":1900},[1899],[1841,3681,3683,3686,3726,3729,3732],{"className":3682},[1904],[1841,3684],{"className":3685,"style":1909},[1908],[1841,3687,3689,3692],{"className":3688},[1913],[1841,3690,1868],{"className":3691,"style":1922},[1913,1914],[1841,3693,3695],{"className":3694},[1926],[1841,3696,3698,3718],{"className":3697},[1930,1931],[1841,3699,3701,3715],{"className":3700},[1935],[1841,3702,3704],{"className":3703,"style":1940},[1939],[1841,3705,3706,3709],{"style":1943},[1841,3707],{"className":3708,"style":1948},[1947],[1841,3710,3712],{"className":3711},[1952,1953,1954,1955],[1841,3713,1871],{"className":3714},[1913,1914,1955],[1841,3716,1963],{"className":3717},[1962],[1841,3719,3721],{"className":3720},[1935],[1841,3722,3724],{"className":3723,"style":1970},[1939],[1841,3725],{},[1841,3727],{"className":3728,"style":1977},[1976],[1841,3730,1875],{"className":3731},[1981],[1841,3733],{"className":3734,"style":1977},[1976],[1841,3736,3738,3741,3744,3747,3750],{"className":3737},[1904],[1841,3739],{"className":3740,"style":2283},[1908],[1841,3742,3647],{"className":3743},[1913,1914],[1841,3745],{"className":3746,"style":2210},[1976],[1841,3748,2129],{"className":3749},[2028],[1841,3751],{"className":3752,"style":2210},[1976],[1841,3754,3756,3760,3763,3812,3815,3818],{"className":3755},[1904],[1841,3757],{"className":3758,"style":3759},[1908],"height:0.9028em;vertical-align:-0.2083em;",[1841,3761,2064],{"className":3762},[1913,1914],[1841,3764,3766,3769],{"className":3765},[1913],[1841,3767,1868],{"className":3768,"style":1922},[1913,1914],[1841,3770,3772],{"className":3771},[1926],[1841,3773,3775,3804],{"className":3774},[1930,1931],[1841,3776,3778,3801],{"className":3777},[1935],[1841,3779,3781],{"className":3780,"style":2010},[1939],[1841,3782,3783,3786],{"style":1943},[1841,3784],{"className":3785,"style":1948},[1947],[1841,3787,3789],{"className":3788},[1952,1953,1954,1955],[1841,3790,3792,3795,3798],{"className":3791},[1913,1955],[1841,3793,1871],{"className":3794},[1913,1914,1955],[1841,3796,1886],{"className":3797},[2028,1955],[1841,3799,1890],{"className":3800},[1913,1955],[1841,3802,1963],{"className":3803},[1962],[1841,3805,3807],{"className":3806},[1935],[1841,3808,3810],{"className":3809,"style":2041},[1939],[1841,3811],{},[1841,3813],{"className":3814,"style":2210},[1976],[1841,3816,2129],{"className":3817},[2028],[1841,3819],{"className":3820,"style":2210},[1976],[1841,3822,3824,3827,3867],{"className":3823},[1904],[1841,3825],{"className":3826,"style":2643},[1908],[1841,3828,3830,3833],{"className":3829},[1913],[1841,3831,2690],{"className":3832},[1913,1914],[1841,3834,3836],{"className":3835},[1926],[1841,3837,3839,3859],{"className":3838},[1930,1931],[1841,3840,3842,3856],{"className":3841},[1935],[1841,3843,3845],{"className":3844,"style":1940},[1939],[1841,3846,3847,3850],{"style":2244},[1841,3848],{"className":3849,"style":1948},[1947],[1841,3851,3853],{"className":3852},[1952,1953,1954,1955],[1841,3854,1871],{"className":3855},[1913,1914,1955],[1841,3857,1963],{"className":3858},[1962],[1841,3860,3862],{"className":3861},[1935],[1841,3863,3865],{"className":3864,"style":1970},[1939],[1841,3866],{},[1841,3868,2110],{"className":3869},[2380],[1798,3871,3872,3873,2160],{},"the stationary mean is 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AR means decaying feedback",[1798,3972,3973],{},"For AR(1),",[1841,3975,3977],{"className":3976},[2048],[1841,3978,3980,4024],{"className":3979},[1844],[1841,3981,3983],{"className":3982},[1848],[1850,3984,3985],{"xmlns":1852,"display":2057},[1854,3986,3987,4021],{},[1857,3988,3989,3995,3997,3999,4011,4013,4019],{},[1864,3990,3991,3993],{},[1860,3992,1868],{},[1860,3994,1871],{},[1873,3996,1875],{},[1860,3998,2064],{},[1864,4000,4001,4003],{},[1860,4002,1868],{},[1857,4004,4005,4007,4009],{},[1860,4006,1871],{},[1873,4008,1886],{},[1888,4010,1890],{},[1873,4012,2129],{},[1864,4014,4015,4017],{},[1860,4016,2690],{},[1860,4018,1871],{},[1860,4020,2160],{"mathvariant":2159},[1892,4022,4023],{"encoding":1894},"X_t=\\phi X_{t-1}+\\varepsilon_t.",[1841,4025,4027,4082,4149],{"className":4026,"ariaHidden":1900},[1899],[1841,4028,4030,4033,4073,4076,4079],{"className":4029},[1904],[1841,4031],{"className":4032,"style":1909},[1908],[1841,4034,4036,4039],{"className":4035},[1913],[1841,4037,1868],{"className":4038,"style":1922},[1913,1914],[1841,4040,4042],{"className":4041},[1926],[1841,4043,4045,4065],{"className":4044},[1930,1931],[1841,4046,4048,4062],{"className":4047},[1935],[1841,4049,4051],{"className":4050,"style":1940},[1939],[1841,4052,4053,4056],{"style":1943},[1841,4054],{"className":4055,"style":1948},[1947],[1841,4057,4059],{"className":4058},[1952,1953,1954,1955],[1841,4060,1871],{"className":4061},[1913,1914,1955],[1841,4063,1963],{"className":4064},[1962],[1841,4066,4068],{"className":4067},[1935],[1841,4069,4071],{"className":4070,"style":1970},[1939],[1841,4072],{},[1841,4074],{"className":4075,"style":1977},[1976],[1841,4077,1875],{"className":4078},[1981],[1841,4080],{"className":4081,"style":1977},[1976],[1841,4083,4085,4088,4091,4140,4143,4146],{"className":4084},[1904],[1841,4086],{"className":4087,"style":3759},[1908],[1841,4089,2064],{"className":4090},[1913,1914],[1841,4092,4094,4097],{"className":4093},[1913],[1841,4095,1868],{"className":4096,"style":1922},[1913,1914],[1841,4098,4100],{"className":4099},[1926],[1841,4101,4103,4132],{"className":4102},[1930,1931],[1841,4104,4106,4129],{"className":4105},[1935],[1841,4107,4109],{"className":4108,"style":2010},[1939],[1841,4110,4111,4114],{"style":1943},[1841,4112],{"className":4113,"style":1948},[1947],[1841,4115,4117],{"className":4116},[1952,1953,1954,1955],[1841,4118,4120,4123,4126],{"className":4119},[1913,1955],[1841,4121,1871],{"className":4122},[1913,1914,1955],[1841,4124,1886],{"className":4125},[2028,1955],[1841,4127,1890],{"className":4128},[1913,1955],[1841,4130,1963],{"className":4131},[1962],[1841,4133,4135],{"className":4134},[1935],[1841,4136,4138],{"className":4137,"style":2041},[1939],[1841,4139],{},[1841,4141],{"className":4142,"style":2210},[1976],[1841,4144,2129],{"className":4145},[2028],[1841,4147],{"className":4148,"style":2210},[1976],[1841,4150,4152,4155,4195],{"className":4151},[1904],[1841,4153],{"className":4154,"style":2796},[1908],[1841,4156,4158,4161],{"className":4157},[1913],[1841,4159,2690],{"className":4160},[1913,1914],[1841,4162,4164],{"className":4163},[1926],[1841,4165,4167,4187],{"className":4166},[1930,1931],[1841,4168,4170,4184],{"className":4169},[1935],[1841,4171,4173],{"className":4172,"style":1940},[1939],[1841,4174,4175,4178],{"style":2244},[1841,4176],{"className":4177,"style":1948},[1947],[1841,4179,4181],{"className":4180},[1952,1953,1954,1955],[1841,4182,1871],{"className":4183},[1913,1914,1955],[1841,4185,1963],{"className":4186},[1962],[1841,4188,4190],{"className":4189},[1935],[1841,4191,4193],{"className":4192,"style":1970},[1939],[1841,4194],{},[1841,4196,2160],{"className":4197},[1913],[1798,4199,4200,4201,4265],{},"It 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",[1841,4202,4204,4228],{"className":4203},[1844],[1841,4205,4207],{"className":4206},[1848],[1850,4208,4209],{"xmlns":1852},[1854,4210,4211,4225],{},[1857,4212,4213,4216,4218,4220,4223],{},[1860,4214,4215],{"mathvariant":2159},"∣",[1860,4217,2064],{},[1860,4219,4215],{"mathvariant":2159},[1873,4221,4222],{},"\u003C",[1888,4224,1890],{},[1892,4226,4227],{"encoding":1894},"|\\phi|\u003C1",[1841,4229,4231,4255],{"className":4230,"ariaHidden":1900},[1899],[1841,4232,4234,4237,4240,4243,4246,4249,4252],{"className":4233},[1904],[1841,4235],{"className":4236,"style":2173},[1908],[1841,4238,4215],{"className":4239},[1913],[1841,4241,2064],{"className":4242},[1913,1914],[1841,4244,4215],{"className":4245},[1913],[1841,4247],{"className":4248,"style":1977},[1976],[1841,4250,4222],{"className":4251},[1981],[1841,4253],{"className":4254,"style":1977},[1976],[1841,4256,4258,4262],{"className":4257},[1904],[1841,4259],{"className":4260,"style":4261},[1908],"height:0.6444em;",[1841,4263,1890],{"className":4264},[1913],", with",[1841,4267,4269],{"className":4268},[2048],[1841,4270,4272,4373],{"className":4271},[1844],[1841,4273,4275],{"className":4274},[1848],[1850,4276,4277],{"xmlns":1852,"display":2057},[1854,4278,4279,4370],{},[1857,4280,4281,4287,4289,4295,4297,4299,4311,4313,4320,4332,4334,4336,4340,4342,4344,4347,4349,4352,4354,4356,4368],{},[1864,4282,4283,4285],{},[1860,4284,1868],{},[1860,4286,1871],{},[1873,4288,1875],{},[1864,4290,4291,4293],{},[1860,4292,2690],{},[1860,4294,1871],{},[1873,4296,2129],{},[1860,4298,2064],{},[1864,4300,4301,4303],{},[1860,4302,2690],{},[1857,4304,4305,4307,4309],{},[1860,4306,1871],{},[1873,4308,1886],{},[1888,4310,1890],{},[1873,4312,2129],{},[2102,4314,4315,4317],{},[1860,4316,2064],{},[1888,4318,4319],{},"2",[1864,4321,4322,4324],{},[1860,4323,2690],{},[1857,4325,4326,4328,4330],{},[1860,4327,1871],{},[1873,4329,1886],{},[1888,4331,4319],{},[1873,4333,2129],{},[1873,4335,2092],{},[4337,4338,4339],"mtext",{}," ",[1873,4341,2110],{"separator":1900},[1976,4343],{"width":2113},[1860,4345,4346],{},"ρ",[1873,4348,2068],{"stretchy":2067},[1860,4350,4351],{},"h",[1873,4353,2073],{"stretchy":2067},[1873,4355,1875],{},[2102,4357,4358,4360],{},[1860,4359,2064],{},[1857,4361,4362,4364,4366],{},[1860,4363,4215],{"mathvariant":2159},[1860,4365,4351],{},[1860,4367,4215],{"mathvariant":2159},[1860,4369,2160],{"mathvariant":2159},[1892,4371,4372],{"encoding":1894},"X_t=\\varepsilon_t+\\phi\\varepsilon_{t-1}+\\phi^2\\varepsilon_{t-2}+\\cdots,\n\\qquad \\rho(h)=\\phi^{|h|}.",[1841,4374,4376,4431,4487,4554,4649,4694],{"className":4375,"ariaHidden":1900},[1899],[1841,4377,4379,4382,4422,4425,4428],{"className":4378},[1904],[1841,4380],{"className":4381,"style":1909},[1908],[1841,4383,4385,4388],{"className":4384},[1913],[1841,4386,1868],{"className":4387,"style":1922},[1913,1914],[1841,4389,4391],{"className":4390},[1926],[1841,4392,4394,4414],{"className":4393},[1930,1931],[1841,4395,4397,4411],{"className":4396},[1935],[1841,4398,4400],{"className":4399,"style":1940},[1939],[1841,4401,4402,4405],{"style":1943},[1841,4403],{"className":4404,"style":1948},[1947],[1841,4406,4408],{"className":4407},[1952,1953,1954,1955],[1841,4409,1871],{"className":4410},[1913,1914,1955],[1841,4412,1963],{"className":4413},[1962],[1841,4415,4417],{"className":4416},[1935],[1841,4418,4420],{"className":4419,"style":1970},[1939],[1841,4421],{},[1841,4423],{"className":4424,"style":1977},[1976],[1841,4426,1875],{"className":4427},[1981],[1841,4429],{"className":4430,"style":1977},[1976],[1841,4432,4434,4438,4478,4481,4484],{"className":4433},[1904],[1841,4435],{"className":4436,"style":4437},[1908],"height:0.7333em;vertical-align:-0.15em;",[1841,4439,4441,4444],{"className":4440},[1913],[1841,4442,2690],{"className":4443},[1913,1914],[1841,4445,4447],{"className":4446},[1926],[1841,4448,4450,4470],{"className":4449},[1930,1931],[1841,4451,4453,4467],{"className":4452},[1935],[1841,4454,4456],{"className":4455,"style":1940},[1939],[1841,4457,4458,4461],{"style":2244},[1841,4459],{"className":4460,"style":1948},[1947],[1841,4462,4464],{"className":4463},[1952,1953,1954,1955],[1841,4465,1871],{"className":4466},[1913,1914,1955],[1841,4468,1963],{"className":4469},[1962],[1841,4471,4473],{"className":4472},[1935],[1841,4474,4476],{"className":4475,"style":1970},[1939],[1841,4477],{},[1841,4479],{"className":4480,"style":2210},[1976],[1841,4482,2129],{"className":4483},[2028],[1841,4485],{"className":4486,"style":2210},[1976],[1841,4488,4490,4493,4496,4545,4548,4551],{"className":4489},[1904],[1841,4491],{"className":4492,"style":3759},[1908],[1841,4494,2064],{"className":4495},[1913,1914],[1841,4497,4499,4502],{"className":4498},[1913],[1841,4500,2690],{"className":4501},[1913,1914],[1841,4503,4505],{"className":4504},[1926],[1841,4506,4508,4537],{"className":4507},[1930,1931],[1841,4509,4511,4534],{"className":4510},[1935],[1841,4512,4514],{"className":4513,"style":2010},[1939],[1841,4515,4516,4519],{"style":2244},[1841,4517],{"className":4518,"style":1948},[1947],[1841,4520,4522],{"className":4521},[1952,1953,1954,1955],[1841,4523,4525,4528,4531],{"className":4524},[1913,1955],[1841,4526,1871],{"className":4527},[1913,1914,1955],[1841,4529,1886],{"className":4530},[2028,1955],[1841,4532,1890],{"className":4533},[1913,1955],[1841,4535,1963],{"className":4536},[1962],[1841,4538,4540],{"className":4539},[1935],[1841,4541,4543],{"className":4542,"style":2041},[1939],[1841,4544],{},[1841,4546],{"className":4547,"style":2210},[1976],[1841,4549,2129],{"className":4550},[2028],[1841,4552],{"className":4553,"style":2210},[1976],[1841,4555,4557,4561,4591,4640,4643,4646],{"className":4556},[1904],[1841,4558],{"className":4559,"style":4560},[1908],"height:1.0724em;vertical-align:-0.2083em;",[1841,4562,4564,4567],{"className":4563},[1913],[1841,4565,2064],{"className":4566},[1913,1914],[1841,4568,4570],{"className":4569},[1926],[1841,4571,4573],{"className":4572},[1930],[1841,4574,4576],{"className":4575},[1935],[1841,4577,4580],{"className":4578,"style":4579},[1939],"height:0.8641em;",[1841,4581,4582,4585],{"style":2367},[1841,4583],{"className":4584,"style":1948},[1947],[1841,4586,4588],{"className":4587},[1952,1953,1954,1955],[1841,4589,4319],{"className":4590},[1913,1955],[1841,4592,4594,4597],{"className":4593},[1913],[1841,4595,2690],{"className":4596},[1913,1914],[1841,4598,4600],{"className":4599},[1926],[1841,4601,4603,4632],{"className":4602},[1930,1931],[1841,4604,4606,4629],{"className":4605},[1935],[1841,4607,4609],{"className":4608,"style":2010},[1939],[1841,4610,4611,4614],{"style":2244},[1841,4612],{"className":4613,"style":1948},[1947],[1841,4615,4617],{"className":4616},[1952,1953,1954,1955],[1841,4618,4620,4623,4626],{"className":4619},[1913,1955],[1841,4621,1871],{"className":4622},[1913,1914,1955],[1841,4624,1886],{"className":4625},[2028,1955],[1841,4627,4319],{"className":4628},[1913,1955],[1841,4630,1963],{"className":4631},[1962],[1841,4633,4635],{"className":4634},[1935],[1841,4636,4638],{"className":4637,"style":2041},[1939],[1841,4639],{},[1841,4641],{"className":4642,"style":2210},[1976],[1841,4644,2129],{"className":4645},[2028],[1841,4647],{"className":4648,"style":2210},[1976],[1841,4650,4652,4655,4658,4661,4664,4667,4670,4673,4676,4679,4682,4685,4688,4691],{"className":4651},[1904],[1841,4653],{"className":4654,"style":2173},[1908],[1841,4656,2092],{"className":4657},[2287],[1841,4659],{"className":4660,"style":2388},[1976],[1841,4662],{"className":4663,"styl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AR(",[1841,4747,4749,4762],{"className":4748},[1844],[1841,4750,4752],{"className":4751},[1848],[1850,4753,4754],{"xmlns":1852},[1854,4755,4756,4760],{},[1857,4757,4758],{},[1860,4759,1798],{},[1892,4761,1798],{"encoding":1894},[1841,4763,4765],{"className":4764,"ariaHidden":1900},[1899],[1841,4766,4768,4771],{"className":4767},[1904],[1841,4769],{"className":4770,"style":2643},[1908],[1841,4772,1798],{"className":4773},[1913,1914],"), all roots of 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must lie ",[4846,4847,4848],"strong",{},"outside"," the unit circle. Equivalently, the companion-matrix eigenvalues lie inside it.",[4851,4852,4854],"h3",{"id":4853},"worked-ar2-root-check","Worked AR(2) root 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polynomial is 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Its roots are 2 and 4, both outside the unit circle, so the process is stationary. Two positive decay rates create a smoother ACF than a single cutoff rule could describe.",[1793,5389,5391],{"id":5390},"_3-companion-and-yulewalker-forms","3. Companion and Yule–Walker forms",[1798,5393,4745,5394,5422],{},[1841,5395,5397,5410],{"className":5396},[1844],[1841,5398,5400],{"className":5399},[1848],[1850,5401,5402],{"xmlns":1852},[1854,5403,5404,5408],{},[1857,5405,5406],{},[1860,5407,1798],{},[1892,5409,1798],{"encoding":1894},[1841,5411,5413],{"className":5412,"ariaHidden":1900},[1899],[1841,5414,5416,5419],{"className":5415},[1904],[1841,5417],{"className":5418,"style":2643},[1908],[1841,5420,1798],{"className":5421},[1913,1914],"), define",[1841,5424,5426],{"className":5425},[2048],[1841,5427,5429,5543],{"className":5428},[1844],[1841,5430,5432],{"className":5431},[1848],[1850,5433,5434],{"xmlns":1852,"display":2057},[1854,5435,5436,5540],{},[1857,5437,5438,5446,5448,5450,5456,5458,5470,5472,5475,5477,5493,5500,5502,5504,5510,5512,5515,5527,5529,5532,5538],{},[1864,5439,5440,5444],{},[1860,5441,5443],{"mathvariant":5442},"bold","s",[1860,5445,1871],{},[1873,5447,1875],{},[1873,5449,2068],{"stretchy":2067},[1864,5451,5452,5454],{},[1860,5453,1868],{},[1860,5455,1871],{},[1873,5457,2110],{"separator":1900},[1864,5459,5460,5462],{},[1860,5461,1868],{},[1857,5463,5464,5466,5468],{},[1860,5465,1871],{},[1873,5467,1886],{},[1888,5469,1890],{},[1873,5471,2110],{"separator":1900},[1873,5473,5474],{},"…",[1873,5476,2110],{"separator":1900},[1864,5478,5479,5481],{},[1860,5480,1868],{},[1857,5482,5483,5485,5487,5489,5491],{},[1860,5484,1871],{},[1873,5486,1886],{},[1860,5488,1798],{},[1873,5490,2129],{},[1888,5492,1890],{},[2102,5494,5495,5497],{},[1873,5496,2073],{"stretchy":2067},[1860,5498,5499],{"mathvariant":2159},"⊤",[1873,5501,2110],{"separator":1900},[1976,5503],{"width":2113},[1864,5505,5506,5508],{},[1860,5507,5443],{"mathvariant":5442},[1860,5509,1871],{},[1873,5511,1875],{},[1860,5513,5514],{},"F",[1864,5516,5517,5519],{},[1860,5518,5443],{"mathvariant":5442},[1857,5520,5521,5523,5525],{},[1860,5522,1871],{},[1873,5524,1886],{},[1888,5526,1890],{},[1873,5528,2129],{},[1860,5530,5531],{},"G",[1864,5533,5534,5536],{},[1860,5535,2690],{},[1860,5537,1871],{},[1873,5539,2110],{"separator":1900},[1892,5541,5542],{"encoding":1894},"\\mathbf s_t=(X_t,X_{t-1},\\ldots,X_{t-p+1})^\\top,\n\\qquad\n\\mathbf s_t=F\\mathbf s_{t-1}+G\\varepsilon_t,",[1841,5544,5546,5603,5869,5937],{"className":5545,"ariaHidden":1900},[1899],[1841,5547,5549,5553,5594,5597,5600],{"className":5548},[1904],[1841,5550],{"className":5551,"style":5552},[1908],"height:0.5944em;vertical-align:-0.15em;",[1841,5554,5556,5560],{"className":5555},[1913],[1841,5557,5443],{"className":5558},[1913,5559],"mathbf",[1841,5561,5563],{"className":5562},[1926],[1841,5564,5566,5586],{"className":5565},[1930,1931],[1841,5567,5569,5583],{"className":5568},[1935],[1841,5570,5572],{"className":5571,"style":1940},[1939],[1841,5573,5574,5577],{"style":2244},[1841,5575],{"className":5576,"style":1948},[1947],[1841,5578,5580],{"className":5579},[1952,1953,1954,1955],[1841,5581,1871],{"className":5582},[1913,1914,1955],[1841,5584,1963],{"className":5585},[1962],[1841,5587,5589],{"className":5588},[1935],[1841,5590,5592],{"className":5591,"style":1970},[1939],[1841,5593],{},[1841,5595],{"className":5596,"style":1977},[1976],[1841,5598,1875],{"className":5599},[1981],[1841,5601],{"className":5602,"style":1977},[1976],[1841,5604,5606,5610,5613,5653,5656,5659,5708,5711,5714,5717,5720,5723,5726,5781,5811,5814,5817,5820,5860,5863,5866],{"className":5605},[1904],[1841,5607],{"className":5608,"style":5609},[1908],"height:1.1852em;vertical-align:-0.2861em;",[1841,5611,2068],{"className":5612},[2180],[1841,5614,5616,5619],{"className":5615},[1913],[1841,5617,1868],{"className":5618,"style":1922},[1913,1914],[1841,5620,5622],{"className":5621},[1926],[1841,5623,5625,5645],{"className":5624},[1930,1931],[1841,5626,5628,5642],{"className":5627},[1935],[1841,5629,5631],{"className":5630,"style":1940},[1939],[1841,5632,5633,5636],{"style":1943},[1841,5634],{"className":5635,"style":1948},[1947],[1841,5637,5639],{"className":5638},[1952,1953,1954,1955],[1841,5640,1871],{"className":5641},[1913,1914,1955],[1841,5643,1963],{"className":5644},[1962],[1841,5646,5648],{"className":5647},[1935],[1841,5649,5651],{"className":5650,"style":1970},[1939],[1841,5652],{},[1841,5654,2110],{"className":5655},[2380],[1841,5657],{"className":5658,"style":2388},[1976],[1841,5660,5662,5665],{"className":5661},[1913],[1841,5663,1868],{"className":5664,"style":1922},[1913,1914],[1841,5666,5668],{"className":5667},[1926],[1841,5669,5671,5700],{"className":5670},[1930,1931],[1841,5672,5674,5697],{"className":5673},[1935],[1841,5675,5677],{"className":5676,"style":2010},[1939],[1841,5678,5679,5682],{"style":1943},[1841,5680],{"className":5681,"style":1948},[1947],[1841,5683,5685],{"className":5684},[1952,1953,1954,1955],[1841,5686,5688,5691,5694],{"className":5687},[1913,1955],[1841,5689,1871],{"className":5690},[1913,1914,1955],[1841,5692,1886],{"className":5693},[2028,1955],[1841,5695,1890],{"className":5696},[1913,1955],[1841,5698,1963],{"className":5699},[1962],[1841,5701,5703],{"className":5702},[1935],[1841,5704,5706],{"className":5705,"style":2041},[1939],[1841,5707],{},[1841,5709,2110],{"className":5710},[2380],[1841,5712],{"className":5713,"style":2388},[1976],[1841,5715,5474],{"className":5716},[2287],[1841,5718],{"className":5719,"style":2388},[1976],[1841,5721,2110],{"className":5722},[2380],[1841,5724],{"className":5725,"style":2388},[1976],[1841,5727,5729,5732],{"className":5728},[1913],[1841,5730,1868],{"className":5731,"style":1922},[1913,1914],[1841,5733,5735],{"className":5734},[1926],[1841,5736,5738,5773],{"className":5737},[1930,1931],[1841,5739,5741,5770],{"className":5740},[1935],[1841,5742,5744],{"className":5743,"style":2010},[1939],[1841,5745,5746,5749],{"style":1943},[1841,5747],{"className":5748,"style":1948},[1947],[1841,5750,5752],{"className":5751},[1952,1953,1954,1955],[1841,5753,5755,5758,5761,5764,5767],{"className":5754},[1913,1955],[1841,5756,1871],{"className":5757},[1913,1914,1955],[1841,5759,1886],{"className":5760},[2028,1955],[1841,5762,1798],{"className":5763},[1913,1914,1955],[1841,5765,2129],{"className":5766},[2028,1955],[1841,5768,1890],{"className":5769},[1913,1955],[1841,5771,1963],{"className":5772},[1962],[1841,5774,5776],{"className":5775},[1935],[1841,5777,5779],{"className":5778,"style":2343},[1939],[1841,5780],{},[1841,5782,5784,5787],{"className":5783},[2187],[1841,5785,2073],{"className":5786},[2187],[1841,5788,5790],{"className":5789},[1926],[1841,5791,5793],{"className":5792},[1930],[1841,5794,5796],{"className":5795},[1935],[1841,5797,5800],{"className":5798,"style":5799},[1939],"height:0.8991em;",[1841,5801,5802,5805],{"style":2367},[1841,5803],{"className":5804,"style":1948},[1947],[1841,5806,5808],{"className":5807},[1952,1953,1954,1955],[1841,5809,5499],{"className":5810},[1913,1955],[1841,5812,2110],{"className":5813},[2380],[1841,5815],{"className":5816,"style":2384},[1976],[1841,5818],{"className":5819,"style":2388},[1976],[1841,5821,5823,5826],{"className":5822},[1913],[1841,5824,5443],{"className":5825},[1913,5559],[1841,5827,5829],{"className":5828},[1926],[1841,5830,5832,5852],{"className":5831},[1930,1931],[1841,5833,5835,5849],{"className":5834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the first row of ",[1841,5994,5996,6009],{"className":5995},[1844],[1841,5997,5999],{"className":5998},[1848],[1850,6000,6001],{"xmlns":1852},[1854,6002,6003,6007],{},[1857,6004,6005],{},[1860,6006,5514],{},[1892,6008,5514],{"encoding":1894},[1841,6010,6012],{"className":6011,"ariaHidden":1900},[1899],[1841,6013,6015,6019],{"className":6014},[1904],[1841,6016],{"className":6017,"style":6018},[1908],"height:0.6833em;",[1841,6020,5514],{"className":6021,"style":5878},[1913,1914]," is 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its first subdiagonal contains ones, and 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verify all three 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roots, companion eigenvalues, and Yule-Walker solve",[1798,7152,7153],{},"The polynomial roots are reciprocals of the companion eigenvalues. The Toeplitz solve returns the original coefficients because it uses population autocorrelations.",[1793,7155,7157],{"id":7156},"_4-ma-means-finite-shock-memory","4. 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\\rho(h)=0\\quad (|h|>1).",[1841,7467,7469,7496,7643,7677],{"className":7468,"ariaHidden":1900},[1899],[1841,7470,7472,7475,7478,7481,7484,7487,7490,7493],{"className":7471},[1904],[1841,7473],{"className":7474,"style":2173},[1908],[1841,7476,4346],{"className":7477},[1913,1914],[1841,7479,2068],{"className":7480},[2180],[1841,7482,1890],{"className":7483},[1913],[1841,7485,2073],{"className":7486},[2187],[1841,7488],{"className":7489,"style":1977},[1976],[1841,7491,1875],{"className":7492},[1981],[1841,7494],{"className":7495,"style":1977},[1976],[1841,7497,7499,7503,7613,7616,7619,7622,7625,7628,7631,7634,7637,7640],{"className":7498},[1904],[1841,7500],{"className":7501,"style":7502},[1908],"height:2.1408em;vertical-align:-0.7693em;",[1841,7504,7506,7510,7610],{"className":7505},[1913],[1841,7507],{"className":7508},[2180,7509],"nulldelimiter",[1841,7511,7513],{"className":7512},[7411],[1841,7514,7516,7601],{"className":7515},[1930,1931],[1841,7517,7519,7598],{"className":7518},[1935],[1841,7520,7523,7575,7586],{"className":7521,"style":7522},[1939],"height:1.3714em;",[1841,7524,7526,7529],{"style":7525},"top:-2.314em;",[1841,7527],{"className":7528,"style":6660},[1947],[1841,7530,7532,7535,7538,7541,7544],{"className":7531},[1913],[1841,7533,1890],{"className":7534},[1913],[1841,7536],{"className":7537,"style":2210},[1976],[1841,7539,2129],{"className":7540},[2028],[1841,7542],{"className":7543,"style":2210},[1976],[1841,7545,7547,7550],{"className":7546},[1913],[1841,7548,2116],{"className":7549,"style":2392},[1913,1914],[1841,7551,7553],{"className":7552},[1926],[1841,7554,7556],{"className":7555},[1930],[1841,7557,7559],{"className":7558},[1935],[1841,7560,7563],{"className":7561,"style":7562},[1939],"height:0.7401em;",[1841,7564,7566,7569],{"style":7565},"top:-2.989em;margin-right:0.05em;",[1841,7567],{"className":7568,"style":1948},[1947],[1841,7570,7572],{"className":7571},[1952,1953,1954,1955],[1841,7573,4319],{"className":7574},[1913,1955],[1841,7576,7578,7581],{"style":7577},"top:-3.23em;",[1841,7579],{"className":7580,"style":6660},[1947],[1841,7582],{"className":7583,"style":7585},[7584],"frac-line","border-bottom-width:0.04em;",[1841,7587,7589,7592],{"style":7588},"top:-3.677em;",[1841,7590],{"className":7591,"style":6660},[1947],[1841,7593,7595],{"className":7594},[1913],[1841,7596,2116],{"className":7597,"style":2392},[1913,1914],[1841,7599,1963],{"className":7600},[1962],[1841,7602,7604],{"className":7603},[1935],[1841,7605,7608],{"className":7606,"style":7607},[1939],"height:0.7693em;",[1841,7609],{},[1841,7611],{"className":7612},[2187,7509],[1841,7614,2110],{"className":7615},[2380],[1841,7617],{"className":7618,"style":2384},[1976],[1841,7620],{"className":7621,"style":2388},[1976],[1841,7623,4346],{"className":7624},[1913,1914],[1841,7626,2068],{"className":7627},[2180],[1841,7629,4351],{"className":7630},[1913,1914],[1841,7632,2073],{"className":7633},[2187],[1841,7635],{"className":7636,"style":1977},[1976],[1841,7638,1875],{"className":7639},[1981],[1841,7641],{"className":7642,"style":1977},[1976],[1841,7644,7646,7649,7652,7656,7659,7662,7665,7668,7671,7674],{"className":7645},[1904],[1841,7647],{"className":7648,"style":2173},[1908],[1841,7650,4800],{"className":7651},[1913],[1841,7653],{"className":7654,"style":7655},[1976],"margin-right:1em;",[1841,7657,2068],{"className":7658},[2180],[1841,7660,4215],{"className":7661},[1913],[1841,7663,4351],{"className":7664},[1913,1914],[1841,7666,4215],{"className":7667},[1913],[1841,7669],{"className":7670,"style":1977},[1976],[1841,7672,7456],{"className":7673},[1981],[1841,7675],{"className":7676,"style":1977},[1976],[1841,7678,7680,7683,7686,7689],{"className":7679},[1904],[1841,7681],{"className":7682,"style":2173},[1908],[1841,7684,1890],{"className":7685},[1913],[1841,7687,2073],{"className":7688},[2187],[1841,7690,2160],{"className":7691},[1913],[1798,7693,7694,7695,7747,7748,7815],{},"With ",[1841,7696,7698,7716],{"className":7697},[1844],[1841,7699,7701],{"className":7700},[1848],[1850,7702,7703],{"xmlns":1852},[1854,7704,7705,7713],{},[1857,7706,7707,7709,7711],{},[1860,7708,2116],{},[1873,7710,1875],{},[1888,7712,5210],{},[1892,7714,7715],{"encoding":1894},"\\theta=0.5",[1841,7717,7719,7738],{"className":7718,"ariaHidden":1900},[1899],[1841,7720,7722,7726,7729,7732,7735],{"className":7721},[1904],[1841,7723],{"className":7724,"style":7725},[1908],"height:0.6944em;",[1841,7727,2116],{"className":7728,"style":2392},[1913,1914],[1841,7730],{"className":7731,"style":1977},[1976],[1841,7733,1875],{"className":7734},[1981],[1841,7736],{"className":7737,"style":1977},[1976],[1841,7739,7741,7744],{"className":7740},[1904],[1841,7742],{"className":7743,"style":4261},[1908],[1841,7745,5210],{"className":7746},[1913],", ",[1841,7749,7751,7776],{"className":7750},[1844],[1841,7752,7754],{"className":7753},[1848],[1850,7755,7756],{"xmlns":1852},[1854,7757,7758,7773],{},[1857,7759,7760,7762,7764,7766,7768,7770],{},[1860,7761,4346],{},[1873,7763,2068],{"stretchy":2067},[1888,7765,1890],{},[1873,7767,2073],{"stretchy":2067},[1873,7769,1875],{},[1888,7771,7772],{},"0.4",[1892,7774,7775],{"encoding":1894},"\\rho(1)=0.4",[1841,7777,7779,7806],{"className":7778,"ariaHidden":1900},[1899],[1841,7780,7782,7785,7788,7791,7794,7797,7800,7803],{"className":7781},[1904],[1841,7783],{"className":7784,"style":2173},[1908],[1841,7786,4346],{"className":7787},[1913,1914],[1841,7789,2068],{"className":7790},[2180],[1841,7792,1890],{"className":7793},[1913],[1841,7795,2073],{"className":7796},[2187],[1841,7798],{"className":7799,"style":1977},[1976],[1841,7801,1875],{"className":7802},[1981],[1841,7804],{"className":7805,"style":1977},[1976],[1841,7807,7809,7812],{"className":7808},[1904],[1841,7810],{"className":7811,"style":4261},[1908],[1841,7813,7772],{"className":7814},[1913],". A shock affects two observations, so the theoretical ACF cuts off after lag 1.",[4851,7817,7819],{"id":7818},"why-invertibility-is-needed","Why invertibility is needed",[1798,7821,7822,7873,7874,7930],{},[1841,7823,7825,7843],{"className":7824},[1844],[1841,7826,7828],{"className":7827},[1848],[1850,7829,7830],{"xmlns":1852},[1854,7831,7832,7840],{},[1857,7833,7834,7836,7838],{},[1860,7835,2116],{},[1873,7837,1875],{},[1888,7839,4319],{},[1892,7841,7842],{"encoding":1894},"\\theta=2",[1841,7844,7846,7864],{"className":7845,"ariaHidden":1900},[1899],[1841,7847,7849,7852,7855,7858,7861],{"className":7848},[1904],[1841,7850],{"className":7851,"style":7725},[1908],[1841,7853,2116],{"className":7854,"style":2392},[1913,1914],[1841,7856],{"className":7857,"style":1977},[1976],[1841,7859,1875],{"className":7860},[1981],[1841,7862],{"className":7863,"style":1977},[1976],[1841,7865,7867,7870],{"className":7866},[1904],[1841,7868],{"className":7869,"style":4261},[1908],[1841,7871,4319],{"className":7872},[1913]," and 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because",[1841,7932,7934],{"className":7933},[2048],[1841,7935,7937,8002],{"className":7936},[1844],[1841,7938,7940],{"className":7939},[1848],[1850,7941,7942],{"xmlns":1852,"display":2057},[1854,7943,7944,7999],{},[1857,7945,7946,7962,7964,7994,7996],{},[7411,7947,7948,7950],{},[1888,7949,4319],{},[1857,7951,7952,7954,7956],{},[1888,7953,1890],{},[1873,7955,2129],{},[2102,7957,7958,7960],{},[1888,7959,4319],{},[1888,7961,4319],{},[1873,7963,1875],{},[7411,7965,7966,7974],{},[1857,7967,7968,7970,7972],{},[1888,7969,1890],{},[1860,7971,3893],{"mathvariant":2159},[1888,7973,4319],{},[1857,7975,7976,7978,7980,7982,7984,7986,7988],{},[1888,7977,1890],{},[1873,7979,2129],{},[1873,7981,2068],{"stretchy":2067},[1888,7983,1890],{},[1860,7985,3893],{"mathvariant":2159},[1888,7987,4319],{},[2102,7989,7990,7992],{},[1873,7991,2073],{"stretchy":2067},[1888,7993,4319],{},[1873,7995,1875],{},[1888,7997,7998],{},"0.4.",[1892,8000,8001],{"encoding":1894},"\\frac{2}{1+2^2}=\\frac{1\u002F2}{1+(1\u002F2)^2}=0.4.",[1841,8003,8005,8122,8246],{"className":8004,"ariaHidden":1900},[1899],[1841,8006,8008,8012,8113,8116,8119],{"className":8007},[1904],[1841,8009],{"className":8010,"style":8011},[1908],"height:2.0908em;vertical-align:-0.7693em;",[1841,8013,8015,8018,8110],{"className":8014},[1913],[1841,8016],{"className":8017},[2180,7509],[1841,8019,8021],{"className":8020},[7411],[1841,8022,8024,8102],{"className":8023},[1930,1931],[1841,8025,8027,8099],{"className":8026},[1935],[1841,8028,8031,8080,8088],{"className":8029,"style":8030},[1939],"height:1.3214em;",[1841,8032,8033,8036],{"style":7525},[1841,8034],{"className":8035,"style":6660},[1947],[1841,8037,8039,8042,8045,8048,8051],{"className":8038},[1913],[1841,8040,1890],{"className":8041},[1913],[1841,8043],{"className":8044,"style":2210},[1976],[1841,8046,2129],{"className":8047},[2028],[1841,8049],{"className":8050,"style":2210},[1976],[1841,8052,8054,8057],{"className":8053},[1913],[1841,8055,4319],{"className":8056},[1913],[1841,8058,8060],{"className":8059},[1926],[1841,8061,8063],{"className":8062},[1930],[1841,8064,8066],{"className":8065},[1935],[1841,8067,8069],{"className":8068,"style":7562},[1939],[1841,8070,8071,8074],{"style":7565},[1841,8072],{"className":8073,"style":1948},[1947],[1841,8075,8077],{"className":8076},[1952,1953,1954,1955],[1841,8078,4319],{"className":8079},[1913,1955],[1841,8081,8082,8085],{"style":7577},[1841,8083],{"className":8084,"style":6660},[1947],[1841,8086],{"className":8087,"style":7585},[7584],[1841,8089,8090,8093],{"style":7588},[1841,8091],{"className":8092,"style":6660},[1947],[1841,8094,8096],{"className":8095},[1913],[1841,8097,4319],{"className":8098},[1913],[1841,8100,1963],{"className":8101},[1962],[1841,8103,8105],{"className":8104},[1935],[1841,8106,8108],{"className":8107,"style":7607},[1939],[1841,8109],{},[1841,8111],{"className":8112},[2187,7509],[1841,8114],{"className":8115,"style":1977},[1976],[1841,8117,1875],{"className":8118},[1981],[1841,8120],{"className":8121,"style":1977},[1976],[1841,8123,8125,8129,8237,8240,8243],{"className":8124},[1904],[1841,8126],{"className":8127,"style":8128},[1908],"height:2.363em;vertical-align:-0.936em;",[1841,8130,8132,8135,8234],{"className":8131},[1913],[1841,8133],{"className":8134},[2180,7509],[1841,8136,8138],{"className":8137},[7411],[1841,8139,8141,8225],{"className":8140},[1930,1931],[1841,8142,8144,8222],{"className":8143},[1935],[1841,8145,8148,8203,8211],{"className":8146,"style":8147},[1939],"height:1.427em;",[1841,8149,8150,8153],{"style":7525},[1841,8151],{"className":8152,"style":6660},[1947],[1841,8154,8156,8159,8162,8165,8168,8171,8174],{"className":8155},[1913],[1841,8157,1890],{"className":8158},[1913],[1841,8160],{"className":8161,"style":2210},[1976],[1841,8163,2129],{"className":8164},[2028],[1841,8166],{"className":8167,"style":2210},[1976],[1841,8169,2068],{"className":8170},[2180],[1841,8172,7929],{"className":8173},[1913],[1841,8175,8177,8180],{"className":8176},[2187],[1841,8178,2073],{"className":8179},[2187],[1841,8181,8183],{"className":8182},[1926],[1841,8184,8186],{"className":8185},[1930],[1841,8187,8189],{"className":8188},[1935],[1841,8190,8192],{"className":8191,"style":7562},[1939],[1841,8193,8194,8197],{"style":7565},[1841,8195],{"className":8196,"style":1948},[1947],[1841,8198,8200],{"className":8199},[1952,1953,1954,1955],[1841,8201,4319],{"className":8202},[1913,1955],[1841,8204,8205,8208],{"style":7577},[1841,8206],{"className":8207,"style":6660},[1947],[1841,8209],{"className":8210,"style":7585},[7584],[1841,8212,8213,8216],{"style":7588},[1841,8214],{"className":8215,"style":6660},[1947],[1841,8217,8219],{"className":8218},[1913],[1841,8220,7929],{"className":8221},[1913],[1841,8223,1963],{"className":8224},[1962],[1841,8226,8228],{"className":8227},[1935],[1841,8229,8232],{"className":8230,"style":8231},[1939],"height:0.936em;",[1841,8233],{},[1841,8235],{"className":8236},[2187,7509],[1841,8238],{"className":8239,"style":1977},[1976],[1841,8241,1875],{"className":8242},[1981],[1841,8244],{"className":8245,"style":1977},[1976],[1841,8247,8249,8252],{"className":8248},[1904],[1841,8250],{"className":8251,"style":4261},[1908],[1841,8253,7998],{"className":8254},[1913],[1798,8256,8257,8258,8319],{},"Invertibility selects the representation whose MA roots lie outside the unit circle—here ",[1841,8259,8261,8283],{"className":8260},[1844],[1841,8262,8264],{"className":8263},[1848],[1850,8265,8266],{"xmlns":1852},[1854,8267,8268,8280],{},[1857,8269,8270,8272,8274,8276,8278],{},[1860,8271,4215],{"mathvariant":2159},[1860,8273,2116],{},[1860,8275,4215],{"mathvariant":2159},[1873,8277,4222],{},[1888,8279,1890],{},[1892,8281,8282],{"encoding":1894},"|\\theta|\u003C1",[1841,8284,8286,8310],{"className":8285,"ariaHidden":1900},[1899],[1841,8287,8289,8292,8295,8298,8301,8304,8307],{"className":8288},[1904],[1841,8290],{"className":8291,"style":2173},[1908],[1841,8293,4215],{"className":8294},[1913],[1841,8296,2116],{"className":8297,"style":2392},[1913,1914],[1841,8299,4215],{"className":8300},[1913],[1841,8302],{"className":8303,"style":1977},[1976],[1841,8305,4222],{"className":8306},[1981],[1841,8308],{"className":8309,"style":1977},[1976],[1841,8311,8313,8316],{"className":8312},[1904],[1841,8314],{"className":8315,"style":4261},[1908],[1841,8317,1890],{"className":8318},[1913]," under this sign convention—so innovations are recoverable from current and past observations and parameters are identified.",[1793,8321,8323],{"id":8322},"_5-acf-and-pacf-are-signatures-not-verdicts","5. ACF and PACF are signatures, not verdicts",[2591,8325,8326,8436],{},[2594,8327,8328],{},[2597,8329,8330,8333,8363,8393],{},[2600,8331,8332],{},"Population pattern",[2600,8334,2617,8335,2073],{},[1841,8336,8338,8351],{"className":8337},[1844],[1841,8339,8341],{"className":8340},[1848],[1850,8342,8343],{"xmlns":1852},[1854,8344,8345,8349],{},[1857,8346,8347],{},[1860,8348,1798],{},[1892,8350,1798],{"encoding":1894},[1841,8352,8354],{"className":8353,"ariaHidden":1900},[1899],[1841,8355,8357,8360],{"className":8356},[1904],[1841,8358],{"className":8359,"style":2643},[1908],[1841,8361,1798],{"className":8362},[1913,1914],[2600,8364,2844,8365,2073],{},[1841,8366,8368,8381],{"className":8367},[1844],[1841,8369,8371],{"className":8370},[1848],[1850,8372,8373],{"xmlns":1852},[1854,8374,8375,8379],{},[1857,8376,8377],{},[1860,8378,2150],{},[1892,8380,2150],{"encoding":1894},[1841,8382,8384],{"className":8383,"ariaHidden":1900},[1899],[1841,8385,8387,8390],{"className":8386},[1904],[1841,8388],{"className":8389,"style":2643},[1908],[1841,8391,2150],{"className":8392,"style":2543},[1913,1914],[2600,8394,3057,8395,2073],{},[1841,8396,8398,8415],{"className":8397},[1844],[1841,8399,8401],{"className":8400},[1848],[1850,8402,8403],{"xmlns":1852},[1854,8404,8405,8413],{},[1857,8406,8407,8409,8411],{},[1860,8408,1798],{},[1873,8410,2110],{"separator":1900},[1860,8412,2150],{},[1892,8414,3078],{"encoding":1894},[1841,8416,8418],{"className":8417,"ariaHidden":1900},[1899],[1841,8419,8421,8424,8427,8430,8433],{"className":8420},[1904],[1841,8422],{"className":8423,"style":2643},[1908],[1841,8425,1798],{"className":8426},[1913,1914],[1841,8428,2110],{"className":8429},[2380],[1841,8431],{"className":8432,"style":2388},[1976],[1841,8434,2150],{"className":8435,"style":2543},[1913,1914],[2610,8437,8438,8479],{},[2597,8439,8440,8443,8446,8477],{},[2615,8441,8442],{},"ACF",[2615,8444,8445],{},"tails off",[2615,8447,8448,8449],{},"cuts off after ",[1841,8450,8452,8465],{"className":8451},[1844],[1841,8453,8455],{"className":8454},[1848],[1850,8456,8457],{"xmlns":1852},[1854,8458,8459,8463],{},[1857,8460,8461],{},[1860,8462,2150],{},[1892,8464,2150],{"encoding":1894},[1841,8466,8468],{"className":8467,"ariaHidden":1900},[1899],[1841,8469,8471,8474],{"className":8470},[1904],[1841,8472],{"className":8473,"style":2643},[1908],[1841,8475,2150],{"className":8476,"style":2543},[1913,1914],[2615,8478,8445],{},[2597,8480,8481,8484,8514,8516],{},[2615,8482,8483],{},"PACF",[2615,8485,8448,8486],{},[1841,8487,8489,8502],{"className":8488},[1844],[1841,8490,8492],{"className":8491},[1848],[1850,8493,8494],{"xmlns":1852},[1854,8495,8496,8500],{},[1857,8497,8498],{},[1860,8499,1798],{},[1892,8501,1798],{"encoding":1894},[1841,8503,8505],{"className":8504,"ariaHidden":1900},[1899],[1841,8506,8508,8511],{"className":8507},[1904],[1841,8509],{"className":8510,"style":2643},[1908],[1841,8512,1798],{"className":8513},[1913,1914],[2615,8515,8445],{},[2615,8517,8445],{},[1798,8519,8520,8521,8614],{},"“Cuts off” is a population result. A sample ACF has noise of roughly order ",[1841,8522,8524,8546],{"className":8523},[1844],[1841,8525,8527],{"className":8526},[1848],[1850,8528,8529],{"xmlns":1852},[1854,8530,8531,8543],{},[1857,8532,8533,8535,8537],{},[1888,8534,1890],{},[1860,8536,3893],{"mathvariant":2159},[8538,8539,8540],"msqrt",{},[1860,8541,8542],{},"n",[1892,8544,8545],{"encoding":1894},"1\u002F\\sqrt n",[1841,8547,8549],{"className":8548,"ariaHidden":1900},[1899],[1841,8550,8552,8556,8560],{"className":8551},[1904],[1841,8553],{"className":8554,"style":8555},[1908],"height:1.0503em;vertical-align:-0.25em;",[1841,8557,8559],{"className":8558},[1913],"1\u002F",[1841,8561,8564],{"className":8562},[1913,8563],"sqrt",[1841,8565,8567,8605],{"className":8566},[1930,1931],[1841,8568,8570,8602],{"className":8569},[1935],[1841,8571,8574,8584],{"className":8572,"style":8573},[1939],"height:0.8003em;",[1841,8575,8577,8580],{"className":8576,"style":6715},[6734],[1841,8578],{"className":8579,"style":6660},[1947],[1841,8581,8542],{"className":8582,"style":8583},[1913,1914],"padding-left:0.833em;",[1841,8585,8587,8590],{"style":8586},"top:-2.7603em;",[1841,8588],{"className":8589,"style":6660},[1947],[1841,8591,8595],{"className":8592,"style":8594},[8593],"hide-tail","min-width:0.853em;height:1.08em;",[6750,8596,8599],{"xmlns":6752,"width":6753,"height":8597,"viewBox":8598,"preserveAspectRatio":6756},"1.08em","0 0 400000 1080",[6758,8600],{"d":8601},"M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 80h400000v40h-400000z",[1841,8603,1963],{"className":8604},[1962],[1841,8606,8608],{"className":8607},[1935],[1841,8609,8612],{"className":8610,"style":8611},[1939],"height:0.2397em;",[1841,8613],{}," under simple white-noise conditions, and inspecting many lags creates multiple-comparison ambiguity. Use ACF\u002FPACF to propose a small candidate set, then estimate, diagnose, and backtest it.",[1793,8616,8618],{"id":8617},"_6-differencing-changes-the-model","6. Differencing changes the model",[1798,8620,8621],{},"First and seasonal differences are",[1841,8623,8625],{"className":8624},[2048],[1841,8626,8628,8707],{"className":8627},[1844],[1841,8629,8631],{"className":8630},[1848],[1850,8632,8633],{"xmlns":1852,"display":2057},[1854,8634,8635,8704],{},[1857,8636,8637,8640,8646,8648,8650,8652,8654,8656,8658,8664,8666,8668,8674,8680,8682,8684,8686,8688,8694,8696,8702],{},[1860,8638,8639],{"mathvariant":2159},"Δ",[1864,8641,8642,8644],{},[1860,8643,1868],{},[1860,8645,1871],{},[1873,8647,1875],{},[1873,8649,2068],{"stretchy":2067},[1888,8651,1890],{},[1873,8653,1886],{},[1860,8655,1862],{},[1873,8657,2073],{"stretchy":2067},[1864,8659,8660,8662],{},[1860,8661,1868],{},[1860,8663,1871],{},[1873,8665,2110],{"separator":1900},[1976,8667],{"width":2113},[1864,8669,8670,8672],{},[1860,8671,8639],{"mathvariant":2159},[1860,8673,5443],{},[1864,8675,8676,8678],{},[1860,8677,1868],{},[1860,8679,1871],{},[1873,8681,1875],{},[1873,8683,2068],{"stretchy":2067},[1888,8685,1890],{},[1873,8687,1886],{},[2102,8689,8690,8692],{},[1860,8691,1862],{},[1860,8693,5443],{},[1873,8695,2073],{"stretchy":2067},[1864,8697,8698,8700],{},[1860,8699,1868],{},[1860,8701,1871],{},[1860,8703,2160],{"mathvariant":2159},[1892,8705,8706],{"encoding":1894},"\\Delta X_t=(1-B)X_t,\n\\qquad\n\\Delta_sX_t=(1-B^s)X_t.",[1841,8708,8710,8768,8789,8939,8960],{"className":8709,"ariaHidden":1900},[1899],[1841,8711,8713,8716,8719,8759,8762,8765],{"className":8712},[1904],[1841,8714],{"className":8715,"style":1909},[1908],[1841,8717,8639],{"className":8718},[1913],[1841,8720,8722,8725],{"className":8721},[1913],[1841,8723,1868],{"className":8724,"style":1922},[1913,1914],[1841,8726,8728],{"className":8727},[1926],[1841,8729,8731,8751],{"className":8730},[1930,1931],[1841,8732,8734,8748],{"className":8733},[1935],[1841,8735,8737],{"className":8736,"style":1940},[1939],[1841,8738,8739,8742],{"style":1943},[1841,8740],{"className":8741,"style":1948},[1947],[1841,8743,8745],{"className":8744},[1952,1953,1954,1955],[1841,8746,1871],{"className":8747},[1913,1914,1955],[1841,8749,1963],{"className":8750},[1962],[1841,8752,8754],{"className":8753},[1935],[1841,8755,8757],{"className":8756,"style":1970},[1939],[1841,8758],{},[1841,8760],{"className":8761,"style":1977},[1976],[1841,8763,1875],{"className":8764},[1981],[1841,8766],{"className":8767,"style":1977},[1976],[1841,8769,8771,8774,8777,8780,8783,8786],{"className":8770},[1904],[1841,8772],{"className":8773,"style":2173},[1908],[1841,8775,2068],{"className":8776},[2180],[1841,8778,1890],{"className":8779},[1913],[1841,8781],{"className":8782,"style":2210},[1976],[1841,8784,1886],{"className":8785},[2028],[1841,8787],{"className":8788,"style":2210},[1976],[1841,8790,8792,8795,8798,8801,8841,8844,8847,8850,8890,8930,8933,8936],{"className":8791},[1904],[1841,8793],{"className":8794,"style":2173},[1908],[1841,8796,1862],{"className":8797,"style":1915},[1913,1914],[1841,8799,2073],{"className":8800},[2187],[1841,8802,8804,8807],{"className":8803},[1913],[1841,8805,1868],{"className":8806,"style":1922},[1913,1914],[1841,8808,8810],{"className":8809},[1926],[1841,8811,8813,8833],{"className":8812},[1930,1931],[1841,8814,8816,8830],{"className":8815},[1935],[1841,8817,8819],{"className":8818,"style":1940},[1939],[1841,8820,8821,8824],{"style":1943},[1841,8822],{"className":8823,"style":1948},[1947],[1841,8825,8827],{"className":8826},[1952,1953,1954,1955],[1841,8828,1871],{"className":8829},[1913,1914,1955],[1841,8831,1963],{"className":8832},[1962],[1841,8834,8836],{"className":8835},[1935],[1841,8837,8839],{"className":8838,"style":1970},[1939],[1841,8840],{},[1841,8842,2110],{"className":8843},[2380],[1841,8845],{"className":8846,"style":2384},[1976],[1841,8848],{"className":8849,"style":2388},[1976],[1841,8851,8853,8856],{"className":8852},[1913],[1841,8854,8639],{"className":8855},[1913],[1841,8857,8859],{"className":8858},[1926],[1841,8860,8862,8882],{"className":8861},[1930,1931],[1841,8863,8865,8879],{"className":8864},[1935],[1841,8866,8868],{"className":8867,"style":2322},[1939],[1841,8869,8870,8873],{"style":2244},[1841,8871],{"className":8872,"style":1948},[1947],[1841,8874,8876],{"className":8875},[1952,1953,1954,1955],[1841,8877,5443],{"className":8878},[1913,1914,1955],[1841,8880,1963],{"className":8881},[1962],[1841,8883,8885],{"className":8884},[1935],[1841,8886,8888],{"className":8887,"style":1970},[1939],[1841,8889],{},[1841,8891,8893,8896],{"className":8892},[1913],[1841,8894,1868],{"className":8895,"style":1922},[1913,1914],[1841,8897,8899],{"className":8898},[1926],[1841,8900,8902,8922],{"className":8901},[1930,1931],[1841,8903,8905,8919],{"className":8904},[1935],[1841,8906,8908],{"className":8907,"style":1940},[1939],[1841,8909,8910,8913],{"style":1943},[1841,8911],{"className":8912,"style":1948},[1947],[1841,8914,8916],{"className":8915},[1952,1953,1954,1955],[1841,8917,1871],{"className":8918},[1913,1914,1955],[1841,8920,1963],{"className":8921},[1962],[1841,8923,8925],{"className":8924},[1935],[1841,8926,8928],{"className":8927,"style":1970},[1939],[1841,8929],{},[1841,8931],{"className":8932,"style":1977},[1976],[1841,8934,1875],{"className":8935},[1981],[1841,8937],{"className":8938,"style":1977},[1976],[1841,8940,8942,8945,8948,8951,8954,8957],{"className":8941},[1904],[1841,8943],{"className":8944,"style":2173},[1908],[1841,8946,2068],{"className":8947},[2180],[1841,8949,1890],{"className":8950},[1913],[1841,8952],{"className":8953,"style":2210},[1976],[1841,8955,1886],{"className":8956},[2028],[1841,8958],{"className":8959,"style":2210},[1976],[1841,8961,8963,8966,8995,8998,9038],{"className":8962},[1904],[1841,8964],{"className":8965,"style":2173},[1908],[1841,8967,8969,8972],{"className":8968},[1913],[1841,8970,1862],{"className":8971,"style":1915},[1913,1914],[1841,8973,8975],{"className":8974},[1926],[1841,8976,8978],{"className":8977},[1930],[1841,8979,8981],{"className":8980},[1935],[1841,8982,8984],{"className":8983,"style":2364},[1939],[1841,8985,8986,8989],{"style":2367},[1841,8987],{"className":8988,"style":1948},[1947],[1841,8990,8992],{"className":8991},[1952,1953,1954,1955],[1841,8993,5443],{"className":8994},[1913,1914,1955],[1841,8996,2073],{"className":8997},[2187],[1841,8999,9001,9004],{"className":9000},[1913],[1841,9002,1868],{"className":9003,"style":1922},[1913,1914],[1841,9005,9007],{"className":9006},[1926],[1841,9008,9010,9030],{"className":9009},[1930,1931],[1841,9011,9013,9027],{"className":9012},[1935],[1841,9014,9016],{"className":9015,"style":1940},[1939],[1841,9017,9018,9021],{"style":1943},[1841,9019],{"className":9020,"style":1948},[1947],[1841,9022,9024],{"className":9023},[1952,1953,1954,1955],[1841,9025,1871],{"className":9026},[1913,1914,1955],[1841,9028,1963],{"className":9029},[1962],[1841,9031,9033],{"className":9032},[1935],[1841,9034,9036],{"className":9035,"style":1970},[1939],[1841,9037],{},[1841,9039,2160],{"className":9040},[1913],[2591,9042,9043,9056],{},[2594,9044,9045],{},[2597,9046,9047,9050,9053],{},[2600,9048,9049],{},"Symptom",[2600,9051,9052],{},"Candidate operation",[2600,9054,9055],{},"Boundary",[2610,9057,9058,9143,9273],{},[2597,9059,9060,9063,9140],{},[2615,9061,9062],{},"stochastic level drift",[2615,9064,9065],{},[1841,9066,9068,9088],{"className":9067},[1844],[1841,9069,9071],{"className":9070},[1848],[1850,9072,9073],{"xmlns":1852},[1854,9074,9075,9085],{},[1857,9076,9077,9079],{},[1860,9078,8639],{"mathvariant":2159},[1864,9080,9081,9083],{},[1860,9082,1868],{},[1860,9084,1871],{},[1892,9086,9087],{"encoding":1894},"\\Delta X_t",[1841,9089,9091],{"className":9090,"ariaHidden":1900},[1899],[1841,9092,9094,9097,9100],{"className":9093},[1904],[1841,9095],{"className":9096,"style":1909},[1908],[1841,9098,8639],{"className":9099},[1913],[1841,9101,9103,9106],{"className":9102},[1913],[1841,9104,1868],{"className":9105,"style":1922},[1913,1914],[1841,9107,9109],{"className":9108},[1926],[1841,9110,9112,9132],{"className":9111},[1930,1931],[1841,9113,9115,9129],{"className":9114},[1935],[1841,9116,9118],{"className":9117,"style":1940},[1939],[1841,9119,9120,9123],{"style":1943},[1841,9121],{"className":9122,"style":1948},[1947],[1841,9124,9126],{"className":9125},[1952,1953,1954,1955],[1841,9127,1871],{"className":9128},[1913,1914,1955],[1841,9130,1963],{"className":9131},[1962],[1841,9133,9135],{"className":9134},[1935],[1841,9136,9138],{"className":9137,"style":1970},[1939],[1841,9139],{},[2615,9141,9142],{},"do not use merely because a deterministic trend exists",[2597,9144,9145,9148,9270],{},[2615,9146,9147],{},"stochastic annual drift in monthly data",[2615,9149,9150],{},[1841,9151,9153,9178],{"className":9152},[1844],[1841,9154,9156],{"className":9155},[1848],[1850,9157,9158],{"xmlns":1852},[1854,9159,9160,9175],{},[1857,9161,9162,9169],{},[1864,9163,9164,9166],{},[1860,9165,8639],{"mathvariant":2159},[1888,9167,9168],{},"12",[1864,9170,9171,9173],{},[1860,9172,1868],{},[1860,9174,1871],{},[1892,9176,9177],{"encoding":1894},"\\Delta_{12}X_t",[1841,9179,9181],{"className":9180,"ariaHidden":1900},[1899],[1841,9182,9184,9187,9230],{"className":9183},[1904],[1841,9185],{"className":9186,"style":1909},[1908],[1841,9188,9190,9193],{"className":9189},[1913],[1841,9191,8639],{"className":9192},[1913],[1841,9194,9196],{"className":9195},[1926],[1841,9197,9199,9222],{"className":9198},[1930,1931],[1841,9200,9202,9219],{"className":9201},[1935],[1841,9203,9205],{"className":9204,"style":2010},[1939],[1841,9206,9207,9210],{"style":2244},[1841,9208],{"className":9209,"style":1948},[1947],[1841,9211,9213],{"className":9212},[1952,1953,1954,1955],[1841,9214,9216],{"className":9215},[1913,1955],[1841,9217,9168],{"className":9218},[1913,1955],[1841,9220,1963],{"className":9221},[1962],[1841,9223,9225],{"className":9224},[1935],[1841,9226,9228],{"className":9227,"style":1970},[1939],[1841,9229],{},[1841,9231,9233,9236],{"className":9232},[1913],[1841,9234,1868],{"className":9235,"style":1922},[1913,1914],[1841,9237,9239],{"className":9238},[1926],[1841,9240,9242,9262],{"className":9241},[1930,1931],[1841,9243,9245,9259],{"className":9244},[1935],[1841,9246,9248],{"className":9247,"style":1940},[1939],[1841,9249,9250,9253],{"style":1943},[1841,9251],{"className":9252,"style":1948},[1947],[1841,9254,9256],{"className":9255},[1952,1953,1954,1955],[1841,9257,1871],{"className":9258},[1913,1914,1955],[1841,9260,1963],{"className":9261},[1962],[1841,9263,9265],{"className":9264},[1935],[1841,9266,9268],{"className":9267,"style":1970},[1939],[1841,9269],{},[2615,9271,9272],{},"month indicators may suit stable seasonal means better",[2597,9274,9275,9278,9366],{},[2615,9276,9277],{},"variance proportional to level",[2615,9279,9280],{},[1841,9281,9283,9306],{"className":9282},[1844],[1841,9284,9286],{"className":9285},[1848],[1850,9287,9288],{"xmlns":1852},[1854,9289,9290,9303],{},[1857,9291,9292,9295,9297],{},[1860,9293,9294],{},"log",[1873,9296,6533],{},[1864,9298,9299,9301],{},[1860,9300,1868],{},[1860,9302,1871],{},[1892,9304,9305],{"encoding":1894},"\\log X_t",[1841,9307,9309],{"className":9308,"ariaHidden":1900},[1899],[1841,9310,9312,9315,9323,9326],{"className":9311},[1904],[1841,9313],{"className":9314,"style":2223},[1908],[1841,9316,9318,9319],{"className":9317},[6792],"lo",[1841,9320,9322],{"style":9321},"margin-right:0.0139em;","g",[1841,9324],{"className":9325,"style":2388},[1976],[1841,9327,9329,9332],{"className":9328},[1913],[1841,9330,1868],{"className":9331,"style":1922},[1913,1914],[1841,9333,9335],{"className":9334},[1926],[1841,9336,9338,9358],{"className":9337},[1930,1931],[1841,9339,9341,9355],{"className":9340},[1935],[1841,9342,9344],{"className":9343,"style":1940},[1939],[1841,9345,9346,9349],{"style":1943},[1841,9347],{"className":9348,"style":1948},[1947],[1841,9350,9352],{"className":9351},[1952,1953,1954,1955],[1841,9353,1871],{"className":9354},[1913,1914,1955],[1841,9356,1963],{"className":9357},[1962],[1841,9359,9361],{"className":9360},[1935],[1841,9362,9364],{"className":9363,"style":1970},[1939],[1841,9365],{},[2615,9367,9368],{},"requires positive data and changes interpretation to relative change",[1798,9370,9371,9372,9589,9590,9661],{},"Over-differencing stationary white noise gives ",[1841,9373,9375,9417],{"className":9374},[1844],[1841,9376,9378],{"className":9377},[1848],[1850,9379,9380],{"xmlns":1852},[1854,9381,9382,9414],{},[1857,9383,9384,9386,9392,9394,9400,9402],{},[1860,9385,8639],{"mathvariant":2159},[1864,9387,9388,9390],{},[1860,9389,1868],{},[1860,9391,1871],{},[1873,9393,1875],{},[1864,9395,9396,9398],{},[1860,9397,2690],{},[1860,9399,1871],{},[1873,9401,1886],{},[1864,9403,9404,9406],{},[1860,9405,2690],{},[1857,9407,9408,9410,9412],{},[1860,9409,1871],{},[1873,9411,1886],{},[1888,9413,1890],{},[1892,9415,9416],{"encoding":1894},"\\Delta X_t=\\varepsilon_t-\\varepsilon_{t-1}",[1841,9418,9420,9478,9533],{"className":9419,"ariaHidden":1900},[1899],[1841,9421,9423,9426,9429,9469,9472,9475],{"className":9422},[1904],[1841,9424],{"className":9425,"style":1909},[1908],[1841,9427,8639],{"className":9428},[1913],[1841,9430,9432,9435],{"className":9431},[1913],[1841,9433,1868],{"className":9434,"style":1922},[1913,1914],[1841,9436,9438],{"className":9437},[1926],[1841,9439,9441,9461],{"className":9440},[1930,1931],[1841,9442,9444,9458],{"className":9443},[1935],[1841,9445,9447],{"className":9446,"style":1940},[1939],[1841,9448,9449,9452],{"style":1943},[1841,9450],{"className":9451,"style":1948},[1947],[1841,9453,9455],{"className":9454},[1952,1953,1954,1955],[1841,9456,1871],{"className":9457},[1913,1914,1955],[1841,9459,1963],{"className":9460},[1962],[1841,9462,9464],{"className":9463},[1935],[1841,9465,9467],{"className":9466,"style":1970},[1939],[1841,9468],{},[1841,9470],{"className":9471,"style":1977},[1976],[1841,9473,1875],{"className":9474},[1981],[1841,9476],{"className":9477,"style":1977},[1976],[1841,9479,9481,9484,9524,9527,9530],{"className":9480},[1904],[1841,9482],{"className":9483,"style":4437},[1908],[1841,9485,9487,9490],{"className":9486},[1913],[1841,9488,2690],{"className":9489},[1913,1914],[1841,9491,9493],{"className":9492},[1926],[1841,9494,9496,9516],{"className":9495},[1930,1931],[1841,9497,9499,9513],{"className":9498},[1935],[1841,9500,9502],{"className":9501,"style":1940},[1939],[1841,9503,9504,9507],{"style":2244},[1841,9505],{"className":9506,"style":1948},[1947],[1841,9508,9510],{"className":9509},[1952,1953,1954,1955],[1841,9511,1871],{"className":9512},[1913,1914,1955],[1841,9514,1963],{"className":9515},[1962],[1841,9517,9519],{"className":9518},[1935],[1841,9520,9522],{"className":9521,"style":1970},[1939],[1841,9523],{},[1841,9525],{"className":9526,"style":2210},[1976],[1841,9528,1886],{"className":9529},[2028],[1841,9531],{"className":9532,"style":2210},[1976],[1841,9534,9536,9540],{"className":9535},[1904],[1841,9537],{"className":9538,"style":9539},[1908],"height:0.6389em;vertical-align:-0.2083em;",[1841,9541,9543,9546],{"className":9542},[1913],[1841,9544,2690],{"className":9545},[1913,1914],[1841,9547,9549],{"className":9548},[1926],[1841,9550,9552,9581],{"className":9551},[1930,1931],[1841,9553,9555,9578],{"className":9554},[1935],[1841,9556,9558],{"className":9557,"style":2010},[1939],[1841,9559,9560,9563],{"style":2244},[1841,9561],{"className":9562,"style":1948},[1947],[1841,9564,9566],{"className":9565},[1952,1953,1954,1955],[1841,9567,9569,9572,9575],{"className":9568},[1913,1955],[1841,9570,1871],{"className":9571},[1913,1914,1955],[1841,9573,1886],{"className":9574},[2028,1955],[1841,9576,1890],{"className":9577},[1913,1955],[1841,9579,1963],{"className":9580},[1962],[1841,9582,9584],{"className":9583},[1935],[1841,9585,9587],{"className":9586,"style":2041},[1939],[1841,9588],{},", an MA(1) boundary case with ",[1841,9591,9593,9619],{"className":9592},[1844],[1841,9594,9596],{"className":9595},[1848],[1850,9597,9598],{"xmlns":1852},[1854,9599,9600,9616],{},[1857,9601,9602,9604,9606,9608,9610,9612,9614],{},[1860,9603,4346],{},[1873,9605,2068],{"stretchy":2067},[1888,9607,1890],{},[1873,9609,2073],{"stretchy":2067},[1873,9611,1875],{},[1873,9613,1886],{},[1888,9615,5210],{},[1892,9617,9618],{"encoding":1894},"\\rho(1)=-0.5",[1841,9620,9622,9649],{"className":9621,"ariaHidden":1900},[1899],[1841,9623,9625,9628,9631,9634,9637,9640,9643,9646],{"className":9624},[1904],[1841,9626],{"className":9627,"style":2173},[1908],[1841,9629,4346],{"className":9630},[1913,1914],[1841,9632,2068],{"className":9633},[2180],[1841,9635,1890],{"className":9636},[1913],[1841,9638,2073],{"className":9639},[2187],[1841,9641],{"className":9642,"style":1977},[1976],[1841,9644,1875],{"className":9645},[1981],[1841,9647],{"className":9648,"style":1977},[1976],[1841,9650,9652,9655,9658],{"className":9651},[1904],[1841,9653],{"className":9654,"style":2203},[1908],[1841,9656,1886],{"className":9657},[1913],[1841,9659,5210],{"className":9660},[1913],". A strong negative lag-1 ACF after transformation is a warning.",[1793,9663,9665],{"id":9664},"_7-see-the-signatures-then-disturb-them","7. See the signatures, then disturb them",[1798,9667,9668,9669,7747,9673,9676,9677,9679],{},"Edit ",[9670,9671,9672],"code",{},"phi",[9670,9674,9675],{},"theta",", and ",[9670,9678,8542],{},". Small samples show why clean textbook cutoffs often look ambiguous.",[7146,9681],{"code64":9682,"layout":7149,"locale":7,"title":9683},"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","AR(1) and MA(1): sample ACF\u002FPACF versus theory",[1793,9685,9687],{"id":9686},"_8-identification-workflow","8. Identification workflow",[9689,9690,9691,9694,9697,9700,9703,9706,9709,9712],"ol",{},[1812,9692,9693],{},"Define target, frequency, origin, and horizon.",[1812,9695,9696],{},"Plot levels; mark trend, seasonality, breaks, and missing values.",[1812,9698,9699],{},"Choose transformations for stated reasons.",[1812,9701,9702],{},"Inspect ACF\u002FPACF and propose at most a few parsimonious orders.",[1812,9704,9705],{},"Check estimated roots and near-cancellation between AR and MA factors.",[1812,9707,9708],{},"Audit residual dependence and parameter stability.",[1812,9710,9711],{},"Compare against naive and seasonal-naive forecasts on rolling origins.",[1812,9713,9714],{},"Prefer the smallest model whose remaining errors are not predictably useful.",[9716,9717,9719],"warning",{"title":9718},"Near cancellation","An ARMA model with nearly identical AR and MA factors can mimic a simpler process while producing unstable estimates. A high-order fit is not evidence of rich dynamics when factors almost cancel.",[1793,9721,9723],{"id":9722},"practice","Practice",[9689,9725,9726,10037,10140,10259,10262],{},[1812,9727,9728,9729,9946,9947,9991,9992,2160],{},"For ",[1841,9730,9732,9775],{"className":9731},[1844],[1841,9733,9735],{"className":9734},[1848],[1850,9736,9737],{"xmlns":1852},[1854,9738,9739,9772],{},[1857,9740,9741,9747,9749,9752,9764,9766],{},[1864,9742,9743,9745],{},[1860,9744,1868],{},[1860,9746,1871],{},[1873,9748,1875],{},[1888,9750,9751],{},"0.6",[1864,9753,9754,9756],{},[1860,9755,1868],{},[1857,9757,9758,9760,9762],{},[1860,9759,1871],{},[1873,9761,1886],{},[1888,9763,1890],{},[1873,9765,2129],{},[1864,9767,9768,9770],{},[1860,9769,2690],{},[1860,9771,1871],{},[1892,9773,9774],{"encoding":1894},"X_t=0.6X_{t-1}+\\varepsilon_t",[1841,9776,9778,9833,9900],{"className":9777,"ariaHidden":1900},[1899],[1841,9779,9781,9784,9824,9827,9830],{"className":9780},[1904],[1841,9782],{"className":9783,"style":1909},[1908],[1841,9785,9787,9790],{"className":9786},[1913],[1841,9788,1868],{"className":9789,"style":1922},[1913,1914],[1841,9791,9793],{"className":9792},[1926],[1841,9794,9796,9816],{"className":9795},[1930,1931],[1841,9797,9799,9813],{"className":9798},[1935],[1841,9800,9802],{"className":9801,"style":1940},[1939],[1841,9803,9804,9807],{"style":1943},[1841,9805],{"className":9806,"style":1948},[1947],[1841,9808,9810],{"className":9809},[1952,1953,1954,1955],[1841,9811,1871],{"className":9812},[1913,1914,1955],[1841,9814,1963],{"className":9815},[1962],[1841,9817,9819],{"className":9818},[1935],[1841,9820,9822],{"className":9821,"style":1970},[1939],[1841,9823],{},[1841,9825],{"className":9826,"style":1977},[1976],[1841,9828,1875],{"className":9829},[1981],[1841,9831],{"className":9832,"style":1977},[1976],[1841,9834,9836,9839,9842,9891,9894,9897],{"className":9835},[1904],[1841,9837],{"className":9838,"style":1991},[1908],[1841,9840,9751],{"className":9841},[1913],[1841,9843,9845,9848],{"className":9844},[1913],[1841,9846,1868],{"className":9847,"style":1922},[1913,1914],[1841,9849,9851],{"className":9850},[1926],[1841,9852,9854,9883],{"className":9853},[1930,1931],[1841,9855,9857,9880],{"className":9856},[1935],[1841,9858,9860],{"className":9859,"style":2010},[1939],[1841,9861,9862,9865],{"style":1943},[1841,9863],{"className":9864,"style":1948},[1947],[1841,9866,9868],{"className":9867},[1952,1953,1954,1955],[1841,9869,9871,9874,9877],{"className":9870},[1913,1955],[1841,9872,1871],{"className":9873},[1913,1914,1955],[1841,9875,1886],{"className":9876},[2028,1955],[1841,9878,1890],{"className":9879},[1913,1955],[1841,9881,1963],{"className":9882},[1962],[1841,9884,9886],{"className":9885},[1935],[1841,9887,9889],{"className":9888,"style":2041},[1939],[1841,9890],{},[1841,9892],{"className":9893,"style":2210},[1976],[1841,9895,2129],{"className":9896},[2028],[1841,9898],{"className":9899,"style":2210},[1976],[1841,9901,9903,9906],{"className":9902},[1904],[1841,9904],{"className":9905,"style":2796},[1908],[1841,9907,9909,9912],{"className":9908},[1913],[1841,9910,2690],{"className":9911},[1913,1914],[1841,9913,9915],{"className":9914},[1926],[1841,9916,9918,9938],{"className":9917},[1930,1931],[1841,9919,9921,9935],{"className":9920},[1935],[1841,9922,9924],{"className":9923,"style":1940},[1939],[1841,9925,9926,9929],{"style":2244},[1841,9927],{"className":9928,"style":1948},[1947],[1841,9930,9932],{"className":9931},[1952,1953,1954,1955],[1841,9933,1871],{"className":9934},[1913,1914,1955],[1841,9936,1963],{"className":9937},[1962],[1841,9939,9941],{"className":9940},[1935],[1841,9942,9944],{"className":9943,"style":1970},[1939],[1841,9945],{},", calculate ",[1841,9948,9950,9970],{"className":9949},[1844],[1841,9951,9953],{"className":9952},[1848],[1850,9954,9955],{"xmlns":1852},[1854,9956,9957,9967],{},[1857,9958,9959,9961,9963,9965],{},[1860,9960,4346],{},[1873,9962,2068],{"stretchy":2067},[1888,9964,1890],{},[1873,9966,2073],{"stretchy":2067},[1892,9968,9969],{"encoding":1894},"\\rho(1)",[1841,9971,9973],{"className":9972,"ariaHidden":1900},[1899],[1841,9974,9976,9979,9982,9985,9988],{"className":9975},[1904],[1841,9977],{"className":9978,"style":2173},[1908],[1841,9980,4346],{"className":9981},[1913,1914],[1841,9983,2068],{"className":9984},[2180],[1841,9986,1890],{"className":9987},[1913],[1841,9989,2073],{"className":9990},[2187]," through ",[1841,9993,9995,10016],{"className":9994},[1844],[1841,9996,9998],{"className":9997},[1848],[1850,9999,10000],{"xmlns":1852},[1854,10001,10002,10013],{},[1857,10003,10004,10006,10008,10011],{},[1860,10005,4346],{},[1873,10007,2068],{"stretchy":2067},[1888,10009,10010],{},"4",[1873,10012,2073],{"stretchy":2067},[1892,10014,10015],{"encoding":1894},"\\rho(4)",[1841,10017,10019],{"className":10018,"ariaHidden":1900},[1899],[1841,10020,10022,10025,10028,10031,10034],{"className":10021},[1904],[1841,10023],{"className":10024,"style":2173},[1908],[1841,10026,4346],{"className":10027},[1913,1914],[1841,10029,2068],{"className":10030},[2180],[1841,10032,10010],{"className":10033},[1913],[1841,10035,2073],{"className":10036},[2187],[1812,10038,10039,10040,9946,10096,10139],{},"For MA(1) with ",[1841,10041,10043,10063],{"className":10042},[1844],[1841,10044,10046],{"className":10045},[1848],[1850,10047,10048],{"xmlns":1852},[1854,10049,10050,10060],{},[1857,10051,10052,10054,10056,10058],{},[1860,10053,2116],{},[1873,10055,1875],{},[1873,10057,1886],{},[1888,10059,5210],{},[1892,10061,10062],{"encoding":1894},"\\theta=-0.5",[1841,10064,10066,10084],{"className":10065,"ariaHidden":1900},[1899],[1841,10067,10069,10072,10075,10078,10081],{"className":10068},[1904],[1841,10070],{"className":10071,"style":7725},[1908],[1841,10073,2116],{"className":10074,"style":2392},[1913,1914],[1841,10076],{"className":10077,"style":1977},[1976],[1841,10079,1875],{"className":10080},[1981],[1841,10082],{"className":10083,"style":1977},[1976],[1841,10085,10087,10090,10093],{"className":10086},[1904],[1841,10088],{"className":10089,"style":2203},[1908],[1841,10091,1886],{"className":10092},[1913],[1841,10094,5210],{"className":10095},[1913],[1841,10097,10099,10118],{"className":10098},[1844],[1841,10100,10102],{"className":10101},[1848],[1850,10103,10104],{"xmlns":1852},[1854,10105,10106,10116],{},[1857,10107,10108,10110,10112,10114],{},[1860,10109,4346],{},[1873,10111,2068],{"stretchy":2067},[1888,10113,1890],{},[1873,10115,2073],{"stretchy":2067},[1892,10117,9969],{"encoding":1894},[1841,10119,10121],{"className":10120,"ariaHidden":1900},[1899],[1841,10122,10124,10127,10130,10133,10136],{"className":10123},[1904],[1841,10125],{"className":10126,"style":2173},[1908],[1841,10128,4346],{"className":10129},[1913,1914],[1841,10131,2068],{"className":10132},[2180],[1841,10134,1890],{"className":10135},[1913],[1841,10137,2073],{"className":10138},[2187]," and describe the visual pattern.",[1812,10141,10142,10143,10258],{},"Factor ",[1841,10144,10146,10178],{"className":10145},[1844],[1841,10147,10149],{"className":10148},[1848],[1850,10150,10151],{"xmlns":1852},[1854,10152,10153,10175],{},[1857,10154,10155,10157,10159,10162,10164,10166,10169],{},[1888,10156,1890],{},[1873,10158,1886],{},[1888,10160,10161],{},"0.9",[1860,10163,4793],{},[1873,10165,2129],{},[1888,10167,10168],{},"0.2",[2102,10170,10171,10173],{},[1860,10172,4793],{},[1888,10174,4319],{},[1892,10176,10177],{"encoding":1894},"1-0.9z+0.2z^2",[1841,10179,10181,10199,10220],{"className":10180,"ariaHidden":1900},[1899],[1841,10182,10184,10187,10190,10193,10196],{"className":10183},[1904],[1841,10185],{"className":10186,"style":2203},[1908],[1841,10188,1890],{"className":10189},[1913],[1841,10191],{"className":10192,"style":2210},[1976],[1841,10194,1886],{"className":10195},[2028],[1841,10197],{"className":10198,"style":2210},[1976],[1841,10200,10202,10205,10208,10211,10214,10217],{"className":10201},[1904],[1841,10203],{"className":10204,"style":2203},[1908],[1841,10206,10161],{"className":10207},[1913],[1841,10209,4793],{"className":10210,"style":4822},[1913,1914],[1841,10212],{"className":10213,"style":2210},[1976],[1841,10215,2129],{"className":10216},[2028],[1841,10218],{"className":10219,"style":2210},[1976],[1841,10221,10223,10226,10229],{"className":10222},[1904],[1841,10224],{"className":10225,"style":5279},[1908],[1841,10227,10168],{"className":10228},[1913],[1841,10230,10232,10235],{"className":10231},[1913],[1841,10233,4793],{"className":10234,"style":4822},[1913,1914],[1841,10236,10238],{"className":10237},[1926],[1841,10239,10241],{"className":10240},[1930],[1841,10242,10244],{"className":10243},[1935],[1841,10245,10247],{"className":10246,"style":5279},[1939],[1841,10248,10249,10252],{"style":3499},[1841,10250],{"className":10251,"style":1948},[1947],[1841,10253,10255],{"className":10254},[1952,1953,1954,1955],[1841,10256,4319],{"className":10257},[1913,1955]," and check stationarity.",[1812,10260,10261],{},"Explain why an MA coefficient outside the invertible region is not necessarily an impossible data-generating process but is a non-unique parameterisation.",[1812,10263,10264,10265,7873,10293,2160],{},"Write the companion matrix for the AR(2) in the worked root check and verify that its eigenvalues are ",[1841,10266,10268,10281],{"className":10267},[1844],[1841,10269,10271],{"className":10270},[1848],[1850,10272,10273],{"xmlns":1852},[1854,10274,10275,10279],{},[1857,10276,10277],{},[1888,10278,5210],{},[1892,10280,5210],{"encoding":1894},[1841,10282,10284],{"className":10283,"ariaHidden":1900},[1899],[1841,10285,10287,10290],{"className":10286},[1904],[1841,10288],{"className":10289,"style":4261},[1908],[1841,10291,5210],{"className":10292},[1913],[1841,10294,10296,10309],{"className":10295},[1844],[1841,10297,10299],{"className":10298},[1848],[1850,10300,10301],{"xmlns":1852},[1854,10302,10303,10307],{},[1857,10304,10305],{},[1888,10306,5223],{},[1892,10308,5223],{"encoding":1894},[1841,10310,10312],{"className":10311,"ariaHidden":1900},[1899],[1841,10313,10315,10318],{"className":10314},[1904],[1841,10316],{"className":10317,"style":4261},[1908],[1841,10319,5223],{"className":10320},[1913],[10322,10323,10325],"legacy-details",{"title":10324},"Answers",[9689,10326,10327,10332,10402,10513,10516],{},[1812,10328,10329,2160],{},[9670,10330,10331],{},"0.6, 0.36, 0.216, 0.1296",[1812,10333,10334,10401],{},[1841,10335,10337,10364],{"className":10336},[1844],[1841,10338,10340],{"className":10339},[1848],[1850,10341,10342],{"xmlns":1852},[1854,10343,10344,10361],{},[1857,10345,10346,10348,10350,10352,10355,10357,10359],{},[1873,10347,1886],{},[1888,10349,5210],{},[1860,10351,3893],{"mathvariant":2159},[1888,10353,10354],{},"1.25",[1873,10356,1875],{},[1873,10358,1886],{},[1888,10360,7772],{},[1892,10362,10363],{"encoding":1894},"-0.5\u002F1.25=-0.4",[1841,10365,10367,10389],{"className":10366,"ariaHidden":1900},[1899],[1841,10368,10370,10373,10376,10380,10383,10386],{"className":10369},[1904],[1841,10371],{"className":10372,"style":2173},[1908],[1841,10374,1886],{"className":10375},[1913],[1841,10377,10379],{"className":10378},[1913],"0.5\u002F1.25",[1841,10381],{"className":10382,"style":1977},[1976],[1841,10384,1875],{"className":10385},[1981],[1841,10387],{"className":10388,"style":1977},[1976],[1841,10390,10392,10395,10398],{"className":10391},[1904],[1841,10393],{"className":10394,"style":2203},[1908],[1841,10396,1886],{"className":10397},[1913],[1841,10399,7772],{"className":10400},[1913],"; adjacent observations tend to alternate around the mean.",[1812,10403,10404,10512],{},[1841,10405,10407,10443],{"className":10406},[1844],[1841,10408,10410],{"className":10409},[1848],[1850,10411,10412],{"xmlns":1852},[1854,10413,10414,10440],{},[1857,10415,10416,10418,10420,10422,10424,10426,10428,10430,10432,10434,10436,10438],{},[1873,10417,2068],{"stretchy":2067},[1888,10419,1890],{},[1873,10421,1886],{},[1888,10423,5210],{},[1860,10425,4793],{},[1873,10427,2073],{"stretchy":2067},[1873,10429,2068],{"stretchy":2067},[1888,10431,1890],{},[1873,10433,1886],{},[1888,10435,7772],{},[1860,10437,4793],{},[1873,10439,2073],{"stretchy":2067},[1892,10441,10442],{"encoding":1894},"(1-0.5z)(1-0.4z)",[1841,10444,10446,10467,10497],{"className":10445,"ariaHidden":1900},[1899],[1841,10447,10449,10452,10455,10458,10461,10464],{"className":10448},[1904],[1841,10450],{"className":10451,"style":2173},[1908],[1841,10453,2068],{"className":10454},[2180],[1841,10456,1890],{"className":10457},[1913],[1841,10459],{"className":10460,"style":2210},[1976],[1841,10462,1886],{"className":10463},[2028],[1841,10465],{"className":10466,"style":2210},[1976],[1841,10468,10470,10473,10476,10479,10482,10485,10488,10491,10494],{"className":10469},[1904],[1841,10471],{"className":10472,"style":2173},[1908],[1841,10474,5210],{"className":10475},[1913],[1841,10477,4793],{"className":10478,"style":4822},[1913,1914],[1841,10480,2073],{"className":10481},[2187],[1841,10483,2068],{"className":10484},[2180],[1841,10486,1890],{"className":10487},[1913],[1841,10489],{"className":10490,"style":2210},[1976],[1841,10492,1886],{"className":10493},[2028],[1841,10495],{"className":10496,"style":2210},[1976],[1841,10498,10500,10503,10506,10509],{"className":10499},[1904],[1841,10501],{"className":10502,"style":2173},[1908],[1841,10504,7772],{"className":10505},[1913],[1841,10507,4793],{"className":10508,"style":4822},[1913,1914],[1841,10510,2073],{"className":10511},[2187]," has roots 2 and 2.5, so it is stationary.",[1812,10514,10515],{},"Its autocovariance can be reproduced by an invertible representation after rescaling the innovation variance; invertibility chooses the unique recoverable-shock representation.",[1812,10517,10518,10743,10744,10855,10856,2160],{},[1841,10519,10521,10585],{"className":10520},[1844],[1841,10522,10524],{"className":10523},[1848],[1850,10525,10526],{"xmlns":1852},[1854,10527,10528,10582],{},[1857,10529,10530,10532,10534],{},[1860,10531,5514],{},[1873,10533,1875],{},[1857,10535,10536,10539,10579],{},[1873,10537,10538],{"fence":1900},"[",[10540,10541,10544,10565],"mtable",{"rowspacing":10542,"columnalign":10543,"columnspacing":7445},"0.16em","center center",[10545,10546,10547,10555],"mtr",{},[10548,10549,10550],"mtd",{},[10551,10552,10553],"mstyle",{"scriptlevel":4800,"displaystyle":2067},[1888,10554,4883],{},[10548,10556,10557],{},[10551,10558,10559],{"scriptlevel":4800,"displaystyle":2067},[1857,10560,10561,10563],{},[1873,10562,1886],{},[1888,10564,4900],{},[10545,10566,10567,10573],{},[10548,10568,10569],{},[10551,10570,10571],{"scriptlevel":4800,"displaystyle":2067},[1888,10572,1890],{},[10548,10574,10575],{},[10551,10576,10577],{"scriptlevel":4800,"displaystyle":2067},[1888,10578,4800],{},[1873,10580,10581],{"fence":1900},"]",[1892,10583,10584],{"encoding":1894},"F=\\begin{bmatrix}0.75&-0.125\\\\1&0\\end{bmatrix}",[1841,10586,10588,10606],{"className":10587,"ariaHidden":1900},[1899],[1841,10589,10591,10594,10597,10600,10603],{"className":10590},[1904],[1841,10592],{"className":10593,"style":6018},[1908],[1841,10595,5514],{"className":10596,"style":5878},[1913,1914],[1841,10598],{"className":10599,"style":1977},[1976],[1841,10601,1875],{"className":10602},[1981],[1841,10604],{"className":10605,"style":1977},[1976],[1841,10607,10609,10613],{"className":10608},[1904],[1841,10610],{"className":10611,"style":10612},[1908],"height:2.4em;vertical-align:-0.95em;",[1841,10614,10616,10625,10737],{"className":10615},[2287],[1841,10617,10621],{"className":10618,"style":10620},[2180,10619],"delimcenter","top:0em;",[1841,10622,10538],{"className":10623},[10624,1954],"delimsizing",[1841,10626,10628],{"className":10627},[1913],[1841,10629,10631,10681,10686,10689],{"className":10630},[10540],[1841,10632,10635],{"className":10633},[10634],"col-align-c",[1841,10636,10638,10672],{"className":10637},[1930,1931],[1841,10639,10641,10669],{"className":10640},[1935],[1841,10642,10645,10657],{"className":10643,"style":10644},[1939],"height:1.45em;",[1841,10646,10648,10651],{"style":10647},"top:-3.61em;",[1841,10649],{"className":10650,"style":6660},[1947],[1841,10652,10654],{"className":10653},[1913],[1841,10655,4883],{"className":10656},[1913],[1841,10658,10660,10663],{"style":10659},"top:-2.41em;",[1841,10661],{"className":10662,"style":6660},[1947],[1841,10664,10666],{"className":10665},[1913],[1841,10667,1890],{"className":10668},[1913],[1841,10670,1963],{"className":10671},[1962],[1841,10673,10675],{"className":10674},[1935],[1841,10676,10679],{"className":10677,"style":10678},[1939],"height:0.95em;",[1841,10680],{},[1841,10682],{"className":10683,"style":10685},[10684],"arraycolsep","width:0.5em;",[1841,10687],{"className":10688,"style":10685},[10684],[1841,10690,10692],{"className":10691},[10634],[1841,10693,10695,10729],{"className":10694},[1930,1931],[1841,10696,10698,10726],{"className":10697},[1935],[1841,10699,10701,10715],{"className":10700,"style":10644},[1939],[1841,10702,10703,10706],{"style":10647},[1841,10704],{"className":10705,"style":6660},[1947],[1841,10707,10709,10712],{"className":10708},[1913],[1841,10710,1886],{"className":10711},[1913],[1841,10713,4900],{"className":10714},[1913],[1841,10716,10717,10720],{"style":10659},[1841,10718],{"className":10719,"style":6660},[1947],[1841,10721,10723],{"className":10722},[1913],[1841,10724,4800],{"className":10725},[1913],[1841,10727,1963],{"className":10728},[1962],[1841,10730,10732],{"className":10731},[1935],[1841,10733,10735],{"className":10734,"style":10678},[1939],[1841,10736],{},[1841,10738,10740],{"className":10739,"style":10620},[2187,10619],[1841,10741,10581],{"className":10742},[10624,1954]," has characteristic polynomial ",[1841,10745,10747,10776],{"className":10746},[1844],[1841,10748,10750],{"className":10749},[1848],[1850,10751,10752],{"xmlns":1852},[1854,10753,10754,10773],{},[1857,10755,10756,10763,10765,10767,10769,10771],{},[2102,10757,10758,10761],{},[1860,10759,10760],{},"λ",[1888,10762,4319],{},[1873,10764,1886],{},[1888,10766,4883],{},[1860,10768,10760],{},[1873,10770,2129],{},[1888,10772,4900],{},[1892,10774,10775],{"encoding":1894},"\\lambda^2-0.75\\lambda+0.125",[1841,10777,10779,10824,10846],{"className":10778,"ariaHidden":1900},[1899],[1841,10780,10782,10786,10815,10818,10821],{"className":10781},[1904],[1841,10783],{"className":10784,"style":10785},[1908],"height:0.8974em;vertical-align:-0.0833em;",[1841,10787,10789,10792],{"className":10788},[1913],[1841,10790,10760],{"className":10791},[1913,1914],[1841,10793,10795],{"className":10794},[1926],[1841,10796,10798],{"className":10797},[1930],[1841,10799,10801],{"className":10800},[1935],[1841,10802,10804],{"className":10803,"style":5279},[1939],[1841,10805,10806,10809],{"style":3499},[1841,10807],{"className":10808,"style":1948},[1947],[1841,10810,10812],{"className":10811},[1952,1953,1954,1955],[1841,10813,4319],{"className":10814},[1913,1955],[1841,10816],{"className":10817,"style":2210},[1976],[1841,10819,1886],{"className":10820},[2028],[1841,10822],{"className":10823,"style":2210},[1976],[1841,10825,10827,10831,10834,10837,10840,10843],{"className":10826},[1904],[1841,10828],{"className":10829,"style":10830},[1908],"height:0.7778em;vertical-align:-0.0833em;",[1841,10832,4883],{"className":10833},[1913],[1841,10835,10760],{"className":10836},[1913,1914],[1841,10838],{"className":10839,"style":2210},[1976],[1841,10841,2129],{"className":10842},[2028],[1841,10844],{"className":10845,"style":2210},[1976],[1841,10847,10849,10852],{"className":10848},[1904],[1841,10850],{"className":10851,"style":4261},[1908],[1841,10853,4900],{"className":10854},[1913]," and eigenvalues ",[1841,10857,10859,10877],{"className":10858},[1844],[1841,10860,10862],{"className":10861},[1848],[1850,10863,10864],{"xmlns":1852},[1854,10865,10866,10874],{},[1857,10867,10868,10870,10872],{},[1888,10869,5210],{},[1873,10871,2110],{"separator":1900},[1888,10873,5223],{},[1892,10875,10876],{"encoding":1894},"0.5,0.25",[1841,10878,10880],{"className":10879,"ariaHidden":1900},[1899],[1841,10881,10883,10887,10890,10893,10896],{"className":10882},[1904],[1841,10884],{"className":10885,"style":10886},[1908],"height:0.8389em;vertical-align:-0.1944em;",[1841,10888,5210],{"className":10889},[1913],[1841,10891,2110],{"className":10892},[2380],[1841,10894],{"className":10895,"style":2388},[1976],[1841,10897,5223],{"className":10898},[1913],[1793,10900,10902],{"id":10901},"takeaway","Takeaway",[1798,10904,10905,10906,2160],{},"ARMA is a disciplined approximation to stable linear dependence. The next module asks what that approximation implies for future values and uncertainty: ",[10907,10908,10910],"a",{"href":10909},"..\u002F03-prediction\u002F","Prediction",{"title":10,"searchDepth":10912,"depth":10912,"links":10913},2,[10914,10915,10916,10917,10921,10924,10927,10928,10929,10930,10931,10932],{"id":1795,"depth":10912,"text":1796},{"id":1803,"depth":10912,"text":1804},{"id":1835,"depth":10912,"text":1836},{"id":3969,"depth":10912,"text":3970,"children":10918},[10919],{"id":4853,"depth":10920,"text":4854},3,{"id":5390,"depth":10912,"text":5391,"children":10922},[10923],{"id":7143,"depth":10920,"text":7144},{"id":7156,"depth":10912,"text":7157,"children":10925},[10926],{"id":7818,"depth":10920,"text":7819},{"id":8322,"depth":10912,"text":8323},{"id":8617,"depth":10912,"text":8618},{"id":9664,"depth":10912,"text":9665},{"id":9686,"depth":10912,"text":9687},{"id":9722,"depth":10912,"text":9723},{"id":10901,"depth":10912,"text":10902},"Build AR, MA, and ARIMA models from lag polynomials, roots, shock propagation, and finite-sample diagnostics.","md",{"sidebar":10936},{"order":10912},true,{"title":965,"description":10933},"YpfZU9oKI9nlzKnHA2b_JxixzrbdYN0YiyLuYHu5Ao0",[10941,10943],{"title":959,"path":960,"stem":961,"description":10942,"children":-1},"Represent a stochastic process through finite random vectors, Toeplitz covariance matrices, stationarity, and Wold innovations.",{"title":971,"path":972,"stem":973,"description":10944,"children":-1},"Derive best linear predictors from partitioned covariance matrices, quantify error with Schur complements, and introduce Kalman recursions.",1785754737859]