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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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z=(z_1,\\ldots,z_T)^\\top",[1802,1874,1877,1903],{"className":1875,"ariaHidden":1844},[1876],"katex-html",[1802,1878,1881,1886,1891,1896,1900],{"className":1879},[1880],"base",[1802,1882],{"className":1883,"style":1885},[1884],"strut","height:0.4444em;",[1802,1887,1824],{"className":1888},[1889,1890],"mord","mathbf",[1802,1892],{"className":1893,"style":1895},[1894],"mspace","margin-right:0.2778em;",[1802,1897,1828],{"className":1898},[1899],"mrel",[1802,1901],{"className":1902,"style":1895},[1894],[1802,1904,1906,1910,1914,1972,1976,1980,1984,1987,1990,1993,2035],{"className":1905},[1880],[1802,1907],{"className":1908,"style":1909},[1884],"height:1.0991em;vertical-align:-0.25em;",[1802,1911,1832],{"className":1912},[1913],"mopen",[1802,1915,1917,1922],{"className":1916},[1889],[1802,1918,1824],{"className":1919,"style":1921},[1889,1920],"mathnormal","margin-right:0.044em;",[1802,1923,1926],{"className":1924},[1925],"msupsub",[1802,1927,1931,1963],{"className":1928},[1929,1930],"vlist-t","vlist-t2",[1802,1932,1935,1958],{"className":1933},[1934],"vlist-r",[1802,1936,1940],{"className":1937,"style":1939},[1938],"vlist","height:0.3011em;",[1802,1941,1943,1948],{"style":1942},"top:-2.55em;margin-left:-0.044em;margin-right:0.05em;",[1802,1944],{"className":1945,"style":1947},[1946],"pstrut","height:2.7em;",[1802,1949,1955],{"className":1950},[1951,1952,1953,1954],"sizing","reset-size6","size3","mtight",[1802,1956,1841],{"className":1957},[1889,1954],[1802,1959,1962],{"className":1960},[1961],"vlist-s","​",[1802,1964,1966],{"className":1965},[1934],[1802,1967,1970],{"className":1968,"style":1969},[1938],"height:0.15em;",[1802,1971],{},[1802,1973,1845],{"className":1974},[1975],"mpunct",[1802,1977],{"className":1978,"style":1979},[1894],"margin-right:0.1667em;",[1802,1981,1848],{"className":1982},[1983],"minner",[1802,1985],{"className":1986,"style":1979},[1894],[1802,1988,1845],{"className":1989},[1975],[1802,1991],{"className":1992,"style":1979},[1894],[1802,1994,1996,1999],{"className":1995},[1889],[1802,1997,1824],{"className":1998,"style":1921},[1889,1920],[1802,2000,2002],{"className":2001},[1925],[1802,2003,2005,2027],{"className":2004},[1929,1930],[1802,2006,2008,2024],{"className":2007},[1934],[1802,2009,2012],{"className":2010,"style":2011},[1938],"height:0.3283em;",[1802,2013,2014,2017],{"style":1942},[1802,2015],{"className":2016,"style":1947},[1946],[1802,2018,2020],{"className":2019},[1951,1952,1953,1954],[1802,2021,1857],{"className":2022,"style":2023},[1889,1920,1954],"margin-right:0.1389em;",[1802,2025,1962],{"className":2026},[1961],[1802,2028,2030],{"className":2029},[1934],[1802,2031,2033],{"className":2032,"style":1969},[1938],[1802,2034],{},[1802,2036,2039,2042],{"className":2037},[2038],"mclose",[1802,2040,1863],{"className":2041},[2038],[1802,2043,2045],{"className":2044},[1925],[1802,2046,2048],{"className":2047},[1929],[1802,2049,2051],{"className":2050},[1934],[1802,2052,2055],{"className":2053,"style":2054},[1938],"height:0.8491em;",[1802,2056,2058,2061],{"style":2057},"top:-3.063em;margin-right:0.05em;",[1802,2059],{"className":2060,"style":1947},[1946],[1802,2062,2064],{"className":2063},[1951,1952,1953,1954],[1802,2065,1867],{"className":2066},[1889,1954]," and analysed observations as",[1802,2069,2072],{"className":2070},[2071],"katex-display",[1802,2073,2075,2101],{"className":2074},[1805],[1802,2076,2078],{"className":2077},[1809],[1811,2079,2081],{"xmlns":1813,"display":2080},"block",[1815,2082,2083,2098],{},[1818,2084,2085,2088,2090,2093,2095],{},[1821,2086,2087],{"mathvariant":1823},"y",[1826,2089,1828],{},[1821,2091,2092],{},"M",[1821,2094,1824],{"mathvariant":1823},[1821,2096,2097],{"mathvariant":1866},".",[1869,2099,2100],{"encoding":1871},"\\mathbf y=M\\mathbf z.",[1802,2102,2104,2124],{"className":2103,"ariaHidden":1844},[1876],[1802,2105,2107,2111,2115,2118,2121],{"className":2106},[1880],[1802,2108],{"className":2109,"style":2110},[1884],"height:0.6389em;vertical-align:-0.1944em;",[1802,2112,2087],{"className":2113,"style":2114},[1889,1890],"margin-right:0.016em;",[1802,2116],{"className":2117,"style":1895},[1894],[1802,2119,1828],{"className":2120},[1899],[1802,2122],{"className":2123,"style":1895},[1894],[1802,2125,2127,2131,2135,2138],{"className":2126},[1880],[1802,2128],{"className":2129,"style":2130},[1884],"height:0.6833em;",[1802,2132,2092],{"className":2133,"style":2134},[1889,1920],"margin-right:0.109em;",[1802,2136,1824],{"className":2137},[1889,1890],[1802,2139,2097],{"className":2140},[1889],[1798,2142,2143,2144,2172],{},"The matrix ",[1802,2145,2147,2160],{"className":2146},[1805],[1802,2148,2150],{"className":2149},[1809],[1811,2151,2152],{"xmlns":1813},[1815,2153,2154,2158],{},[1818,2155,2156],{},[1821,2157,2092],{},[1869,2159,2092],{"encoding":1871},[1802,2161,2163],{"className":2162,"ariaHidden":1844},[1876],[1802,2164,2166,2169],{"className":2165},[1880],[1802,2167],{"className":2168,"style":2130},[1884],[1802,2170,2092],{"className":2171,"style":2134},[1889,1920]," is not preprocessing trivia. It determines the units, timing, and economic meaning of every coefficient that follows.",[1793,2174,2176],{"id":2175},"finance-from-recorded-price-to-investable-return","Finance: from recorded price to investable return",[1798,2178,2179,2180,2255],{},"For an adjusted price 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the log return is",[1802,2257,2259],{"className":2258},[2071],[1802,2260,2262,2316],{"className":2261},[1805],[1802,2263,2265],{"className":2264},[1809],[1811,2266,2267],{"xmlns":1813,"display":2080},[1815,2268,2269,2313],{},[1818,2270,2271,2278,2280,2283,2286,2292,2295,2297,2299,2311],{},[1834,2272,2273,2276],{},[1821,2274,2275],{},"r",[1821,2277,2199],{},[1826,2279,1828],{},[1821,2281,2282],{},"log",[1826,2284,2285],{},"⁡",[1834,2287,2288,2290],{},[1821,2289,2196],{},[1821,2291,2199],{},[1826,2293,2294],{},"−",[1821,2296,2282],{},[1826,2298,2285],{},[1834,2300,2301,2303],{},[1821,2302,2196],{},[1818,2304,2305,2307,2309],{},[1821,2306,2199],{},[1826,2308,2294],{},[1839,2310,1841],{},[1821,2312,2097],{"mathvariant":1866},[1869,2314,2315],{"encoding":1871},"r_t=\\log P_t-\\log P_{t-1}.",[1802,2317,2319,2377,2447],{"className":2318,"ariaHidden":1844},[1876],[1802,2320,2322,2326,2368,2371,2374],{"className":2321},[1880],[1802,2323],{"className":2324,"style":2325},[1884],"height:0.5806em;vertical-align:-0.15em;",[1802,2327,2329,2333],{"className":2328},[1889],[1802,2330,2275],{"className":2331,"style":2332},[1889,1920],"margin-right:0.0278em;",[1802,2334,2336],{"className":2335},[1925],[1802,2337,2339,2360],{"className":2338},[1929,1930],[1802,2340,2342,2357],{"className":2341},[1934],[1802,2343,2345],{"className":2344,"style":2231},[1938],[1802,2346,2348,2351],{"style":2347},"top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;",[1802,2349],{"className":2350,"style":1947},[1946],[1802,2352,2354],{"className":2353},[1951,1952,1953,1954],[1802,2355,2199],{"className":2356},[1889,1920,1954],[1802,2358,1962],{"className":2359},[1961],[1802,2361,2363],{"className":2362},[1934],[1802,2364,2366],{"className":2365,"style":1969},[1938],[1802,2367],{},[1802,2369],{"className":2370,"style":1895},[1894],[1802,2372,1828],{"className":2373},[1899],[1802,2375],{"className":2376,"style":1895},[1894],[1802,2378,2380,2384,2393,2396,2436,2440,2444],{"className":2379},[1880],[1802,2381],{"className":2382,"style":2383},[1884],"height:0.8889em;vertical-align:-0.1944em;",[1802,2385,2388,2389],{"className":2386},[2387],"mop","lo",[1802,2390,2392],{"style":2391},"margin-right:0.0139em;","g",[1802,2394],{"className":2395,"style":1979},[1894],[1802,2397,2399,2402],{"className":2398},[1889],[1802,2400,2196],{"className":2401,"style":2023},[1889,1920],[1802,2403,2405],{"className":2404},[1925],[1802,2406,2408,2428],{"className":2407},[1929,1930],[1802,2409,2411,2425],{"className":2410},[1934],[1802,2412,2414],{"className":2413,"style":2231},[1938],[1802,2415,2416,2419],{"style":2234},[1802,2417],{"className":2418,"style":1947},[1946],[1802,2420,2422],{"className":2421},[1951,1952,1953,1954],[1802,2423,2199],{"className":2424},[1889,1920,1954],[1802,2426,1962],{"className":2427},[1961],[1802,2429,2431],{"className":2430},[1934],[1802,2432,2434],{"className":2433,"style":1969},[1938],[1802,2435],{},[1802,2437],{"className":2438,"style":2439},[1894],"margin-right:0.2222em;",[1802,2441,2294],{"className":2442},[2443],"mbin",[1802,2445],{"className":2446,"style":2439},[1894],[1802,2448,2450,2454,2459,2462,2512],{"className":2449},[1880],[1802,2451],{"className":2452,"style":2453},[1884],"height:0.9028em;vertical-align:-0.2083em;",[1802,2455,2388,2457],{"className":2456},[2387],[1802,2458,2392],{"style":2391},[1802,2460],{"className":2461,"style":1979},[1894],[1802,2463,2465,2468],{"className":2464},[1889],[1802,2466,2196],{"className":2467,"style":2023},[1889,1920],[1802,2469,2471],{"className":2470},[1925],[1802,2472,2474,2503],{"className":2473},[1929,1930],[1802,2475,2477,2500],{"className":2476},[1934],[1802,2478,2480],{"className":2479,"style":1939},[1938],[1802,2481,2482,2485],{"style":2234},[1802,2483],{"className":2484,"style":1947},[1946],[1802,2486,2488],{"className":2487},[1951,1952,1953,1954],[1802,2489,2491,2494,2497],{"className":2490},[1889,1954],[1802,2492,2199],{"className":2493},[1889,1920,1954],[1802,2495,2294],{"className":2496},[2443,1954],[1802,2498,1841],{"className":2499},[1889,1954],[1802,2501,1962],{"className":2502},[1961],[1802,2504,2506],{"className":2505},[1934],[1802,2507,2510],{"className":2508,"style":2509},[1938],"height:0.2083em;",[1802,2511],{},[1802,2513,2097],{"className":2514},[1889],[1798,2516,2517,2518,2744],{},"If ",[1802,2519,2521,2571],{"className":2520},[1805],[1802,2522,2524],{"className":2523},[1809],[1811,2525,2526],{"xmlns":1813},[1815,2527,2528,2568],{},[1818,2529,2530,2532,2534,2536,2538,2540,2546,2548,2550,2552,2554,2556,2562],{},[1821,2531,1798],{"mathvariant":1823},[1826,2533,1828],{},[1826,2535,1832],{"stretchy":1831},[1821,2537,2282],{},[1826,2539,2285],{},[1834,2541,2542,2544],{},[1821,2543,2196],{},[1839,2545,1841],{},[1826,2547,1845],{"separator":1844},[1826,2549,1848],{},[1826,2551,1845],{"separator":1844},[1821,2553,2282],{},[1826,2555,2285],{},[1834,2557,2558,2560],{},[1821,2559,2196],{},[1821,2561,1857],{},[1859,2563,2564,2566],{},[1826,2565,1863],{"stretchy":1831},[1821,2567,1867],{"mathvariant":1866},[1869,2569,2570],{"encoding":1871},"\\mathbf p=(\\log P_1,\\ldots,\\log 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time:",[1802,3525,3527],{"className":3526},[2071],[1802,3528,3530,3606],{"className":3529},[1805],[1802,3531,3533],{"className":3532},[1809],[1811,3534,3535],{"xmlns":1813,"display":2080},[1815,3536,3537,3603],{},[1818,3538,3539,3557,3570,3572,3574,3576,3578,3590,3593,3599,3601],{},[3540,3541,3542,3545,3554],"munderover",{},[1826,3543,3544],{},"∑",[1818,3546,3547,3550,3552],{},[1821,3548,3549],{},"j",[1826,3551,1828],{},[1839,3553,1841],{},[1821,3555,3556],{},"h",[1834,3558,3559,3561],{},[1821,3560,2275],{},[1818,3562,3563,3565,3568],{},[1821,3564,2199],{},[1826,3566,3567],{},"+",[1821,3569,3549],{},[1826,3571,1828],{},[1821,3573,2282],{},[1826,3575,2285],{},[1826,3577,1832],{"stretchy":1831},[1834,3579,3580,3582],{},[1821,3581,2196],{},[1818,3583,3584,3586,3588],{},[1821,3585,2199],{},[1826,3587,3567],{},[1821,3589,3556],{},[1821,3591,3592],{"mathvariant":1866},"\u002F",[1834,3594,3595,3597],{},[1821,3596,2196],{},[1821,3598,2199],{},[1826,3600,1863],{"stretchy":1831},[1821,3602,2097],{"mathvariant":1866},[1869,3604,3605],{"encoding":1871},"\\sum_{j=1}^{h}r_{t+j}=\\log(P_{t+h}\u002FP_t).",[1802,3607,3609,3756],{"className":3608,"ariaHidden":1844},[1876],[1802,3610,3612,3616,3693,3696,3747,3750,3753],{"className":3611},[1880],[1802,3613],{"className":3614,"style":3615},[1884],"height:3.2499em;vertical-align:-1.4138em;",[1802,3617,3620],{"className":3618},[2387,3619],"op-limits",[1802,3621,3623,3684],{"className":3622},[1929,1930],[1802,3624,3626,3681],{"className":3625},[1934],[1802,3627,3630,3653,3666],{"className":3628,"style":3629},[1938],"height:1.8361em;",[1802,3631,3633,3637],{"style":3632},"top:-1.8723em;margin-left:0em;",[1802,3634],{"className":3635,"style":3636},[1946],"height:3.05em;",[1802,3638,3640],{"className":3639},[1951,1952,1953,1954],[1802,3641,3643,3647,3650],{"className":3642},[1889,1954],[1802,3644,3549],{"className":3645,"style":3646},[1889,1920,1954],"margin-right:0.0572em;",[1802,3648,1828],{"className":3649},[1899,1954],[1802,3651,1841],{"className":3652},[1889,1954],[1802,3654,3656,3659],{"style":3655},"top:-3.05em;",[1802,3657],{"className":3658,"style":3636},[1946],[1802,3660,3661],{},[1802,3662,3544],{"className":3663},[2387,3664,3665],"op-symbol","large-op",[1802,3667,3669,3672],{"style":3668},"top:-4.3em;margin-left:0em;",[1802,3670],{"className":3671,"style":3636},[1946],[1802,3673,3675],{"className":3674},[1951,1952,1953,1954],[1802,3676,3678],{"className":3677},[1889,1954],[1802,3679,3556],{"className":3680},[1889,1920,1954],[1802,3682,1962],{"className":3683},[1961],[1802,3685,3687],{"className":3686},[1934],[1802,3688,3691],{"className":3689,"style":3690},[1938],"height:1.4138em;",[1802,3692],{},[1802,3694],{"className":3695,"style":1979},[1894],[1802,3697,3699,3702],{"className":3698},[1889],[1802,3700,2275],{"className":3701,"style":2332},[1889,1920],[1802,3703,3705],{"className":3704},[1925],[1802,3706,3708,3738],{"className":3707},[1929,1930],[1802,3709,3711,3735],{"className":3710},[1934],[1802,3712,3715],{"className":3713,"style":3714},[1938],"height:0.3117em;",[1802,3716,3717,3720],{"style":2347},[1802,3718],{"className":3719,"style":1947},[1946],[1802,3721,3723],{"className":3722},[1951,1952,1953,1954],[1802,3724,3726,3729,3732],{"className":3725},[1889,1954],[1802,3727,2199],{"className":3728},[1889,1920,1954],[1802,3730,3567],{"className":3731},[2443,1954],[1802,3733,3549],{"className":3734,"style":3646},[1889,1920,1954],[1802,3736,1962],{"className":3737},[1961],[1802,3739,3741],{"className":3740},[1934],[1802,3742,3745],{"className":3743,"style":3744},[1938],"height:0.2861em;",[1802,3746],{},[1802,3748],{"className":3749,"style":1895},[1894],[1802,3751,1828],{"className":3752},[1899],[1802,3754],{"className":3755,"style":1895},[1894],[1802,3757,3759,3763,3768,3771,3821,3824,3864,3867],{"className":3758},[1880],[1802,3760],{"className":3761,"style":3762},[1884],"height:1em;vertical-align:-0.25em;",[1802,3764,2388,3766],{"className":3765},[2387],[1802,3767,2392],{"style":2391},[1802,3769,1832],{"className":3770},[1913],[1802,3772,3774,3777],{"className":3773},[1889],[1802,3775,2196],{"className":3776,"style":2023},[1889,1920],[1802,3778,3780],{"className":3779},[1925],[1802,3781,3783,3813],{"className":3782},[1929,1930],[1802,3784,3786,3810],{"className":3785},[1934],[1802,3787,3790],{"className":3788,"style":3789},[1938],"height:0.3361em;",[1802,3791,3792,3795],{"style":2234},[1802,3793],{"className":3794,"style":1947},[1946],[1802,3796,3798],{"className":3797},[1951,1952,1953,1954],[1802,3799,3801,3804,3807],{"className":3800},[1889,1954],[1802,3802,2199],{"className":3803},[1889,1920,1954],[1802,3805,3567],{"className":3806},[2443,1954],[1802,3808,3556],{"className":3809},[1889,1920,1954],[1802,3811,1962],{"className":3812},[1961],[1802,3814,3816],{"className":3815},[1934],[1802,3817,3819],{"className":3818,"style":2509},[1938],[1802,3820],{},[1802,3822,3592],{"className":3823},[1889],[1802,3825,3827,3830],{"className":3826},[1889],[1802,3828,2196],{"className":3829,"style":2023},[1889,1920],[1802,3831,3833],{"className":3832},[1925],[1802,3834,3836,3856],{"className":3835},[1929,1930],[1802,3837,3839,3853],{"className":3838},[1934],[1802,3840,3842],{"className":3841,"style":2231},[1938],[1802,3843,3844,3847],{"style":2234},[1802,3845],{"className":3846,"style":1947},[1946],[1802,3848,3850],{"className":3849},[1951,1952,1953,1954],[1802,3851,2199],{"className":3852},[1889,1920,1954],[1802,3854,1962],{"className":3855},[1961],[1802,3857,3859],{"className":3858},[1934],[1802,3860,3862],{"className":3861,"style":1969},[1938],[1802,3863],{},[1802,3865,1863],{"className":3866},[2038],[1802,3868,2097],{"className":3869},[1889],[1798,3871,3872],{},"Before using this identity, resolve:",[3874,3875,3876,3880,3883,3886,3889],"ul",{},[3877,3878,3879],"li",{},"splits and dividends: use a documented total-return or adjusted-price convention;",[3877,3881,3882],{},"non-trading days: calendar time and trading time are not interchangeable;",[3877,3884,3885],{},"bid–ask bounce and asynchronous prices: intraday observations can create mechanical serial dependence;",[3877,3887,3888],{},"currency and timezone: a “daily” return must have a common valuation instant;",[3877,3890,3891],{},"survivorship and delisting: today's constituent list cannot define yesterday's investable universe.",[1798,3893,3894],{},"Arithmetic returns compound rather than add:",[1802,3896,3898],{"className":3897},[2071],[1802,3899,3901,3972],{"className":3900},[1805],[1802,3902,3904],{"className":3903},[1809],[1811,3905,3906],{"xmlns":1813,"display":2080},[1815,3907,3908,3969],{},[1818,3909,3910,3927,3929,3944,3946,3948,3950,3962,3964,3966],{},[1834,3911,3912,3915],{},[1821,3913,3914],{},"R",[1818,3916,3917,3919,3921,3923,3925],{},[1821,3918,2199],{},[1826,3920,1845],{"separator":1844},[1821,3922,2199],{},[1826,3924,3567],{},[1821,3926,3556],{},[1826,3928,1828],{},[3540,3930,3931,3934,3942],{},[1826,3932,3933],{},"∏",[1818,3935,3936,3938,3940],{},[1821,3937,3549],{},[1826,3939,1828],{},[1839,3941,1841],{},[1821,3943,3556],{},[1826,3945,1832],{"stretchy":1831},[1839,3947,1841],{},[1826,3949,3567],{},[1834,3951,3952,3954],{},[1821,3953,3914],{},[1818,3955,3956,3958,3960],{},[1821,3957,2199],{},[1826,3959,3567],{},[1821,3961,3549],{},[1826,3963,1863],{"stretchy":1831},[1826,3965,2294],{},[1839,3967,3968],{},"1.",[1869,3970,3971],{"encoding":1871},"R_{t,t+h}=\\prod_{j=1}^h(1+R_{t+j})-1.",[1802,3973,3975,4048,4133,4201],{"className":3974,"ariaHidden":1844},[1876],[1802,3976,3978,3982,4039,4042,4045],{"className":3977},[1880],[1802,3979],{"className":3980,"style":3981},[1884],"height:0.9694em;vertical-align:-0.2861em;",[1802,3983,3985,3989],{"className":3984},[1889],[1802,3986,3914],{"className":3987,"style":3988},[1889,1920],"margin-right:0.0077em;",[1802,3990,3992],{"className":3991},[1925],[1802,3993,3995,4031],{"className":3994},[1929,1930],[1802,3996,3998,4028],{"className":3997},[1934],[1802,3999,4001],{"className":4000,"style":3789},[1938],[1802,4002,4004,4007],{"style":4003},"top:-2.55em;margin-left:-0.0077em;margin-right:0.05em;",[1802,4005],{"className":4006,"style":1947},[1946],[1802,4008,4010],{"className":4009},[1951,1952,1953,1954],[1802,4011,4013,4016,4019,4022,4025],{"className":4012},[1889,1954],[1802,4014,2199],{"className":4015},[1889,1920,1954],[1802,4017,1845],{"className":4018},[1975,1954],[1802,4020,2199],{"className":4021},[1889,1920,1954],[1802,4023,3567],{"className":4024},[2443,1954],[1802,4026,3556],{"className":4027},[1889,1920,1954],[1802,4029,1962],{"className":4030},[1961],[1802,4032,4034],{"className":4033},[1934],[1802,4035,4037],{"className":4036,"style":3744},[1938],[1802,4038],{},[1802,4040],{"className":4041,"style":1895},[1894],[1802,4043,1828],{"className":4044},[1899],[1802,4046],{"className":4047,"style":1895},[1894],[1802,4049,4051,4054,4118,4121,4124,4127,4130],{"className":4050},[1880],[1802,4052],{"className":4053,"style":3615},[1884],[1802,4055,4057],{"className":4056},[2387,3619],[1802,4058,4060,4110],{"className":4059},[1929,1930],[1802,4061,4063,4107],{"className":4062},[1934],[1802,4064,4066,4086,4096],{"className":4065,"style":3629},[1938],[1802,4067,4068,4071],{"style":3632},[1802,4069],{"className":4070,"style":3636},[1946],[1802,4072,4074],{"className":4073},[1951,1952,1953,1954],[1802,4075,4077,4080,4083],{"className":4076},[1889,1954],[1802,4078,3549],{"className":4079,"style":3646},[1889,1920,1954],[1802,4081,1828],{"className":4082},[1899,1954],[1802,4084,1841],{"className":4085},[1889,1954],[1802,4087,4088,4091],{"style":3655},[1802,4089],{"className":4090,"style":3636},[1946],[1802,4092,4093],{},[1802,4094,3933],{"className":4095},[2387,3664,3665],[1802,4097,4098,4101],{"style":3668},[1802,4099],{"className":4100,"style":3636},[1946],[1802,4102,4104],{"className":4103},[1951,1952,1953,1954],[1802,4105,3556],{"className":4106},[1889,1920,1954],[1802,4108,1962],{"className":4109},[1961],[1802,4111,4113],{"className":4112},[1934],[1802,4114,4116],{"className":4115,"style":3690},[1938],[1802,4117],{},[1802,4119,1832],{"className":4120},[1913],[1802,4122,1841],{"className":4123},[1889],[1802,4125],{"className":4126,"style":2439},[1894],[1802,4128,3567],{"className":4129},[2443],[1802,4131],{"className":4132,"style":2439},[1894],[1802,4134,4136,4140,4189,4192,4195,4198],{"className":4135},[1880],[1802,4137],{"className":4138,"style":4139},[1884],"height:1.0361em;vertical-align:-0.2861em;",[1802,4141,4143,4146],{"className":4142},[1889],[1802,4144,3914],{"className":4145,"style":3988},[1889,1920],[1802,4147,4149],{"className":4148},[1925],[1802,4150,4152,4181],{"className":4151},[1929,1930],[1802,4153,4155,4178],{"className":4154},[1934],[1802,4156,4158],{"className":4157,"style":3714},[1938],[1802,4159,4160,4163],{"style":4003},[1802,4161],{"className":4162,"style":1947},[1946],[1802,4164,4166],{"className":4165},[1951,1952,1953,1954],[1802,4167,4169,4172,4175],{"className":4168},[1889,1954],[1802,4170,2199],{"className":4171},[1889,1920,1954],[1802,4173,3567],{"className":4174},[2443,1954],[1802,4176,3549],{"className":4177,"style":3646},[1889,1920,1954],[1802,4179,1962],{"className":4180},[1961],[1802,4182,4184],{"className":4183},[1934],[1802,4185,4187],{"className":4186,"style":3744},[1938],[1802,4188],{},[1802,4190,1863],{"className":4191},[2038],[1802,4193],{"className":4194,"style":2439},[1894],[1802,4196,2294],{"classN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sums with compounding is a units error, not a model-choice error.",[1793,4215,4217],{"id":4216},"economics-levels-growth-gaps-and-releases","Economics: levels, growth, gaps, and releases",[1798,4219,4220,4221,4293],{},"For a positive level 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common targets include:",[1802,4295,4297],{"className":4296},[2071],[1802,4298,4300,4385],{"className":4299},[1805],[1802,4301,4303],{"className":4302},[1809],[1811,4304,4305],{"xmlns":1813,"display":2080},[1815,4306,4307,4382],{},[1818,4308,4309,4324,4326,4329,4332,4334,4336,4342,4344,4346,4361,4363,4365,4368,4370,4372,4374,4380],{},[4310,4311,4312,4314,4316],"msubsup",{},[1821,4313,2392],{},[1821,4315,2199],{},[1818,4317,4318,4320,4322],{},[1826,4319,1832],{"stretchy":1831},[1839,4321,1841],{},[1826,4323,1863],{"stretchy":1831},[1826,4325,1828],{},[1839,4327,4328],{},"100",[1821,4330,4331],{"mathvariant":1866},"Δ",[1821,4333,2282],{},[1826,4335,2285],{},[1834,4337,4338,4340],{},[1821,4339,4237],{},[1821,4341,2199],{},[1826,4343,1845],{"separator":1844},[1894,4345],{"width":2773},[4310,4347,4348,4350,4352],{},[1821,4349,2392],{},[1821,4351,2199],{},[1818,4353,4354,4356,4359],{},[1826,4355,1832],{"stretchy":1831},[1821,4357,4358],{},"a",[1826,4360,1863],{"stretchy":1831},[1826,4362,1828],{},[1839,4364,4328],{},[1821,4366,4367],{},"m",[1821,4369,4331],{"mathvariant":1866},[1821,4371,2282],{},[1826,4373,2285],{},[1834,4375,4376,4378],{},[1821,4377,4237],{},[1821,4379,2199],{},[1826,4381,1845],{"separator":1844},[1869,4383,4384],{"encoding":1871},"g_t^{(1)}=100\\Delta\\log Y_t,\n\\qquad\ng_t^{(a)}=100m\\Delta\\log Y_t,",[1802,4386,4388,4469,4608],{"className":4387,"ariaHidden":1844},[1876],[1802,4389,4391,4395,4460,4463,4466],{"className":4390},[1880],[1802,4392],{"className":4393,"style":4394},[1884],"height:1.2906em;vertical-align:-0.2458em;",[1802,4396,4398,4402],{"className":4397},[1889],[1802,4399,2392],{"className":4400,"style":4401},[1889,1920],"margin-right:0.0359em;",[1802,4403,4405],{"className":4404},[1925],[1802,4406,4408,4451],{"className":4407},[1929,1930],[1802,4409,4411,4448],{"className":4410},[1934],[1802,4412,4415,4427],{"className":4413,"style":4414},[1938],"height:1.0448em;",[1802,4416,4418,4421],{"style":4417},"top:-2.4542em;margin-left:-0.0359em;margin-right:0.05em;",[1802,4419],{"className":4420,"style":1947},[1946],[1802,4422,4424],{"className":4423},[1951,1952,1953,1954],[1802,4425,2199],{"className":4426},[1889,1920,1954],[1802,4428,4430,4433],{"style":4429},"top:-3.2198em;margin-right:0.05em;",[1802,4431],{"className":4432,"style":1947},[1946],[1802,4434,4436],{"className":4435},[1951,1952,1953,1954],[1802,4437,4439,4442,4445],{"className":4438},[1889,1954],[1802,4440,1832],{"className":4441},[1913,1954],[1802,4443,1841],{"className":4444},[1889,1954],[1802,4446,1863],{"className":4447},[2038,1954],[1802,4449,1962],{"className":4450},[1961],[1802,4452,4454],{"className":4453},[1934],[1802,4455,4458],{"className":4456,"style":4457},[1938],"height:0.2458em;",[1802,4459],{},[1802,4461],{"className":4462,"style":1895},[1894],[1802,4464,1828],{"className":4465},[1899],[1802,4467],{"className":4468,"style":1895},[1894],[1802,4470,4472,4475,4479,4482,4487,4490,4530,4533,4536,4539,4599,4602,4605],{"className":4471},[1880],[1802,4473],{"className":4474,"style":4394},[1884],[1802,4476,4478],{"className":4477},[1889],"100Δ",[1802,4480],{"className":4481,"style":1979},[1894],[1802,4483,2388,4485],{"className":4484},[2387],[1802,4486,2392],{"style":2391},[1802,4488],{"className":4489,"style":1979},[1894],[1802,4491,4493,4496],{"className":4492},[1889],[1802,4494,4237],{"className":4495,"style":2439},[1889,1920],[1802,4497,4499],{"className":4498},[1925],[1802,4500,4502,4522],{"className":4501},[1929,1930],[1802,4503,4505,4519],{"className":4504},[1934],[1802,4506,4508],{"className":4507,"style":2231},[1938],[1802,4509,4510,4513],{"style":4272},[1802,4511],{"className":4512,"style":1947},[1946],[1802,4514,4516],{"className":4515},[1951,1952,1953,1954],[1802,4517,2199],{"className":4518},[1889,1920,1954],[1802,4520,1962],{"className":4521},[1961],[1802,4523,4525],{"className":4524},[1934],[1802,4526,4528],{"className":4527,"style":1969},[1938],[1802,4529],{},[1802,4531,1845],{"className":4532},[1975],[1802,4534],{"className":4535,"style":3000},[1894],[1802,4537],{"className":4538,"style":1979},[1894],[1802,4540,4542,4545],{"className":4541},[1889],[1802,4543,2392],{"className":4544,"style":4401},[1889,1920],[1802,4546,4548],{"className":4547},[1925],[1802,4549,4551,4591],{"className":4550},[1929,1930],[1802,4552,4554,4588],{"className":4553},[1934],[1802,4555,4557,4568],{"className":4556,"style":4414},[1938],[1802,4558,4559,4562],{"style":4417},[1802,4560],{"className":4561,"style":1947},[1946],[1802,4563,4565],{"className":4564},[1951,1952,1953,1954],[1802,4566,2199],{"className":4567},[1889,1920,1954],[1802,4569,4570,4573],{"style":4429},[1802,4571],{"className":4572,"style":1947},[1946],[1802,4574,4576],{"className":4575},[1951,1952,1953,1954],[1802,4577,4579,4582,4585],{"className":4578},[1889,1954],[1802,4580,1832],{"className":4581},[1913,1954],[1802,4583,4358],{"className":4584},[1889,1920,1954],[1802,4586,1863],{"className":4587},[2038,1954],[1802,4589,1962],{"className":4590},[1961],[1802,4592,4594],{"className":4593},[1934],[1802,4595,4597],{"className":4596,"style":4457},[1938],[1802,4598],{},[1802,4600],{"className":4601,"style":1895},[1894],[1802,4603,1828],{"className":4604},[1899],[1802,4606],{"className":4607,"style":1895},[1894],[1802,4609,4611,4614,4617,4620,4623,4626,4631,4634,4674],{"className":4610},[1880],[1802,4612],{"className":4613,"style":2383},[1884],[1802,4615,4328],{"className":4616},[1889],[1802,4618,4367],{"className":4619},[1889,1920],[1802,4621,4331],{"className":4622},[1889],[1802,4624],{"className":4625,"style":1979},[1894],[1802,4627,2388,4629],{"className":4628},[2387],[1802,4630,2392],{"style":2391},[1802,4632],{"className":4633,"style":1979},[1894],[1802,4635,4637,4640],{"className":4636},[1889],[1802,4638,4237],{"className":4639,"style":2439},[1889,1920],[1802,4641,4643],{"className":4642},[1925],[1802,4644,4646,4666],{"className":4645},[1929,1930],[1802,4647,4649,4663],{"className":4648},[1934],[1802,4650,4652],{"className":4651,"style":2231},[1938],[1802,4653,4654,4657],{"style":4272},[1802,4655],{"className":4656,"style":1947},[1946],[1802,4658,4660],{"className":4659},[1951,1952,1953,1954],[1802,4661,2199],{"className":4662},[1889,1920,1954],[1802,4664,1962],{"className":4665},[1961],[1802,4667,4669],{"className":4668},[1934],[1802,4670,4672],{"className":4671,"style":1969},[1938],[1802,4673],{},[1802,4675,1845],{"className":4676},[1975],[1798,4678,4679,4680,4733,4734,4786],{},"where ",[1802,4681,4683,4702],{"className":4682},[1805],[1802,4684,4686],{"className":4685},[1809],[1811,4687,4688],{"xmlns":1813},[1815,4689,4690,4699],{},[1818,4691,4692,4694,4696],{},[1821,4693,4367],{},[1826,4695,1828],{},[1839,4697,4698],{},"12",[1869,4700,4701],{"encoding":1871},"m=12",[1802,4703,4705,4724],{"className":4704,"ariaHidden":1844},[1876],[1802,4706,4708,4712,4715,4718,4721],{"className":4707},[1880],[1802,4709],{"className":4710,"style":4711},[1884],"height:0.4306em;",[1802,4713,4367],{"className":4714},[1889,1920],[1802,4716],{"className":4717,"style":1895},[1894],[1802,4719,1828],{"className":4720},[1899],[1802,4722],{"className":4723,"style":1895},[1894],[1802,4725,4727,4730],{"className":4726},[1880],[1802,4728],{"className":4729,"style":4207},[1884],[1802,4731,4698],{"className":4732},[1889]," for annualised monthly growth and ",[1802,4735,4737,4756],{"className":4736},[1805],[1802,4738,4740],{"className":4739},[1809],[1811,4741,4742],{"xmlns":1813},[1815,4743,4744,4753],{},[1818,4745,4746,4748,4750],{},[1821,4747,4367],{},[1826,4749,1828],{},[1839,4751,4752],{},"4",[1869,4754,4755],{"encoding":1871},"m=4",[1802,4757,4759,4777],{"className":4758,"ariaHidden":1844},[1876],[1802,4760,4762,4765,4768,4771,4774],{"className":4761},[1880],[1802,4763],{"className":4764,"style":4711},[1884],[1802,4766,4367],{"className":4767},[1889,1920],[1802,4769],{"className":4770,"style":1895},[1894],[1802,4772,1828],{"className":4773},[1899],[1802,4775],{"className":4776,"style":1895},[1894],[1802,4778,4780,4783],{"className":4779},[1880],[1802,4781],{"className":4782,"style":4207},[1884],[1802,4784,4752],{"className":4785},[1889]," for annualised quarterly growth. Year-over-year growth is instead",[1802,4788,4790],{"className":4789},[2071],[1802,4791,4793,4861],{"className":4792},[1805],[1802,4794,4796],{"className":4795},[1809],[1811,4797,4798],{"xmlns":1813,"display":2080},[1815,4799,4800,4858],{},[1818,4801,4802,4820,4822,4824,4826,4828,4830,4836,4838,4840,4842,4854,4856],{},[4310,4803,4804,4806,4808],{},[1821,4805,2392],{},[1821,4807,2199],{},[1818,4809,4810,4812,4814,4816,4818],{},[1826,4811,1832],{"stretchy":1831},[1821,4813,2087],{},[1821,4815,3592],{"mathvariant":1866},[1821,4817,2087],{},[1826,4819,1863],{"stretchy":1831},[1826,4821,1828],{},[1839,4823,4328],{},[1826,4825,1832],{"stretchy":1831},[1821,4827,2282],{},[1826,4829,2285],{},[1834,4831,4832,4834],{},[1821,4833,4237],{},[1821,4835,2199],{},[1826,4837,2294],{},[1821,4839,2282],{},[1826,4841,2285],{},[1834,4843,4844,4846],{},[1821,4845,4237],{},[1818,4847,4848,4850,4852],{},[1821,4849,2199],{},[1826,4851,2294],{},[1821,4853,4367],{},[1826,4855,1863],{"stretchy":1831},[1821,4857,2097],{"mathvariant":1866},[1869,4859,4860],{"encoding":1871},"g_t^{(y\u002Fy)}=100(\\log Y_t-\\log Y_{t-m}).",[1802,4862,4864,4945,5014],{"className":4863,"ariaHidden":1844},[1876],[1802,4865,4867,4870,4936,4939,4942],{"className":4866},[1880],[1802,4868],{"className":4869,"style":4394},[1884],[1802,4871,4873,4876],{"className":4872},[1889],[1802,4874,2392],{"className":4875,"style":4401},[1889,1920],[1802,4877,4879],{"className":4878},[1925],[1802,4880,4882,4928],{"className":4881},[1929,1930],[1802,4883,4885,4925],{"className":4884},[1934],[1802,4886,4888,4899],{"className":4887,"style":4414},[1938],[1802,4889,4890,4893],{"style":4417},[1802,4891],{"className":4892,"style":1947},[1946],[1802,4894,4896],{"className":4895},[1951,1952,1953,1954],[1802,4897,2199],{"className":4898},[1889,1920,1954],[1802,4900,4901,4904],{"style":4429},[1802,4902],{"className":4903,"style":1947},[1946],[1802,4905,4907],{"className":4906},[1951,1952,1953,1954],[1802,4908,4910,4913,4916,4919,4922],{"className":4909},[1889,1954],[1802,4911,1832],{"className":4912},[1913,1954],[1802,4914,2087],{"className":4915,"style":4401},[1889,1920,1954],[1802,4917,3592],{"className":4918},[1889,1954],[1802,4920,2087],{"className":4921,"style":4401},[1889,1920,1954],[1802,4923,1863],{"className":4924},[2038,1954],[1802,4926,1962],{"className":4927},[1961],[1802,4929,4931],{"className":4930},[1934],[1802,4932,4934],{"className":4933,"style":4457},[1938],[1802,4935],{},[1802,4937],{"className":4938,"style":1895},[1894],[1802,4940,1828],{"className":4941},[1899],[1802,4943],{"className":4944,"style":1895},[1894],[1802,4946,4948,4951,4954,4957,4962,4965,5005,5008,5011],{"className":4947},[1880],[1802,4949],{"className":4950,"style":3762},[1884],[1802,4952,4328],{"className":4953},[1889],[1802,4955,1832],{"className":4956},[1913],[1802,4958,2388,4960],{"className":4959},[2387],[1802,4961,2392],{"style":2391},[1802,4963],{"className":4964,"style":1979},[1894],[1802,4966,4968,4971],{"className":4967},[1889],[1802,4969,4237],{"className":4970,"style":2439},[1889,1920],[1802,4972,4974],{"className":4973},[1925],[1802,4975,4977,4997],{"className":4976},[1929,1930],[1802,4978,4980,4994],{"className":4979},[1934],[1802,4981,4983],{"className":4982,"style":2231},[1938],[1802,4984,4985,4988],{"style":4272},[1802,4986],{"className":4987,"style":1947},[1946],[1802,4989,4991],{"className":4990},[1951,1952,1953,1954],[1802,4992,2199],{"className":4993},[1889,1920,1954],[1802,4995,1962],{"className":4996},[1961],[1802,4998,5000],{"className":4999},[1934],[1802,5001,5003],{"className":5002,"style":1969},[1938],[1802,5004],{},[1802,5006],{"className":5007,"style":2439},[1894],[1802,5009,2294],{"className":5010},[2443],[1802,5012],{"className":5013,"style":2439},[1894],[1802,5015,5017,5020,5025,5028,5077,5080],{"className":5016},[1880],[1802,5018],{"className":5019,"style":3762},[1884],[1802,5021,2388,5023],{"className":5022},[2387],[1802,5024,2392],{"style":2391},[1802,5026],{"className":5027,"style":1979},[1894],[1802,5029,5031,5034],{"className":5030},[1889],[1802,5032,4237],{"className":5033,"style":2439},[1889,1920],[1802,5035,5037],{"className":5036},[1925],[1802,5038,5040,5069],{"className":5039},[1929,1930],[1802,5041,5043,5066],{"className":5042},[1934],[1802,5044,5046],{"className":5045,"style":2231},[1938],[1802,5047,5048,5051],{"style":4272},[1802,5049],{"className":5050,"style":1947},[1946],[1802,5052,5054],{"className":5053},[1951,1952,1953,1954],[1802,5055,5057,5060,5063],{"className":5056},[1889,1954],[1802,5058,2199],{"className":5059},[1889,1920,1954],[1802,5061,2294],{"className":5062},[2443,1954],[1802,5064,4367],{"className":5065},[1889,1920,1954],[1802,5067,1962],{"className":5068},[1961],[1802,5070,5072],{"className":5071},[1934],[1802,5073,5075],{"className":5074,"style":2509},[1938],[1802,5076],{},[1802,5078,1863],{"className":5079},[2038],[1802,5081,2097],{"className":5082},[1889],[1798,5084,5085],{},"These targets answer different questions. Annualising one-period growth rescales the latest pace; year-over-year growth compares levels a year apart and smooths short-run movement.",[1798,5087,5088],{},"For macro data, record three dates:",[5090,5091,5092,5099,5105],"ol",{},[3877,5093,5094,5098],{},[5095,5096,5097],"strong",{},"reference period:"," the month or quarter being measured;",[3877,5100,5101,5104],{},[5095,5102,5103],{},"release date:"," when the estimate became public;",[3877,5106,5107,5110],{},[5095,5108,5109],{},"vintage date:"," which subsequently revised value is stored.",[1798,5112,5113,5119,5120,5125],{},[4358,5114,5118],{"href":5115,"rel":5116},"https:\u002F\u002Falfred.stlouisfed.org\u002Fhelp",[5117],"nofollow","ALFRED"," preserves historical vintages, and the ",[4358,5121,5124],{"href":5122,"rel":5123},"https:\u002F\u002Ffred.stlouisfed.org\u002Fdocs\u002Fapi\u002Ffred\u002Frealtime_period.html",[5117],"FRED real-time-period documentation"," explains why observation dates and real-time dates are separate. A real-time forecast must not use a later revision.",[1793,5127,5129],{"id":5128},"aggregation-is-also-a-matrix","Aggregation is also a matrix",[1798,5131,5132,5133,5205],{},"Suppose monthly growth is ",[1802,5134,5136,5154],{"className":5135},[1805],[1802,5137,5139],{"className":5138},[1809],[1811,5140,5141],{"xmlns":1813},[1815,5142,5143,5151],{},[1818,5144,5145],{},[1834,5146,5147,5149],{},[1821,5148,2392],{"mathvariant":1823},[1821,5150,4367],{},[1869,5152,5153],{"encoding":1871},"\\mathbf g_m",[1802,5155,5157],{"className":5156,"ariaHidden":1844},[1876],[1802,5158,5160,5163],{"className":5159},[1880],[1802,5161],{"className":5162,"style":2110},[1884],[1802,5164,5166,5169],{"className":5165},[1889],[1802,5167,2392],{"className":5168,"style":2114},[1889,1890],[1802,5170,5172],{"className":5171},[1925],[1802,5173,5175,5197],{"className":5174},[1929,1930],[1802,5176,5178,5194],{"className":5177},[1934],[1802,5179,5182],{"className":5180,"style":5181},[1938],"height:0.1514em;",[1802,5183,5185,5188],{"style":5184},"top:-2.55em;margin-left:-0.016em;margin-right:0.05em;",[1802,5186],{"className":5187,"style":1947},[1946],[1802,5189,5191],{"className":5190},[1951,1952,1953,1954],[1802,5192,4367],{"className":5193},[1889,1920,1954],[1802,5195,1962],{"className":5196},[1961],[1802,5198,5200],{"className":5199},[1934],[1802,5201,5203],{"className":5202,"style":1969},[1938],[1802,5204],{},". Quarterly log growth is obtained by summing non-overlapping blocks:",[1802,5207,5209],{"className":5208},[2071],[1802,5210,5212,5393],{"className":5211},[1805],[1802,5213,5215],{"className":5214},[1809],[1811,5216,5217],{"xmlns":1813,"display":2080},[1815,5218,5219,5390],{},[1818,5220,5221,5228,5230,5233,5239,5241,5243,5245,5247,5388],{},[1834,5222,5223,5225],{},[1821,5224,2392],{"mathvariant":1823},[1821,5226,5227],{},"q",[1826,5229,1828],{},[1821,5231,5232],{},"A",[1834,5234,5235,5237],{},[1821,5236,2392],{"mathvariant":1823},[1821,5238,4367],{},[1826,5240,1845],{"separator":1844},[1894,5242],{"width":2773},[1821,5244,5232],{},[1826,5246,1828],{},[1818,5248,5249,5251,5386],{},[1826,5250,2782],{"fence":1844},[2784,5252,5254,5298,5342],{"rowspacing":2786,"columnalign":5253,"columnspacing":2788},"center center center center center center center",[2790,5255,5256,5262,5268,5274,5280,5286,5292],{},[2793,5257,5258],{},[2796,5259,5260],{"scriptlevel":2798,"displaystyle":1831},[1839,5261,1841],{},[2793,5263,5264],{},[2796,5265,5266],{"scriptlevel":2798,"displaystyle":1831},[1839,5267,1841],{},[2793,5269,5270],{},[2796,5271,5272],{"scriptlevel":2798,"displaystyle":1831},[1839,5273,1841],{},[2793,5275,5276],{},[2796,5277,5278],{"scriptlevel":2798,"displaystyle":1831},[1839,5279,2798],{},[2793,5281,5282],{},[2796,5283,5284],{"scriptlevel":2798,"displaystyle":1831},[1839,5285,2798],{},[2793,5287,5288],{},[2796,5289,5290],{"scriptlevel":2798,"displaystyle":1831},[1839,5291,2798],{},[2793,5293,5294],{},[2796,5295,5296],{"scriptlevel":2798,"displaystyle":1831},[1826,5297,2824],{"lspace":2823,"rspace":2823},[2790,5299,5300,5306,5312,5318,5324,5330,5336],{},[2793,5301,5302],{},[2796,5303,5304],{"scriptlevel":2798,"displaystyle":1831},[1839,5305,2798],{},[2793,5307,5308],{},[2796,5309,5310],{"scriptlevel":2798,"displaystyle":1831},[1839,5311,2798],{},[2793,5313,5314],{},[2796,5315,5316],{"scriptlevel":2798,"displaystyle":1831},[1839,5317,2798],{},[2793,5319,5320],{},[2796,5321,5322],{"scriptlevel":2798,"displaystyle":1831},[1839,5323,1841],{},[2793,5325,5326],{},[2796,5327,5328],{"scriptlevel":2798,"displaystyle":1831},[1839,5329,1841],{},[2793,5331,5332],{},[2796,5333,5334],{"scriptlevel":2798,"displaystyle":1831},[1839,5335,1841],{},[2793,5337,5338],{},[2796,5339,5340],{"scriptlevel":2798,"displaystyle":1831},[1826,5341,2824],{"lspace":2823,"rspace":2823},[2790,5343,5344,5356,5362,5368,5374,5380],{},[2793,5345,5346],{},[2796,5347,5348],{"scriptlevel":2798,"displaystyle":1831},[1818,5349,5350,5352],{},[1821,5351,2877],{"mathvariant":1866},[2879,5353,5354],{"height":2823,"voffset":2823},[1894,5355],{"mathbackground":2883,"width":2823,"height":2884},[2793,5357,5358],{},[2796,5359,5360],{"scriptlevel":2798,"displaystyle":1831},[1818,5361],{},[2793,5363,5364],{},[2796,5365,5366],{"scriptlevel":2798,"displaystyle":1831},[1818,5367],{},[2793,5369,5370],{},[2796,5371,5372],{"scriptlevel":2798,"displaystyle":1831},[1818,5373],{},[2793,5375,5376],{},[2796,5377,5378],{"scriptlevel":2798,"displaystyle":1831},[1818,5379],{},[2793,5381,5382],{},[2796,5383,5384],{"scriptlevel":2798,"displaystyle":1831},[1826,5385,2897],{"lspace":2823,"rspace":2823},[1826,5387,2954],{"fence":1844},[1821,5389,2097],{"mathvariant":1866},[1869,5391,5392],{"encoding":1871},"\\mathbf g_q=A\\mathbf g_m,\n\\qquad\nA=\n\\begin{bmatrix}\n1&1&1&0&0&0&\\cdots\\\\\n0&0&0&1&1&1&\\cdots\\\\\n\\vdots&&&&&\\ddots\n\\end{bmatrix}.",[1802,5394,5396,5452,5522],{"className":5395,"ariaHidden":1844},[1876],[1802,5397,5399,5403,5443,5446,5449],{"className":5398},[1880],[1802,5400],{"className":5401,"style":5402},[1884],"height:0.7305em;vertical-align:-0.2861em;",[1802,5404,5406,5409],{"className":5405},[1889],[1802,5407,2392],{"className":5408,"style":2114},[1889,1890],[1802,5410,5412],{"className":5411},[1925],[1802,5413,5415,5435],{"className":5414},[1929,1930],[1802,5416,5418,5432],{"className":5417},[1934],[1802,5419,5421],{"className":5420,"style":5181},[1938],[1802,5422,5423,5426],{"style":5184},[1802,5424],{"className":5425,"style":1947},[1946],[1802,5427,5429],{"className":5428},[1951,1952,1953,1954],[1802,5430,5227],{"className":5431,"style":4401},[1889,1920,1954],[1802,5433,1962],{"className":5434},[1961],[1802,5436,5438],{"className":5437},[1934],[1802,5439,5441],{"className":5440,"style":3744},[1938],[1802,5442],{},[1802,5444],{"className":5445,"style":1895},[1894],[1802,5447,1828],{"className":5448},[1899],[1802,5450],{"className":5451,"style":1895},[1894],[1802,5453,5455,5458,5461,5501,5504,5507,5510,5513,5516,5519],{"className":5454},[1880],[1802,5456],{"className":5457,"style":2987},[1884],[1802,5459,5232],{"className":5460},[1889,1920],[1802,5462,5464,5467],{"className":5463},[1889],[1802,5465,2392],{"className":5466,"style":2114},[1889,1890],[1802,5468,5470],{"className":5469},[1925],[1802,5471,5473,5493],{"className":5472},[1929,1930],[1802,5474,5476,5490],{"className":5475},[1934],[1802,5477,5479],{"className":5478,"style":5181},[1938],[1802,5480,5481,5484],{"style":5184},[1802,5482],{"className":5483,"style":1947},[1946],[1802,5485,5487],{"className":5486},[1951,1952,1953,1954],[1802,5488,4367],{"className":5489},[1889,1920,1954],[1802,5491,1962],{"className":5492},[1961],[1802,5494,5496],{"className":5495},[1934],[1802,5497,5499],{"className":5498,"style":1969},[1938],[1802,5500],{},[1802,5502,1845],{"className":5503},[1975],[1802,5505],{"className":5506,"style":3000},[1894],[1802,5508],{"className":5509,"style":1979},[1894],[1802,5511,5232],{"className":5512},[1889,1920],[1802,5514],{"className":5515,"style":1895},[1894],[1802,5517,1828],{"className":5518},[1899],[1802,5520],{"className":5521,"style":1895},[1894],[1802,5523,5525,5529,6044,6047],{"className":5524},[1880],[1802,5526],{"className":5527,"style":5528},[1884],"height:4.26em;vertical-align:-1.88em;",[1802,5530,5532,5577,6006],{"className":5531},[1983],[1802,5533,5535],{"className":5534},[1913],[1802,5536,5538],{"className":5537},[3032,3033],[1802,5539,5541,5568],{"className":5540},[1929,1930],[1802,5542,5544,5565],{"className":5543},[1934],[1802,5545,5548],{"className":5546,"style":5547},[1938],"height:2.35em;",[1802,5549,5551,5555],{"style":5550},"top:-4.35em;",[1802,5552],{"className":5553,"style":5554},[1946],"height:6.2em;",[1802,5556,5558],{"style":5557},"width:0.667em;height:4.2em;",[3055,5559,5562],{"xmlns":3057,"width":3058,"height":5560,"viewBox":5561},"4.2em","0 0 667 4200",[3062,5563],{"d":5564},"M403 1759 V84 H666 V0 H319 V1759 v600 v1759 v84 h347 v-84\nH403z M403 1759 V0 H319 V1759 v600 v1759 v84 h84z",[1802,5566,1962],{"className":5567},[1961],[1802,5569,5571],{"className":5570},[1934],[1802,5572,5575],{"className":5573,"style":5574},[1938],"height:1.85em;",[1802,5576],{},[1802,5578,5580],{"className":5579},[1889],[1802,5581,5583,5650,5653,5656,5712,5715,5718,5771,5774,5777,5830,5833,5836,5889,5892,5895,5951,5954,5957],{"className":5582},[2784],[1802,5584,5586],{"className":5585},[3086],[1802,5587,5589,5641],{"className":5588},[1929,1930],[1802,5590,5592,5638],{"className":5591},[1934],[1802,5593,5596,5608,5620],{"className":5594,"style":5595},[1938],"height:2.38em;",[1802,5597,5599,5602],{"style":5598},"top:-5.2275em;",[1802,5600],{"className":5601,"style":3103},[1946],[1802,5603,5605],{"className":5604},[1889],[1802,5606,1841],{"className":5607},[1889],[1802,5609,5611,5614],{"style":5610},"top:-4.0275em;",[1802,5612],{"className":5613,"style":3103},[1946],[1802,5615,5617],{"className":5616},[1889],[1802,5618,2798],{"className":5619},[1889],[1802,5621,5623,5626],{"style":5622},"top:-2.1675em;",[1802,5624],{"className":5625,"style":3103},[1946],[1802,5627,5629],{"className":5628},[1889],[1802,5630,5632,5635],{"className":5631},[1889],[1802,5633,2877],{"className":5634},[1889],[1802,5636],{"className":5637,"style":3144},[1889,3143],[1802,5639,1962],{"className":5640},[1961],[1802,5642,5644],{"className":5643},[1934],[1802,5645,5648],{"className":5646,"style":5647},[1938],"height:1.88em;",[1802,5649],{},[1802,5651],{"className":5652,"style":3173},[3172],[1802,5654],{"className":5655,"style":3173},[3172],[1802,5657,5659],{"className":5658},[3086],[1802,5660,5662,5704],{"className":5661},[1929,1930],[1802,5663,5665,5701],{"className":5664},[1934],[1802,5666,5668,5680,5692],{"className":5667,"style":5595},[1938],[1802,5669,5671,5674],{"style":5670},"top:-5.04em;",[1802,5672],{"className":5673,"style":3195},[1946],[1802,5675,5677],{"className":5676},[1889],[1802,5678,1841],{"className":5679},[1889],[1802,5681,5683,5686],{"style":5682},"top:-3.84em;",[1802,5684],{"className":5685,"style":3195},[1946],[1802,5687,5689],{"className":5688},[1889],[1802,5690,2798],{"className":5691},[1889],[1802,5693,5695,5698],{"style":5694},"top:-1.98em;",[1802,5696],{"className":5697,"style":3195},[1946],[1802,5699],{"className":5700},[1889],[1802,5702,1962],{"className":5703},[1961],[1802,5705,5707],{"className":5706},[1934],[1802,5708,5710],{"className":5709,"style":5647},[1938],[1802,5711],{},[1802,5713],{"className":5714,"style":3173},[3172],[1802,5716],{"className":5717,"style":3173},[3172],[1802,5719,5721],{"className":5720},[3086],[1802,5722,5724,5763],{"className":5723},[1929,1930],[1802,5725,5727,5760],{"className":5726},[1934],[1802,5728,5730,5741,5752],{"className":5729,"style":5595},[1938],[1802,5731,5732,5735],{"style":5670},[1802,5733],{"className":5734,"style":3195},[1946],[1802,5736,5738],{"className":5737},[1889],[1802,5739,1841],{"className":5740},[1889],[1802,5742,5743,5746],{"style":5682},[1802,5744],{"className":5745,"style":3195},[1946],[1802,5747,5749],{"className":5748},[1889],[1802,5750,2798],{"className":5751},[1889],[1802,5753,5754,5757],{"style":5694},[1802,5755],{"className":5756,"style":3195},[1946],[1802,5758],{"className":5759},[1889],[1802,5761,1962],{"className":5762},[1961],[1802,5764,5766],{"className":5765},[1934],[1802,5767,5769],{"className":5768,"style":5647},[1938],[1802,5770],{},[1802,5772],{"className":5773,"style":3173},[3172],[1802,5775],{"className":5776,"style":3173},[3172],[1802,5778,5780],{"className":5779},[3086],[1802,5781,5783,5822],{"className":5782},[1929,1930],[1802,5784,5786,5819],{"className":5785},[1934],[1802,5787,5789,5800,5811],{"className":5788,"style":5595},[1938],[1802,5790,5791,5794],{"style":5670},[1802,5792],{"className":5793,"style":3195},[1946],[1802,5795,5797],{"className":5796},[1889],[1802,5798,2798],{"className":5799},[1889],[1802,5801,5802,5805],{"style":5682},[1802,5803],{"className":5804,"style":3195},[1946],[1802,5806,5808],{"className":5807},[1889],[1802,5809,1841],{"className":5810},[1889],[1802,5812,5813,5816],{"style":5694},[1802,5814],{"className":5815,"style":3195},[1946],[1802,5817],{"className":5818},[1889],[1802,5820,1962],{"className":5821},[1961],[1802,5823,5825],{"className":5824},[1934],[1802,5826,5828],{"className":5827,"style":5647},[1938],[1802,5829],{},[1802,5831],{"className":5832,"style":3173},[3172],[1802,5834],{"className":5835,"style":3173},[3172],[1802,5837,5839],{"className":5838},[3086],[1802,5840,5842,5881],{"className":5841},[1929,1930],[1802,5843,5845,5878],{"className":5844},[1934],[1802,5846,5848,5859,5870],{"className":5847,"style":5595},[1938],[1802,5849,5850,5853],{"style":5670},[1802,5851],{"className":5852,"style":3195},[1946],[1802,5854,5856],{"className":5855},[1889],[1802,5857,2798],{"className":5858},[1889],[1802,5860,5861,5864],{"style":5682},[1802,5862],{"className":5863,"style":3195},[1946],[1802,5865,5867],{"className":5866},[1889],[1802,5868,1841],{"className":5869},[1889],[1802,5871,5872,5875],{"style":5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1759 V0 H0 V84 H263 V1759 v600 v1759 H0 v84 H347z\nM347 1759 V0 H263 V1759 v600 v1759 h84z",[1802,6034,1962],{"className":6035},[1961],[1802,6037,6039],{"className":6038},[1934],[1802,6040,6042],{"className":6041,"style":5574},[1938],[1802,6043],{},[1802,6045],{"className":6046,"style":1979},[1894],[1802,6048,2097],{"className":6049},[1889],[1798,6051,6052],{},"Stocks and flows aggregate differently:",[6054,6055,6056,6072],"table",{},[6057,6058,6059],"thead",{},[6060,6061,6062,6066,6069],"tr",{},[6063,6064,6065],"th",{},"Variable",[6063,6067,6068],{},"Economic type",[6063,6070,6071],{},"Typical quarterly mapping",[6073,6074,6075,6087,6098,6109],"tbody",{},[6060,6076,6077,6081,6084],{},[6078,6079,6080],"td",{},"end-of-month interest rate",[6078,6082,6083],{},"stock",[6078,6085,6086],{},"last observation or average, depending on question",[6060,6088,6089,6092,6095],{},[6078,6090,6091],{},"monthly sales",[6078,6093,6094],{},"flow",[6078,6096,6097],{},"sum",[6060,6099,6100,6103,6106],{},[6078,6101,6102],{},"price index",[6078,6104,6105],{},"index",[6078,6107,6108],{},"average level, then compute change with stated convention",[6060,6110,6111,6114,6117],{},[6078,6112,6113],{},"log growth",[6078,6115,6116],{},"rate of change",[6078,6118,6119],{},"sum for exact log change",[1798,6121,6122],{},"There is no universal “convert monthly to quarterly” command.",[1793,6124,6126],{"id":6125},"r-laboratory-make-the-operators-visible","R laboratory: make the operators visible",[6128,6129],"web-r",{"code64":6130,"layout":6131,"locale":7,"title":6132},"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","vertical","Price returns and monthly-to-quarterly aggregation",[1798,6134,6135],{},"The three errors should be at machine precision. The important result is not the printed percentage; it is that the differencing and aggregation claims are explicit linear maps.",[1793,6137,6139],{"id":6138},"worked-choice-level-change-or-gap","Worked choice: level, change, or gap?",[1798,6141,6142],{},"Suppose the question is “Does the yield curve forecast recession?”",[3874,6144,6145,6148,6151,6154],{},[3877,6146,6147],{},"If the predictor is the ten-year minus three-month yield, the level difference is already an economically defined spread.",[3877,6149,6150],{},"If the outcome is quarterly real GDP growth, use a documented growth convention.",[3877,6152,6153],{},"If the outcome is a recession indicator, the model and loss must respect a binary event.",[3877,6155,6156],{},"Differencing the spread merely because it is persistent changes the question from the curve's shape to the change in its shape.",[1798,6158,6159],{},"The transformation should preserve the substantive signal the question names.",[1793,6161,6163],{"id":6162},"transformation-audit","Transformation audit",[1798,6165,6166],{},"Before estimation, write a one-row data contract for every variable:",[6054,6168,6169,6179],{},[6057,6170,6171],{},[6060,6172,6173,6176],{},[6063,6174,6175],{},"Field",[6063,6177,6178],{},"Required statement",[6073,6180,6181,6189,6197,6205,6213,6221,6229,6237],{},[6060,6182,6183,6186],{},[6078,6184,6185],{},"raw source",[6078,6187,6188],{},"provider, series, and access date",[6060,6190,6191,6194],{},[6078,6192,6193],{},"observation unit",[6078,6195,6196],{},"currency, index, percentage points, or return",[6060,6198,6199,6202],{},[6078,6200,6201],{},"reference clock",[6078,6203,6204],{},"calendar, trading, month, quarter",[6060,6206,6207,6210],{},[6078,6208,6209],{},"availability",[6078,6211,6212],{},"release lag and publication timestamp",[6060,6214,6215,6218],{},[6078,6216,6217],{},"revision",[6078,6219,6220],{},"first release, specified vintage, or latest revised",[6060,6222,6223,6226],{},[6078,6224,6225],{},"transformation",[6078,6227,6228],{},"exact formula and order of operations",[6060,6230,6231,6234],{},[6078,6232,6233],{},"missing values",[6078,6235,6236],{},"why absent and how treated",[6060,6238,6239,6242],{},[6078,6240,6241],{},"target horizon",[6078,6243,6244,6245,6274],{},"one period, fixed ",[1802,6246,6248,6261],{"className":6247},[1805],[1802,6249,6251],{"className":6250},[1809],[1811,6252,6253],{"xmlns":1813},[1815,6254,6255,6259],{},[1818,6256,6257],{},[1821,6258,3556],{},[1869,6260,3556],{"encoding":1871},[1802,6262,6264],{"className":6263,"ariaHidden":1844},[1876],[1802,6265,6267,6271],{"className":6266},[1880],[1802,6268],{"className":6269,"style":6270},[1884],"height:0.6944em;",[1802,6272,3556],{"className":6273},[1889,1920],", or cumulative\u002Foverlapping",[1793,6276,6278],{"id":6277},"practice","Practice",[5090,6280,6281,6341,6453],{},[3877,6282,6283,6284,6340],{},"Show that ",[1802,6285,6287,6307],{"className":6286},[1805],[1802,6288,6290],{"className":6289},[1809],[1811,6291,6292],{"xmlns":1813},[1815,6293,6294,6304],{},[1818,6295,6296,6298,6300,6302],{},[1821,6297,2766],{},[1839,6299,1841],{"mathvariant":1823},[1826,6301,1828],{},[1839,6303,2798],{},[1869,6305,6306],{"encoding":1871},"D\\mathbf 1=0",[1802,6308,6310,6331],{"className":6309,"ariaHidden":1844},[1876],[1802,6311,6313,6316,6319,6322,6325,6328],{"className":6312},[1880],[1802,6314],{"className":6315,"style":2130},[1884],[1802,6317,2766],{"className":6318,"style":2332},[1889,1920],[1802,6320,1841],{"className":6321},[1889,1890],[1802,6323],{"className":6324,"style":1895},[1894],[1802,6326,1828],{"className":6327},[1899],[1802,6329],{"className":6330,"style":1895},[1894],[1802,6332,6334,6337],{"className":6333},[1880],[1802,6335],{"className":6336,"style":4207},[1884],[1802,6338,2798],{"className":6339},[1889],". What information does differencing remove?",[3877,6342,6343,6344,6372,6373,6452],{},"Replace the quarterly rows of ",[1802,6345,6347,6360],{"className":6346},[1805],[1802,6348,6350],{"className":6349},[1809],[1811,6351,6352],{"xmlns":1813},[1815,6353,6354,6358],{},[1818,6355,6356],{},[1821,6357,5232],{},[1869,6359,5232],{"encoding":1871},[1802,6361,6363],{"className":6362,"ariaHidden":1844},[1876],[1802,6364,6366,6369],{"className":6365},[1880],[1802,6367],{"className":6368,"style":2130},[1884],[1802,6370,5232],{"className":6371},[1889,1920]," by weights ",[1802,6374,6376,6415],{"className":6375},[1805],[1802,6377,6379],{"className":6378},[1809],[1811,6380,6381],{"xmlns":1813},[1815,6382,6383,6412],{},[1818,6384,6385,6387,6389,6391,6394,6396,6398,6400,6402,6404,6406,6408,6410],{},[1826,6386,1832],{"stretchy":1831},[1839,6388,1841],{},[1821,6390,3592],{"mathvariant":1866},[1839,6392,6393],{},"3",[1826,6395,1845],{"separator":1844},[1839,6397,1841],{},[1821,6399,3592],{"mathvariant":1866},[1839,6401,6393],{},[1826,6403,1845],{"separator":1844},[1839,6405,1841],{},[1821,6407,3592],{"mathvariant":1866},[1839,6409,6393],{},[1826,6411,1863],{"stretchy":1831},[1869,6413,6414],{"encoding":1871},"(1\u002F3,1\u002F3,1\u002F3)",[1802,6416,6418],{"className":6417,"ariaHidden":1844},[1876],[1802,6419,6421,6424,6427,6431,6434,6437,6440,6443,6446,6449],{"className":6420},[1880],[1802,6422],{"className":6423,"style":3762},[1884],[1802,6425,1832],{"className":6426},[1913],[1802,6428,6430],{"className":6429},[1889],"1\u002F3",[1802,6432,1845],{"className":6433},[1975],[1802,6435],{"className":6436,"style":1979},[1894],[1802,6438,6430],{"className":6439},[1889],[1802,6441,1845],{"className":6442},[1975],[1802,6444],{"className":6445,"style":1979},[1894],[1802,6447,6430],{"className":6448},[1889],[1802,6450,1863],{"className":6451},[2038],". Which variables would this suit?",[3877,6454,6455],{},"A backtest formed in January uses a GDP value revised in June. Name the failure.",[6457,6458,6460],"legacy-details",{"title":6459},"Answers",[5090,6461,6462,6545,6548],{},[3877,6463,6464,6465,6544],{},"Every row contains ",[1802,6466,6468,6492],{"className":6467},[1805],[1802,6469,6471],{"className":6470},[1809],[1811,6472,6473],{"xmlns":1813},[1815,6474,6475,6489],{},[1818,6476,6477,6479,6481,6483,6485,6487],{},[1826,6478,2294],{},[1839,6480,1841],{},[1826,6482,3567],{},[1839,6484,1841],{},[1826,6486,1828],{},[1839,6488,2798],{},[1869,6490,6491],{"encoding":1871},"-1+1=0",[1802,6493,6495,6517,6535],{"className":6494,"ariaHidden":1844},[1876],[1802,6496,6498,6502,6505,6508,6511,6514],{"className":6497},[1880],[1802,6499],{"className":6500,"style":6501},[1884],"height:0.7278em;vertical-align:-0.0833em;",[1802,6503,2294],{"className":6504},[1889],[1802,6506,1841],{"className":6507},[1889],[1802,6509],{"className":6510,"style":2439},[1894],[1802,6512,3567],{"className":6513},[2443],[1802,6515],{"className":6516,"style":2439},[1894],[1802,6518,6520,6523,6526,6529,6532],{"className":6519},[1880],[1802,6521],{"className":6522,"style":4207},[1884],[1802,6524,1841],{"className":6525},[1889],[1802,6527],{"className":6528,"style":1895},[1894],[1802,6530,1828],{"className":6531},[1899],[1802,6533],{"className":6534,"style":1895},[1894],[1802,6536,6538,6541],{"className":6537},[1880],[1802,6539],{"className":6540,"style":4207},[1884],[1802,6542,2798],{"className":6543},[1889],"; differencing removes a constant level and loses the initial condition.",[3877,6546,6547],{},"A variable whose quarterly concept is an average stock or index, provided that convention matches the source.",[3877,6549,6550],{},"Look-ahead through data revision: the June vintage was outside January's information set.",[1798,6552,6553,6554,2097],{},"Next: ",[4358,6555,430],{"href":6556},"..\u002F03-predictive-regressions\u002F",{"title":10,"searchDepth":6558,"depth":6558,"links":6559},2,[6560,6561,6562,6563,6564,6565,6566,6567],{"id":1795,"depth":6558,"text":1796},{"id":2175,"depth":6558,"text":2176},{"id":4216,"depth":6558,"text":4217},{"id":5128,"depth":6558,"text":5129},{"id":6125,"depth":6558,"text":6126},{"id":6138,"depth":6558,"text":6139},{"id":6162,"depth":6558,"text":6163},{"id":6277,"depth":6558,"text":6278},"Transform prices and macroeconomic releases with explicit differencing, aggregation, timing, and vintage operators.","md",{"sidebar":6571},{"order":6558},true,{"title":424,"description":6568},"kuBY9JK-nHHvDuXkYW0IaMIOToDH-cGX1FL7VeTLAwQ",[6576,6578],{"title":418,"path":419,"stem":420,"description":6577,"children":-1},"A decision guide to classical statistical, financial, and economic time series, with matched examples and method-selection rules.",{"title":430,"path":431,"stem":432,"description":6579,"children":-1},"Matrix derivations for forecasting regressions, overlapping horizons, persistent predictors, and Newey–West inference.",1785754723768]