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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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does not mean flat or independent. It means that dependence operates under a stable rule, so different parts of one path can inform the same population quantities.",[1793,2301,2303],{"id":2302},"three-processes-three-diagnoses","Three processes, three diagnoses",[2305,2306,2307,2323],"table",{},[2308,2309,2310],"thead",{},[2311,2312,2313,2317,2320],"tr",{},[2314,2315,2316],"th",{},"Process",[2314,2318,2319],{},"What a shock 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as ",[1807,2704,2706,2725],{"className":2705},[1814],[1807,2707,2709],{"className":2708},[1818],[1820,2710,2711],{"xmlns":1822},[1825,2712,2713,2722],{},[1828,2714,2715],{},[2716,2717,2718,2720],"msup",{},[1891,2719,2500],{},[1831,2721,1928],{},[1945,2723,2724],{"encoding":1947},"0.8^h",[1807,2726,2728],{"className":2727,"ariaHidden":1860},[1952],[1807,2729,2731,2735,2739],{"className":2730},[1956],[1807,2732],{"className":2733,"style":2734},[1960],"height:0.8491em;",[1807,2736,2738],{"className":2737},[1965],"0.",[1807,2740,2742,2746],{"className":2741},[1965],[1807,2743,2745],{"className":2744},[1965],"8",[1807,2747,2749],{"className":2748},[1982],[1807,2750,2752],{"className":2751},[1986],[1807,2753,2755],{"className":2754},[1991],[1807,2756,2758],{"className":2757,"style":2734},[1995],[1807,2759,2761,2764],{"style":2760},"top:-3.063em;margin-right:0.05em;",[1807,2762],{"className":2763,"style":2004},[2003],[1807,2765,2767],{"className":2766},[2008,2009,2010,2011],[1807,2768,1928],{"className":2769},[1965,1977,2011],[2329,2771,2772],{},"yes",[2311,2774,2775,2988,2991],{},[2329,2776,2777],{},[1807,2778,2780,2820],{"className":2779},[1814],[1807,2781,2783],{"className":2782},[1818],[1820,2784,2785],{"xmlns":1822},[1825,2786,2787,2817],{},[1828,2788,2789,2795,2797,2809,2811],{},[1841,2790,2791,2793],{},[1831,2792,1845],{},[1831,2794,1848],{},[1836,2796,1854],{},[1841,2798,2799,2801],{},[1831,2800,1845],{},[1828,2802,2803,2805,2807],{},[1831,2804,1848],{},[1836,2806,1925],{},[1891,2808,2513],{},[1836,2810,2516],{},[1841,2812,2813,2815],{},[1831,2814,2355],{},[1831,2816,1848],{},[1945,2818,2819],{"encoding":1947},"X_t=X_{t-1}+\\varepsilon_t",[1807,2821,2823,2878,2942],{"className":2822,"ariaHidden":1860},[1952],[1807,2824,2826,2829,2869,2872,2875],{"className":2825},[1956],[1807,2827],{"className":2828,"style":2370},[1960],[1807,2830,2832,2835],{"className":2831},[1965],[1807,2833,1845],{"className":2834,"style":1978},[1965,1977],[1807,2836,2838],{"className":2837},[1982],[1807,2839,2841,2861],{"className":2840},[1986,1987],[1807,2842,2844,2858],{"className":2843},[1991],[1807,2845,2847],{"className":2846,"style":1996},[1995],[1807,2848,2849,2852],{"style":1999},[1807,2850],{"className":2851,"style":2004},[2003],[1807,2853,2855],{"className":2854},[2008,2009,2010,2011],[1807,2856,1848],{"className":2857},[1965,1977,2011],[1807,2859,2019],{"className":2860},[2018],[1807,2862,2864],{"className":2863},[1991],[1807,2865,2867],{"className":2866,"style":2026},[1995],[1807,2868],{},[1807,2870],{"className":2871,"style":2036},[1863],[1807,2873,1854],{"className":2874},[2040],[1807,2876],{"className":2877,"style":2036},[1863],[1807,2879,2881,2884,2933,2936,2939],{"className":2880},[1956],[1807,2882],{"className":2883,"style":2590},[1960],[1807,2885,2887,2890],{"className":2886},[1965],[1807,2888,1845],{"className":2889,"style":1978},[1965,1977],[1807,2891,2893],{"className":2892},[1982],[1807,2894,2896,2925],{"className":2895},[1986,1987],[1807,2897,2899,2922],{"className":2898},[1991],[1807,2900,2902],{"className":2901,"style":2612},[1995],[1807,2903,2904,2907],{"style":1999},[1807,2905],{"className":2906,"style":2004},[2003],[1807,2908,2910],{"className":2909},[2008,2009,2010,2011],[1807,2911,2913,2916,2919],{"className":2912},[1965,2011],[1807,2914,1848],{"className":2915},[1965,1977,2011],[1807,2917,1925],{"className":2918},[2248,2011],[1807,2920,2513],{"className":2921},[1965,2011],[1807,2923,2019],{"className":2924},[2018],[1807,2926,2928],{"className":2927},[1991],[1807,2929,2931],{"className":2930,"style":2261},[1995],[1807,2932],{},[1807,2934],{"className":2935,"style":2647},[1863],[1807,2937,2516],{"className":2938},[2248],[1807,2940],{"className":2941,"style":2647},[1863],[1807,2943,2945,2948],{"className":2944},[1956],[1807,2946],{"className":2947,"style":2426},[1960],[1807,2949,2951,2954],{"className":2950},[1965],[1807,2952,2355],{"className":2953},[1965,1977],[1807,2955,2957],{"className":2956},[1982],[1807,2958,2960,2980],{"className":2959},[1986,1987],[1807,2961,2963,2977],{"className":2962},[1991],[1807,2964,2966],{"className":2965,"style":1996},[1995],[1807,2967,2968,2971],{"style":2447},[1807,2969],{"className":2970,"style":2004},[2003],[1807,2972,2974],{"className":2973},[2008,2009,2010,2011],[1807,2975,1848],{"className":2976},[1965,1977,2011],[1807,2978,2019],{"className":2979},[2018],[1807,2981,2983],{"className":2982},[1991],[1807,2984,2986],{"className":2985,"style":2026},[1995],[1807,2987],{},[2329,2989,2990],{},"remains 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},[1965,1977],[1807,3336,3338],{"className":3337},[1982],[1807,3339,3341,3370],{"className":3340},[1986,1987],[1807,3342,3344,3367],{"className":3343},[1991],[1807,3345,3347],{"className":3346,"style":2612},[1995],[1807,3348,3349,3352],{"style":2447},[1807,3350],{"className":3351,"style":2004},[2003],[1807,3353,3355],{"className":3354},[2008,2009,2010,2011],[1807,3356,3358,3361,3364],{"className":3357},[1965,2011],[1807,3359,1848],{"className":3360},[1965,1977,2011],[1807,3362,1925],{"className":3363},[2248,2011],[1807,3365,3079],{"className":3366},[1965,2011],[1807,3368,2019],{"className":3369},[2018],[1807,3371,3373],{"className":3372},[1991],[1807,3374,3376],{"className":3375,"style":2261},[1995],[1807,3377],{},[1807,3379],{"className":3380,"style":2647},[1863],[1807,3382,2516],{"className":3383},[2248],[1807,3385],{"className":3386,"style":2647},[1863],[1807,3388,3390,3394,3398,3401,3404],{"className":3389},[1956],[1807,3391],{"className":3392,"style":3393},[1960],"height:0.313em;",[1807,3395,3096],{"className":3396},[3397],"minner",[1807,3399],{"className":3400,"style":2064},[1863],[1807,3402],{"className":3403,"style":2064},[1863],[1807,3405,1943],{"className":3406},[1965],[1798,3408,3409,3410,3524],{},"If ",[1807,3411,3413,3444],{"className":3412},[1814],[1807,3414,3416],{"className":3415},[1818],[1820,3417,3418],{"xmlns":1822},[1825,3419,3420,3441],{},[1828,3421,3422,3424,3426,3428,3434,3436,3438],{},[1831,3423,1869],{"mathvariant":1868},[1836,3425,1872],{},[1836,3427,1839],{"stretchy":1838},[1841,3429,3430,3432],{},[1831,3431,2355],{},[1831,3433,1848],{},[1836,3435,1851],{"stretchy":1838},[1836,3437,1854],{},[1891,3439,3440],{},"4",[1945,3442,3443],{"encoding":1947},"\\operatorname{Var}(\\varepsilon_t)=4",[1807,3445,3447,3514],{"className":3446,"ariaHidden":1860},[1952],[1807,3448,3450,3453,3459,3462,3502,3505,3508,3511],{"className":3449},[1956],[1807,3451],{"className":3452,"style":1961},[1960],[1807,3454,3456],{"className":3455},[2068],[1807,3457,1869],{"className":3458},[1965,2072],[1807,3460,1839],{"className":3461},[1970],[1807,3463,3465,3468],{"className":3464},[1965],[1807,3466,2355],{"className":3467},[1965,1977],[1807,3469,3471],{"className":3470},[1982],[1807,3472,3474,3494],{"className":3473},[1986,1987],[1807,3475,3477,3491],{"className":3476},[1991],[1807,3478,3480],{"className":3479,"style":1996},[1995],[1807,3481,3482,3485],{"style":2447},[1807,3483],{"className":3484,"style":2004},[2003],[1807,3486,3488],{"className":3487},[2008,2009,2010,2011],[1807,3489,1848],{"className":3490},[1965,1977,2011],[1807,3492,2019],{"className":3493},[2018],[1807,3495,3497],{"className":3496},[1991],[1807,3498,3500],{"className":3499,"style":2026},[1995],[1807,3501],{},[1807,3503,1851],{"className":3504},[2032],[1807,3506],{"className":3507,"style":2036},[1863],[1807,3509,1854],{"className":3510},[2040],[1807,3512],{"className":3513,"style":2036},[1863],[1807,3515,3517,3521],{"className":3516},[1956],[1807,3518],{"className":3519,"style":3520},[1960],"height:0.6444em;",[1807,3522,3440],{"className":3523},[1965],", then",[1807,3526,3528],{"className":3527},[1810],[1807,3529,3531,3581],{"className":3530},[1814],[1807,3532,3534],{"className":3533},[1818],[1820,3535,3536],{"xmlns":1822,"display":1823},[1825,3537,3538,3578],{},[1828,3539,3540,3542,3544,3546,3552,3554,3556,3573,3575],{},[1831,3541,1869],{"mathvariant":1868},[1836,3543,1872],{},[1836,3545,1839],{"stretchy":1838},[1841,3547,3548,3550],{},[1831,3549,1845],{},[1831,3551,1848],{},[1836,3553,1851],{"stretchy":1838},[1836,3555,1854],{},[3557,3558,3559,3561],"mfrac",{},[1891,3560,3440],{},[1828,3562,3563,3565,3567],{},[1891,3564,2513],{},[1836,3566,1925],{},[2716,3568,3569,3571],{},[1891,3570,2500],{},[1891,3572,3079],{},[1836,3574,1854],{},[1891,3576,3577],{},"11.11.",[1945,3579,3580],{"encoding":1947},"\\operatorname{Var}(X_t)=\\frac{4}{1-0.8^2}=11.11.",[1807,3582,3584,3651,3781],{"className":3583,"ariaHidden":1860},[1952],[1807,3585,3587,3590,3596,3599,3639,3642,3645,3648],{"className":3586},[1956],[1807,3588],{"className":3589,"style":1961},[1960],[1807,3591,3593],{"className":3592},[2068],[1807,3594,1869],{"className":3595},[1965,2072],[1807,3597,1839],{"className":3598},[1970],[1807,3600,3602,3605],{"className":3601},[1965],[1807,3603,1845],{"className":3604,"style":1978},[1965,1977],[1807,3606,3608],{"className":3607},[1982],[1807,3609,3611,3631],{"className":3610},[1986,1987],[1807,3612,3614,3628],{"className":3613},[1991],[1807,3615,3617],{"className":3616,"style":1996},[1995],[1807,3618,3619,3622],{"style":1999},[1807,3620],{"className":3621,"style":2004},[2003],[1807,3623,3625],{"className":3624},[2008,2009,2010,2011],[1807,3626,1848],{"className":3627},[1965,1977,2011],[1807,3629,2019],{"className":3630},[2018],[1807,3632,3634],{"className":3633},[1991],[1807,3635,3637],{"className":3636,"style":2026},[1995],[1807,3638],{},[1807,3640,1851],{"className":3641},[2032],[1807,3643],{"className":3644,"style":2036},[1863],[1807,3646,1854],{"className":3647},[2040],[1807,3649],{"className":3650,"style":2036},[1863],[1807,3652,3654,3658,3772,3775,3778],{"className":3653},[1956],[1807,3655],{"className":3656,"style":3657},[1960],"height:2.0908em;vertical-align:-0.7693em;",[1807,3659,3661,3665,3769],{"className":3660},[1965],[1807,3662],{"className":3663},[1970,3664],"nulldelimiter",[1807,3666,3668],{"className":3667},[3557],[1807,3669,3671,3760],{"className":3670},[1986,1987],[1807,3672,3674,3757],{"className":3673},[1991],[1807,3675,3678,3734,3745],{"className":3676,"style":3677},[1995],"height:1.3214em;",[1807,3679,3681,3685],{"style":3680},"top:-2.314em;",[1807,3682],{"className":3683,"style":3684},[2003],"height:3em;",[1807,3686,3688,3691,3694,3697,3700,3703],{"className":3687},[1965],[1807,3689,2513],{"className":3690},[1965],[1807,3692],{"className":3693,"style":2647},[1863],[1807,3695,1925],{"className":3696},[2248],[1807,3698],{"className":3699,"style":2647},[1863],[1807,3701,2738],{"className":3702},[1965],[1807,3704,3706,3709],{"className":3705},[1965],[1807,3707,2745],{"className":3708},[1965],[1807,3710,3712],{"className":3711},[1982],[1807,3713,3715],{"className":3714},[1986],[1807,3716,3718],{"className":3717},[1991],[1807,3719,3722],{"className":3720,"style":3721},[1995],"height:0.7401em;",[1807,3723,3725,3728],{"style":3724},"top:-2.989em;margin-right:0.05em;",[1807,3726],{"className":3727,"style":2004},[2003],[1807,3729,3731],{"className":3730},[2008,2009,2010,2011],[1807,3732,3079],{"className":3733},[1965,2011],[1807,3735,3737,3740],{"style":3736},"top:-3.23em;",[1807,3738],{"className":3739,"style":3684},[2003],[1807,3741],{"className":3742,"style":3744},[3743],"frac-line","border-bottom-width:0.04em;",[1807,3746,3748,3751],{"style":3747},"top:-3.677em;",[1807,3749],{"className":3750,"style":3684},[2003],[1807,3752,3754],{"className":3753},[1965],[1807,3755,3440],{"className":3756},[1965],[1807,3758,2019],{"className":3759},[2018],[1807,3761,3763],{"className":3762},[1991],[1807,3764,3767],{"className":3765,"style":3766},[1995],"height:0.7693em;",[1807,3768],{},[1807,3770],{"className":3771},[2032,3664],[1807,3773],{"className":3774,"style":2036},[1863],[1807,3776,1854],{"className":3777},[2040],[1807,3779],{"className":3780,"style":2036},[1863],[1807,3782,3784,3787],{"className":3783},[1956],[1807,3785],{"className":3786,"style":3520},[1960],[1807,3788,3577],{"className":3789},[1965],[1798,3791,3792,3793,4020,4021,4138],{},"For the random walk, ",[1807,3794,3796,3839],{"className":3795},[1814],[1807,3797,3799],{"className":3798},[1818],[1820,3800,3801],{"xmlns":1822},[1825,3802,3803,3836],{},[1828,3804,3805,3811,3813,3830],{},[1841,3806,3807,3809],{},[1831,3808,1845],{},[1831,3810,1848],{},[1836,3812,1854],{},[3814,3815,3816,3819,3828],"msubsup",{},[1836,3817,3818],{},"∑",[1828,3820,3821,3824,3826],{},[1831,3822,3823],{},"j",[1836,3825,1854],{},[1891,3827,2513],{},[1831,3829,1848],{},[1841,3831,3832,3834],{},[1831,3833,2355],{},[1831,3835,3823],{},[1945,3837,3838],{"encoding":1947},"X_t=\\sum_{j=1}^{t}\\varepsilon_j",[1807,3840,3842,3897],{"className":3841,"ariaHidden":1860},[1952],[1807,3843,3845,3848,3888,3891,3894],{"className":3844},[1956],[1807,3846],{"className":3847,"style":2370},[1960],[1807,3849,3851,3854],{"className":3850},[1965],[1807,3852,1845],{"className":3853,"style":1978},[1965,1977],[1807,3855,3857],{"className":3856},[1982],[1807,3858,3860,3880],{"className":3859},[1986,1987],[1807,3861,3863,3877],{"className":3862},[1991],[1807,3864,3866],{"className":3865,"style":1996},[1995],[1807,3867,3868,3871],{"style":1999},[1807,3869],{"className":3870,"style":2004},[2003],[1807,3872,3874],{"className":3873},[2008,2009,2010,2011],[1807,3875,1848],{"className":3876},[1965,1977,2011],[1807,3878,2019],{"className":3879},[2018],[1807,3881,3883],{"className":3882},[1991],[1807,3884,3886],{"className":3885,"style":2026},[1995],[1807,3887],{},[1807,3889],{"className":3890,"style":2036},[1863],[1807,3892,1854],{"className":3893},[2040],[1807,3895],{"className":3896,"style":2036},[1863],[1807,3898,3900,3904,3975,3978],{"className":3899},[1956],[1807,3901],{"className":3902,"style":3903},[1960],"height:1.3693em;vertical-align:-0.4358em;",[1807,3905,3907,3913],{"className":3906},[2068],[1807,3908,3818],{"className":3909,"style":3912},[2068,3910,3911],"op-symbol","small-op","position:relative;top:0em;",[1807,3914,3916],{"className":3915},[1982],[1807,3917,3919,3966],{"className":3918},[1986,1987],[1807,3920,3922,3963],{"className":3921},[1991],[1807,3923,3926,3948],{"className":3924,"style":3925},[1995],"height:0.9335em;",[1807,3927,3929,3932],{"style":3928},"top:-2.4003em;margin-left:0em;margin-right:0.05em;",[1807,3930],{"className":3931,"style":2004},[2003],[1807,3933,3935],{"className":3934},[2008,2009,2010,2011],[1807,3936,3938,3942,3945],{"className":3937},[1965,2011],[1807,3939,3823],{"className":3940,"style":3941},[1965,1977,2011],"margin-right:0.0572em;",[1807,3943,1854],{"className":3944},[2040,2011],[1807,3946,2513],{"className":3947},[1965,2011],[1807,3949,3951,3954],{"style":3950},"top:-3.2029em;margin-right:0.05em;",[1807,3952],{"className":3953,"style":2004},[2003],[1807,3955,3957],{"className":3956},[2008,2009,2010,2011],[1807,3958,3960],{"className":3959},[1965,2011],[1807,3961,1848],{"className":3962},[1965,1977,2011],[1807,3964,2019],{"className":3965},[2018],[1807,3967,3969],{"className":3968},[1991],[1807,3970,3973],{"className":3971,"style":3972},[1995],"height:0.4358em;",[1807,3974],{},[1807,3976],{"className":3977,"style":2064},[1863],[1807,3979,3981,3984],{"className":3980},[1965],[1807,3982,2355],{"className":3983},[1965,1977],[1807,3985,3987],{"className":3986},[1982],[1807,3988,3990,4011],{"className":3989},[1986,1987],[1807,3991,3993,4008],{"className":3992},[1991],[1807,3994,3997],{"className":3995,"style":3996},[1995],"height:0.3117em;",[1807,3998,3999,4002],{"style":2447},[1807,4000],{"className":4001,"style":2004},[2003],[1807,4003,4005],{"className":4004},[2008,2009,2010,2011],[1807,4006,3823],{"className":4007,"style":3941},[1965,1977,2011],[1807,4009,2019],{"className":4010},[2018],[1807,4012,4014],{"className":4013},[1991],[1807,4015,4018],{"className":4016,"style":4017},[1995],"height:0.2861em;",[1807,4019],{},", so ",[1807,4022,4024,4056],{"className":4023},[1814],[1807,4025,4027],{"className":4026},[1818],[1820,4028,4029],{"xmlns":1822},[1825,4030,4031,4053],{},[1828,4032,4033,4035,4037,4039,4045,4047,4049,4051],{},[1831,4034,1869],{"mathvariant":1868},[1836,4036,1872],{},[1836,4038,1839],{"stretchy":1838},[1841,4040,4041,4043],{},[1831,4042,1845],{},[1831,4044,1848],{},[1836,4046,1851],{"stretchy":1838},[1836,4048,1854],{},[1891,4050,3440],{},[1831,4052,1848],{},[1945,4054,4055],{"encoding":1947},"\\operatorname{Var}(X_t)=4t",[1807,4057,4059,4126],{"className":4058,"ariaHidden":1860},[1952],[1807,4060,4062,4065,4071,4074,4114,4117,4120,4123],{"className":4061},[1956],[1807,4063],{"className":4064,"style":1961},[1960],[1807,4066,4068],{"className":4067},[2068],[1807,4069,1869],{"className":4070},[1965,2072],[1807,4072,1839],{"className":4073},[1970],[1807,4075,4077,4080],{"className":4076},[1965],[1807,4078,1845],{"className":4079,"style":1978},[1965,1977],[1807,4081,4083],{"className":4082},[1982],[1807,4084,4086,4106],{"className":4085},[1986,1987],[1807,4087,4089,4103],{"className":4088},[1991],[1807,4090,4092],{"className":4091,"style":1996},[1995],[1807,4093,4094,4097],{"style":1999},[1807,4095],{"className":4096,"style":2004},[2003],[1807,4098,4100],{"className":4099},[2008,2009,2010,2011],[1807,4101,1848],{"className":4102},[1965,1977,2011],[1807,4104,2019],{"className":4105},[2018],[1807,4107,4109],{"className":4108},[1991],[1807,4110,4112],{"className":4111,"style":2026},[1995],[1807,4113],{},[1807,4115,1851],{"className":4116},[2032],[1807,4118],{"className":4119,"style":2036},[1863],[1807,4121,1854],{"className":4122},[2040],[1807,4124],{"className":4125,"style":2036},[1863],[1807,4127,4129,4132,4135],{"className":4128},[1956],[1807,4130],{"className":4131,"style":3520},[1960],[1807,4133,3440],{"className":4134},[1965],[1807,4136,1848],{"className":4137},[1965,1977],". The calendar time now changes the distribution.",[1793,4140,4142],{"id":4141},"do-not-collapse-five-different-problems-into-non-stationary","Do not collapse five different problems into “non-stationary”",[2305,4144,4145,4158],{},[2308,4146,4147],{},[2311,4148,4149,4152,4155],{},[2314,4150,4151],{},"Pattern",[2314,4153,4154],{},"Small example",[2314,4156,4157],{},"First response",[2324,4159,4160,4171,4182,4193,4204,4215],{},[2311,4161,4162,4165,4168],{},[2329,4163,4164],{},"deterministic trend",[2329,4166,4167],{},"demand rises by 2 MWh each year",[2329,4169,4170],{},"trend regressor or detrending",[2311,4172,4173,4176,4179],{},[2329,4174,4175],{},"stochastic trend\u002Funit root",[2329,4177,4178],{},"shocks permanently shift the level",[2329,4180,4181],{},"first difference, if justified",[2311,4183,4184,4187,4190],{},[2329,4185,4186],{},"deterministic seasonality",[2329,4188,4189],{},"every January is about 10 units higher",[2329,4191,4192],{},"month indicators or seasonal terms",[2311,4194,4195,4198,4201],{},[2329,4196,4197],{},"seasonal unit root",[2329,4199,4200],{},"this January resembles last January through accumulated shocks",[2329,4202,4203],{},"seasonal difference",[2311,4205,4206,4209,4212],{},[2329,4207,4208],{},"structural break",[2329,4210,4211],{},"a heat pump raises demand after installation",[2329,4213,4214],{},"intervention term, regime model, or shorter window",[2311,4216,4217,4220,4223],{},[2329,4218,4219],{},"changing variance",[2329,4221,4222],{},"seasonal amplitude grows with level",[2329,4224,4225],{},"log\u002FBox–Cox transform or variance model",[1798,4227,4228],{},"Different operations answer different diagnoses. Applying log, first difference, and seasonal difference automatically can destroy useful structure.",[1793,4230,4232],{"id":4231},"a-useful-counterexample-over-differencing","A useful counterexample: over-differencing",[1798,4234,4235,4236,4368],{},"Suppose ",[1807,4237,4239,4264],{"className":4238},[1814],[1807,4240,4242],{"className":4241},[1818],[1820,4243,4244],{"xmlns":1822},[1825,4245,4246,4262],{},[1828,4247,4248,4254,4256],{},[1841,4249,4250,4252],{},[1831,4251,1845],{},[1831,4253,1848],{},[1836,4255,1854],{},[1841,4257,4258,4260],{},[1831,4259,2355],{},[1831,4261,1848],{},[1945,4263,2360],{"encoding":1947},[1807,4265,4267,4322],{"className":4266,"ariaHidden":1860},[1952],[1807,4268,4270,4273,4313,4316,4319],{"className":4269},[1956],[1807,4271],{"className":4272,"style":2370},[1960],[1807,4274,4276,4279],{"className":4275},[1965],[1807,4277,1845],{"className":4278,"style":1978},[1965,1977],[1807,4280,4282],{"className":4281},[1982],[1807,4283,4285,4305],{"className":4284},[1986,1987],[1807,4286,4288,4302],{"className":4287},[1991],[1807,4289,4291],{"className":4290,"style":1996},[1995],[1807,4292,4293,4296],{"style":1999},[1807,4294],{"className":4295,"style":2004},[2003],[1807,4297,4299],{"className":4298},[2008,2009,2010,2011],[1807,4300,1848],{"className":4301},[1965,1977,2011],[1807,4303,2019],{"className":4304},[2018],[1807,4306,4308],{"className":4307},[1991],[1807,4309,4311],{"className":4310,"style":2026},[1995],[1807,4312],{},[1807,4314],{"className":4315,"style":2036},[1863],[1807,4317,1854],{"className":4318},[2040],[1807,4320],{"className":4321,"style":2036},[1863],[1807,4323,4325,4328],{"className":4324},[1956],[1807,4326],{"className":4327,"style":2426},[1960],[1807,4329,4331,4334],{"className":4330},[1965],[1807,4332,2355],{"className":4333},[1965,1977],[1807,4335,4337],{"className":4336},[1982],[1807,4338,4340,4360],{"className":4339},[1986,1987],[1807,4341,4343,4357],{"className":4342},[1991],[1807,4344,4346],{"className":4345,"style":1996},[1995],[1807,4347,4348,4351],{"style":2447},[1807,4349],{"className":4350,"style":2004},[2003],[1807,4352,4354],{"className":4353},[2008,2009,2010,2011],[1807,4355,1848],{"className":4356},[1965,1977,2011],[1807,4358,2019],{"className":4359},[2018],[1807,4361,4363],{"className":4362},[1991],[1807,4364,4366],{"className":4365,"style":2026},[1995],[1807,4367],{}," is already white noise. Differencing gives",[1807,4370,4372],{"className":4371},[1810],[1807,4373,4375,4420],{"className":4374},[1814],[1807,4376,4378],{"className":4377},[1818],[1820,4379,4380],{"xmlns":1822,"display":1823},[1825,4381,4382,4417],{},[1828,4383,4384,4387,4393,4395,4401,4403,4415],{},[1831,4385,4386],{"mathvariant":1868},"Δ",[1841,4388,4389,4391],{},[1831,4390,1845],{},[1831,4392,1848],{},[1836,4394,1854],{},[1841,4396,4397,4399],{},[1831,4398,2355],{},[1831,4400,1848],{},[1836,4402,1925],{},[1841,4404,4405,4407],{},[1831,4406,2355],{},[1828,4408,4409,4411,4413],{},[1831,4410,1848],{},[1836,4412,1925],{},[1891,4414,2513],{},[1836,4416,1861],{"separator":1860},[1945,4418,4419],{"encoding":1947},"\\Delta X_t=\\varepsilon_t-\\varepsilon_{t-1},",[1807,4421,4423,4481,4536],{"className":4422,"ariaHidden":1860},[1952],[1807,4424,4426,4429,4432,4472,4475,4478],{"className":4425},[1956],[1807,4427],{"className":4428,"style":2370},[1960],[1807,4430,4386],{"className":4431},[1965],[1807,4433,4435,4438],{"className":4434},[1965],[1807,4436,1845],{"className":4437,"style":1978},[1965,1977],[1807,4439,4441],{"className":4440},[1982],[1807,4442,4444,4464],{"className":4443},[1986,1987],[1807,4445,4447,4461],{"className":4446},[1991],[1807,4448,4450],{"className":4449,"style":1996},[1995],[1807,4451,4452,4455],{"style":1999},[1807,4453],{"className":4454,"style":2004},[2003],[1807,4456,4458],{"className":4457},[2008,2009,2010,2011],[1807,4459,1848],{"className":4460},[1965,1977,2011],[1807,4462,2019],{"className":4463},[2018],[1807,4465,4467],{"className":4466},[1991],[1807,4468,4470],{"className":4469,"style":2026},[1995],[1807,4471],{},[1807,4473],{"className":4474,"style":2036},[1863],[1807,4476,1854],{"className":4477},[2040],[1807,4479],{"className":4480,"style":2036},[1863],[1807,4482,4484,4487,4527,4530,4533],{"className":4483},[1956],[1807,4485],{"className":4486,"style":3170},[1960],[1807,4488,4490,4493],{"className":4489},[1965],[1807,4491,2355],{"className":4492},[1965,1977],[1807,4494,4496],{"className":4495},[1982],[1807,4497,4499,4519],{"className":4498},[1986,1987],[1807,4500,4502,4516],{"className":4501},[1991],[1807,4503,4505],{"className":4504,"style":1996},[1995],[1807,4506,4507,4510],{"style":2447},[1807,4508],{"className":4509,"style":2004},[2003],[1807,4511,4513],{"className":4512},[2008,2009,2010,2011],[1807,4514,1848],{"className":4515},[1965,1977,2011],[1807,4517,2019],{"className":4518},[2018],[1807,4520,4522],{"className":4521},[1991],[1807,4523,4525],{"className":4524,"style":2026},[1995],[1807,4526],{},[1807,4528],{"className":4529,"style":2647},[1863],[1807,4531,1925],{"className":4532},[2248],[1807,4534],{"className":4535,"style":2647},[1863],[1807,4537,4539,4543,4592],{"className":4538},[1956],[1807,4540],{"className":4541,"style":4542},[1960],"height:0.6389em;vertical-align:-0.2083em;",[1807,4544,4546,4549],{"className":4545},[1965],[1807,4547,2355],{"className":4548},[1965,1977],[1807,4550,4552],{"className":4551},[1982],[1807,4553,4555,4584],{"className":4554},[1986,1987],[1807,4556,4558,4581],{"className":4557},[1991],[1807,4559,4561],{"className":4560,"style":2612},[1995],[1807,4562,4563,4566],{"style":2447},[1807,4564],{"className":4565,"style":2004},[2003],[1807,4567,4569],{"className":4568},[2008,2009,2010,2011],[1807,4570,4572,4575,4578],{"className":4571},[1965,2011],[1807,4573,1848],{"className":4574},[1965,1977,2011],[1807,4576,1925],{"className":4577},[2248,2011],[1807,4579,2513],{"className":4580},[1965,2011],[1807,4582,2019],{"className":4583},[2018],[1807,4585,4587],{"className":4586},[1991],[1807,4588,4590],{"className":4589,"style":2261},[1995],[1807,4591],{},[1807,4593,1861],{"className":4594},[2056],[1798,4596,4597,4598,4633,4634,4674],{},"an MA(1) process with coefficient ",[1807,4599,4601,4617],{"className":4600},[1814],[1807,4602,4604],{"className":4603},[1818],[1820,4605,4606],{"xmlns":1822},[1825,4607,4608,4614],{},[1828,4609,4610,4612],{},[1836,4611,1925],{},[1891,4613,2513],{},[1945,4615,4616],{"encoding":1947},"-1",[1807,4618,4620],{"className":4619,"ariaHidden":1860},[1952],[1807,4621,4623,4627,4630],{"className":4622},[1956],[1807,4624],{"className":4625,"style":4626},[1960],"height:0.7278em;vertical-align:-0.0833em;",[1807,4628,1925],{"className":4629},[1965],[1807,4631,2513],{"className":4632},[1965]," and lag-1 autocorrelation ",[1807,4635,4637,4658],{"className":4636},[1814],[1807,4638,4640],{"className":4639},[1818],[1820,4641,4642],{"xmlns":1822},[1825,4643,4644,4655],{},[1828,4645,4646,4648,4650,4653],{},[1836,4647,1925],{},[1891,4649,2513],{},[1831,4651,4652],{"mathvariant":1868},"\u002F",[1891,4654,3079],{},[1945,4656,4657],{"encoding":1947},"-1\u002F2",[1807,4659,4661],{"className":4660,"ariaHidden":1860},[1952],[1807,4662,4664,4667,4670],{"className":4663},[1956],[1807,4665],{"className":4666,"style":1961},[1960],[1807,4668,1925],{"className":4669},[1965],[1807,4671,4673],{"className":4672},[1965],"1\u002F2",". The transformation has manufactured dependence and made the model non-invertible. “More stationary-looking” is not always better.",[1793,4676,4678],{"id":4677},"trend-stationary-or-difference-stationary","Trend-stationary or difference-stationary?",[1798,4680,4681],{},"Two upward paths can look alike:",[1807,4683,4685],{"className":4684},[1810],[1807,4686,4688,4732],{"className":4687},[1814],[1807,4689,4691],{"className":4690},[1818],[1820,4692,4693],{"xmlns":1822,"display":1823},[1825,4694,4695,4729],{},[1828,4696,4697,4700,4706,4708,4711,4713,4716,4718,4720,4727],{},[3098,4698,4699],{},"trend-stationary: ",[1841,4701,4702,4704],{},[1831,4703,1845],{},[1831,4705,1848],{},[1836,4707,1854],{},[1831,4709,4710],{},"α",[1836,4712,2516],{},[1831,4714,4715],{},"β",[1831,4717,1848],{},[1836,4719,2516],{},[1841,4721,4722,4725],{},[1831,4723,4724],{},"u",[1831,4726,1848],{},[1836,4728,1861],{"separator":1860},[1945,4730,4731],{"encoding":1947},"\\text{trend-stationary: }X_t=\\alpha+\\beta t+u_t,",[1807,4733,4735,4798,4818,4840],{"className":4734,"ariaHidden":1860},[1952],[1807,4736,4738,4742,4749,4789,4792,4795],{"className":4737},[1956],[1807,4739],{"className":4740,"style":4741},[1960],"height:0.8889em;vertical-align:-0.1944em;",[1807,4743,4746],{"className":4744},[1965,4745],"text",[1807,4747,4699],{"className":4748},[1965],[1807,4750,4752,4755],{"className":4751},[1965],[1807,4753,1845],{"className":4754,"style":1978},[1965,1977],[1807,4756,4758],{"className":4757},[1982],[1807,4759,4761,4781],{"className":4760},[1986,1987],[1807,4762,4764,4778],{"className":4763},[1991],[1807,4765,4767],{"className":4766,"style":1996},[1995],[1807,4768,4769,4772],{"style":1999},[1807,4770],{"className":4771,"style":2004},[2003],[1807,4773,4775],{"className":4774},[2008,2009,2010,2011],[1807,4776,1848],{"className":4777},[1965,1977,2011],[1807,4779,2019],{"className":4780},[2018],[1807,4782,4784],{"className":4783},[1991],[1807,4785,4787],{"className":4786,"style":2026},[1995],[1807,4788],{},[1807,4790],{"className":4791,"style":2036},[1863],[1807,4793,1854],{"className":4794},[2040],[1807,4796],{"className":4797,"style":2036},[1863],[1807,4799,4801,4805,4809,4812,4815],{"className":4800},[1956],[1807,4802],{"className":4803,"style":4804},[1960],"height:0.6667em;vertical-align:-0.0833em;",[1807,4806,4710],{"className":4807,"style":4808},[1965,1977],"margin-right:0.0037em;",[1807,4810],{"className":4811,"style":2647},[1863],[1807,4813,2516],{"className":4814},[2248],[1807,4816],{"className":4817,"style":2647},[1863],[1807,4819,4821,4824,4828,4831,4834,4837],{"className":4820},[1956],[1807,4822],{"className":4823,"style":4741},[1960],[1807,4825,4715],{"className":4826,"style":4827},[1965,1977],"margin-right:0.0528em;",[1807,4829,1848],{"className":4830},[1965,1977],[1807,4832],{"className":4833,"style":2647},[1863],[1807,4835,2516],{"className":4836},[2248],[1807,4838],{"className":4839,"style":2647},[1863],[1807,4841,4843,4847,4887],{"className":4842},[1956],[1807,4844],{"className":4845,"style":4846},[1960],"height:0.625em;vertical-align:-0.1944em;",[1807,4848,4850,4853],{"className":4849},[1965],[1807,4851,4724],{"className":4852},[1965,1977],[1807,4854,4856],{"className":4855},[1982],[1807,4857,4859,4879],{"className":4858},[1986,1987],[1807,4860,4862,4876],{"className":4861},[1991],[1807,4863,4865],{"className":4864,"style":1996},[1995],[1807,4866,4867,4870],{"style":2447},[1807,4868],{"className":4869,"style":2004},[2003],[1807,4871,4873],{"className":4872},[2008,2009,2010,2011],[1807,4874,1848],{"className":4875},[1965,1977,2011],[1807,4877,2019],{"className":4878},[2018],[1807,4880,4882],{"className":4881},[1991],[1807,4883,4885],{"className":4884,"style":2026},[1995],[1807,4886],{},[1807,4888,1861],{"className":4889},[2056],[1807,4891,4893],{"className":4892},[1810],[1807,4894,4896,4946],{"className":4895},[1814],[1807,4897,4899],{"className":4898},[1818],[1820,4900,4901],{"xmlns":1822,"display":1823},[1825,4902,4903,4943],{},[1828,4904,4905,4908,4914,4916,4928,4930,4933,4935,4941],{},[3098,4906,4907],{},"difference-stationary: ",[1841,4909,4910,4912],{},[1831,4911,1845],{},[1831,4913,1848],{},[1836,4915,1854],{},[1841,4917,4918,4920],{},[1831,4919,1845],{},[1828,4921,4922,4924,4926],{},[1831,4923,1848],{},[1836,4925,1925],{},[1891,4927,2513],{},[1836,4929,2516],{},[1831,4931,4932],{},"c",[1836,4934,2516],{},[1841,4936,4937,4939],{},[1831,4938,2355],{},[1831,4940,1848],{},[1831,4942,1943],{"mathvariant":1868},[1945,4944,4945],{"encoding":1947},"\\text{difference-stationary: }X_t=X_{t-1}+c+\\varepsilon_t.",[1807,4947,4949,5010,5074,5092],{"className":4948,"ariaHidden":1860},[1952],[1807,4950,4952,4955,4961,5001,5004,5007],{"className":4951},[1956],[1807,4953],{"className":4954,"style":4741},[1960],[1807,4956,4958],{"className":4957},[1965,4745],[1807,4959,4907],{"className":4960},[1965],[1807,4962,4964,4967],{"className":4963},[1965],[1807,4965,1845],{"className":4966,"style":1978},[1965,1977],[1807,4968,4970],{"className":4969},[1982],[1807,4971,4973,4993],{"className":4972},[1986,1987],[1807,4974,4976,4990],{"className":4975},[1991],[1807,4977,4979],{"className":4978,"style":1996},[1995],[1807,4980,4981,4984],{"style":1999},[1807,4982],{"className":4983,"style":2004},[2003],[1807,4985,4987],{"className":4986},[2008,2009,2010,2011],[1807,4988,1848],{"className":4989},[1965,1977,2011],[1807,4991,2019],{"className":4992},[2018],[1807,4994,4996],{"className":4995},[1991],[1807,4997,4999],{"className":4998,"style":2026},[1995],[1807,5000],{},[1807,5002],{"className":5003,"style":2036},[1863],[1807,5005,1854],{"className":5006},[2040],[1807,5008],{"className":5009,"style":2036},[1863],[1807,5011,5013,5016,5065,5068,5071],{"className":5012},[1956],[1807,5014],{"className":5015,"style":2590},[1960],[1807,5017,5019,5022],{"className":5018},[1965],[1807,5020,1845],{"className":5021,"style":1978},[1965,1977],[1807,5023,5025],{"className":5024},[1982],[1807,5026,5028,5057],{"className":5027},[1986,1987],[1807,5029,5031,5054],{"className":5030},[1991],[1807,5032,5034],{"className":5033,"style":2612},[1995],[1807,5035,5036,5039],{"style":1999},[1807,5037],{"className":5038,"style":2004},[2003],[1807,5040,5042],{"className":5041},[2008,2009,2010,2011],[1807,5043,5045,5048,5051],{"className":5044},[1965,2011],[1807,5046,1848],{"className":5047},[1965,1977,2011],[1807,5049,1925],{"className":5050},[2248,2011],[1807,5052,2513],{"className":5053},[1965,2011],[1807,5055,2019],{"className":5056},[2018],[1807,5058,5060],{"className":5059},[1991],[1807,5061,5063],{"className":5062,"style":2261},[1995],[1807,5064],{},[1807,5066],{"className":5067,"style":2647},[1863],[1807,5069,2516],{"className":5070},[2248],[1807,5072],{"className":5073,"style":2647},[1863],[1807,5075,5077,5080,5083,5086,5089],{"className":5076},[1956],[1807,5078],{"className":5079,"style":4804},[1960],[1807,5081,4932],{"className":5082},[1965,1977],[1807,5084],{"className":5085,"style":2647},[1863],[1807,5087,2516],{"className":5088},[2248],[1807,5090],{"className":5091,"style":2647},[1863],[1807,5093,5095,5098,5138],{"className":5094},[1956],[1807,5096],{"className":5097,"style":2426},[1960],[1807,5099,5101,5104],{"className":5100},[1965],[1807,5102,2355],{"className":5103},[1965,1977],[1807,5105,5107],{"className":5106},[1982],[1807,5108,5110,5130],{"className":5109},[1986,1987],[1807,5111,5113,5127],{"className":5112},[1991],[1807,5114,5116],{"className":5115,"style":1996},[1995],[1807,5117,5118,5121],{"style":2447},[1807,5119],{"className":5120,"style":2004},[2003],[1807,5122,5124],{"className":5123},[2008,2009,2010,2011],[1807,5125,1848],{"className":5126},[1965,1977,2011],[1807,5128,2019],{"className":5129},[2018],[1807,5131,5133],{"className":5132},[1991],[1807,5134,5136],{"className":5135,"style":2026},[1995],[1807,5137],{},[1807,5139,1943],{"className":5140},[1965],[1798,5142,5143],{},"After a shock, the first returns toward its deterministic trend; the second carries the shock forward. Detrending is appropriate for the first and differencing for the second. A short sample may not distinguish them cleanly, so report uncertainty rather than declaring a diagnosis from one test.",[1793,5145,5147],{"id":5146},"adf-and-kpss-ask-opposite-questions","ADF and KPSS ask opposite questions",[2305,5149,5150,5163],{},[2308,5151,5152],{},[2311,5153,5154,5157,5160],{},[2314,5155,5156],{},"Test",[2314,5158,5159],{},"Null hypothesis",[2314,5161,5162],{},"A small p-value suggests",[2324,5164,5165,5176],{},[2311,5166,5167,5170,5173],{},[2329,5168,5169],{},"ADF",[2329,5171,5172],{},"a unit root is present",[2329,5174,5175],{},"evidence against a unit root",[2311,5177,5178,5181,5184],{},[2329,5179,5180],{},"KPSS",[2329,5182,5183],{},"the series is level- or trend-stationary",[2329,5185,5186],{},"evidence against stationarity",[1798,5188,5189],{},"Read them with plots, subject knowledge, and break dates. A break can make a stationary regime look like a unit root; low power can make a genuinely persistent process inconclusive.",[5191,5192,5194],"warning",{"title":5193},"The disciplined wording","Do not write “the ADF proves stationarity.” Write: “At the stated deterministic terms and lag choice, the test rejects\u002Fdoes not reject a unit root; plots, KPSS evidence, and break sensitivity lead us to…”",[1793,5196,5198],{"id":5197},"four-case-interpretation","Four-case interpretation",[2305,5200,5201,5212],{},[2308,5202,5203],{},[2311,5204,5205,5207,5209],{},[2314,5206,5169],{},[2314,5208,5180],{},[2314,5210,5211],{},"Reasonable next step",[2324,5213,5214,5225,5234,5243],{},[2311,5215,5216,5219,5222],{},[2329,5217,5218],{},"rejects",[2329,5220,5221],{},"does not reject",[2329,5223,5224],{},"stationary modeling is plausible",[2311,5226,5227,5229,5231],{},[2329,5228,5221],{},[2329,5230,5218],{},[2329,5232,5233],{},"differencing or a unit-root model is plausible",[2311,5235,5236,5238,5240],{},[2329,5237,5218],{},[2329,5239,5218],{},[2329,5241,5242],{},"inspect breaks, nonlinearity, variance, and test specification",[2311,5244,5245,5247,5249],{},[2329,5246,5221],{},[2329,5248,5221],{},[2329,5250,5251],{},"sample may be weakly informative; compare robust alternatives",[1793,5253,5255],{"id":5254},"thirty-minute-diagnostic-routine","Thirty-minute diagnostic routine",[5257,5258,5259,5266,5272,5278,5284,5290,5296,5302],"ol",{},[5260,5261,5262,5265],"li",{},[1802,5263,5264],{},"Name the unit and frequency."," A “lag of 12” means nothing without monthly sampling.",[5260,5267,5268,5271],{},[1802,5269,5270],{},"Plot levels and mark interventions."," A break is not an autocorrelation pattern.",[5260,5273,5274,5277],{},[1802,5275,5276],{},"Compare seasonal positions."," Ask whether January behaves like January.",[5260,5279,5280,5283],{},[1802,5281,5282],{},"Inspect variance against level."," Log only when a proportional interpretation is sensible.",[5260,5285,5286,5289],{},[1802,5287,5288],{},"Compare detrending and differencing."," Explain which shock behavior each assumes.",[5260,5291,5292,5295],{},[1802,5293,5294],{},"Use ADF\u002FKPSS as supporting evidence."," State deterministic terms and lag choice.",[5260,5297,5298,5301],{},[1802,5299,5300],{},"Replot and inspect the transformed series."," Watch for strong negative lag-1 correlation from over-differencing.",[5260,5303,5304,5307],{},[1802,5305,5306],{},"Validate both choices out of sample."," Transformation is part of the model, not a preprocessing fact.",[1793,5309,5311],{"id":5310},"exit-check","Exit check",[1798,5313,5314],{},"For each statement, say true or false and give one sentence:",[5257,5316,5317,5324,5330,5336,5343],{},[5260,5318,5319,5320,5323],{},"A stationary series must be independent. ",[1802,5321,5322],{},"False","—its lag covariance may be non-zero.",[5260,5325,5326,5327,5329],{},"A random walk with zero drift has constant mean, so it is stationary. ",[1802,5328,5322],{},"—its variance grows.",[5260,5331,5332,5333,5335],{},"Seasonal differencing and month indicators express the same assumption. ",[1802,5334,5322],{},"—one removes a seasonal stochastic trend; the other models stable seasonal means.",[5260,5337,5338,5339,5342],{},"Differencing can harm a stationary series. ",[1802,5340,5341],{},"True","—it can inject an MA unit root.",[5260,5344,5345,5346,5348],{},"Passing one unit-root test settles the model. ",[1802,5347,5322],{},"—specification, breaks, power, and the forecast task still matter.",[1798,5350,5351,5352,5357],{},"Continue to ",[5353,5354,5356],"a",{"href":5355},"..\u002F01-stochastic-process\u002F","Stochastic Processes and Stationarity"," for the population language behind these decisions.",{"title":10,"searchDepth":5359,"depth":5359,"links":5360},2,[5361,5362,5363,5364,5365,5366,5367,5368,5369],{"id":1795,"depth":5359,"text":1796},{"id":2302,"depth":5359,"text":2303},{"id":4141,"depth":5359,"text":4142},{"id":4231,"depth":5359,"text":4232},{"id":4677,"depth":5359,"text":4678},{"id":5146,"depth":5359,"text":5147},{"id":5197,"depth":5359,"text":5198},{"id":5254,"depth":5359,"text":5255},{"id":5310,"depth":5359,"text":5311},"A compact diagnostic primer on stable dependence, trends, unit roots, seasonality, and breaks.","md",{"sidebar":5373},{"order":5374},1,true,{"title":955,"description":5370},"TxNGMnyBLH_cOYsxmZyt2RilXOdySDazZM8Flk6jne4",[5379,5381],{"title":949,"path":950,"stem":951,"description":5380,"children":-1},"A matrix-first course in covariance-stationary processes, ARMA equations, linear prediction, likelihood, state space, and spectra.",{"title":959,"path":960,"stem":961,"description":5382,"children":-1},"Represent a stochastic process through finite random vectors, Toeplitz covariance matrices, stationarity, and Wold innovations.",1785754737466]