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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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",[1830,1831,1834,1863],"span",{"className":1832},[1833],"katex",[1830,1835,1838],{"className":1836},[1837],"katex-mathml",[1839,1840,1842],"math",{"xmlns":1841},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[1843,1844,1845,1858],"semantics",{},[1846,1847,1848],"mrow",{},[1849,1850,1851,1855],"msub",{},[1852,1853,1854],"mi",{},"r",[1852,1856,1857],{},"t",[1859,1860,1862],"annotation",{"encoding":1861},"application\u002Fx-tex","r_t",[1830,1864,1868],{"className":1865,"ariaHidden":1867},[1866],"katex-html","true",[1830,1869,1872,1877],{"className":1870},[1871],"base",[1830,1873],{"className":1874,"style":1876},[1875],"strut","height:0.5806em;vertical-align:-0.15em;",[1830,1878,1881,1886],{"className":1879},[1880],"mord",[1830,1882,1854],{"className":1883,"style":1885},[1880,1884],"mathnormal","margin-right:0.0278em;",[1830,1887,1890],{"className":1888},[1889],"msupsub",[1830,1891,1895,1927],{"className":1892},[1893,1894],"vlist-t","vlist-t2",[1830,1896,1899,1922],{"className":1897},[1898],"vlist-r",[1830,1900,1904],{"className":1901,"style":1903},[1902],"vlist","height:0.2806em;",[1830,1905,1907,1912],{"style":1906},"top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;",[1830,1908],{"className":1909,"style":1911},[1910],"pstrut","height:2.7em;",[1830,1913,1919],{"className":1914},[1915,1916,1917,1918],"sizing","reset-size6","size3","mtight",[1830,1920,1857],{"className":1921},[1880,1884,1918],[1830,1923,1926],{"className":1924},[1925],"vlist-s","​",[1830,1928,1930],{"className":1929},[1898],[1830,1931,1934],{"className":1932,"style":1933},[1902],"height:0.15em;",[1830,1935],{},"，最基本的时间序列模型之一是 ARMA(p, q)：",[1830,1938,1941],{"className":1939},[1940],"katex-display",[1830,1942,1944,2061],{"className":1943},[1833],[1830,1945,1947],{"className":1946},[1837],[1839,1948,1950],{"xmlns":1841,"display":1949},"block",[1843,1951,1952,2058],{},[1846,1953,1954,1960,1964,1967,1970,1989,1996,2009,2011,2027,2034,2047,2049,2055],{},[1849,1955,1956,1958],{},[1852,1957,1854],{},[1852,1959,1857],{},[1961,1962,1963],"mo",{},"=",[1852,1965,1966],{},"c",[1961,1968,1969],{},"+",[1971,1972,1973,1976,1987],"munderover",{},[1961,1974,1975],{},"∑",[1846,1977,1978,1981,1983],{},[1852,1979,1980],{},"i",[1961,1982,1963],{},[1984,1985,1986],"mn",{},"1",[1852,1988,1792],{},[1849,1990,1991,1994],{},[1852,1992,1993],{},"ϕ",[1852,1995,1980],{},[1849,1997,1998,2000],{},[1852,1999,1854],{},[1846,2001,2002,2004,2007],{},[1852,2003,1857],{},[1961,2005,2006],{},"−",[1852,2008,1980],{},[1961,2010,1969],{},[1971,2012,2013,2015,2024],{},[1961,2014,1975],{},[1846,2016,2017,2020,2022],{},[1852,2018,2019],{},"j",[1961,2021,1963],{},[1984,2023,1986],{},[1852,2025,2026],{},"q",[1849,2028,2029,2032],{},[1852,2030,2031],{},"θ",[1852,2033,2019],{},[1849,2035,2036,2039],{},[1852,2037,2038],{},"ϵ",[1846,2040,2041,2043,2045],{},[1852,2042,1857],{},[1961,2044,2006],{},[1852,2046,2019],{},[1961,2048,1969],{},[1849,2050,2051,2053],{},[1852,2052,2038],{},[1852,2054,1857],{},[1961,2056,2057],{"separator":1867},",",[1859,2059,2060],{"encoding":1861}," r_t = c + \\sum_{i=1}^p \\phi_i r_{t-i} + \\sum_{j=1}^q \\theta_j \\epsilon_{t-j} + \\epsilon_t,",[1830,2062,2064,2122,2143,2329,2505],{"className":2063,"ariaHidden":1867},[1866],[1830,2065,2067,2070,2110,2115,2119],{"className":2066},[1871],[1830,2068],{"className":2069,"style":1876},[1875],[1830,2071,2073,2076],{"className":2072},[1880],[1830,2074,1854],{"className":2075,"style":1885},[1880,1884],[1830,2077,2079],{"className":2078},[1889],[1830,2080,2082,2102],{"className":2081},[1893,1894],[1830,2083,2085,2099],{"className":2084},[1898],[1830,2086,2088],{"className":2087,"style":1903},[1902],[1830,2089,2090,2093],{"style":1906},[1830,2091],{"className":2092,"style":1911},[1910],[1830,2094,2096],{"className":2095},[1915,1916,1917,1918],[1830,2097,1857],{"className":2098},[1880,1884,1918],[1830,2100,1926],{"className":2101},[1925],[1830,2103,2105],{"className":2104},[1898],[1830,2106,2108],{"className":2107,"style":1933},[1902],[1830,2109],{},[1830,2111],{"className":2112,"style":2114},[2113],"mspace","margin-right:0.2778em;",[1830,2116,1963],{"className":2117},[2118],"mrel",[1830,2120],{"className":2121,"style":2114},[2113],[1830,2123,2125,2129,2132,2136,2140],{"className":2124},[1871],[1830,2126],{"className":2127,"style":2128},[1875],"height:0.6667em;vertical-align:-0.0833em;",[1830,2130,1966],{"className":2131},[1880,1884],[1830,2133],{"className":2134,"style":2135},[2113],"margin-right:0.2222em;",[1830,2137,1969],{"className":2138},[2139],"mbin",[1830,2141],{"className":2142,"style":2135},[2113],[1830,2144,2146,2150,2224,2228,2270,2320,2323,2326],{"className":2145},[1871],[1830,2147],{"className":2148,"style":2149},[1875],"height:2.9762em;vertical-align:-1.2777em;",[1830,2151,2155],{"className":2152},[2153,2154],"mop","op-limits",[1830,2156,2158,2215],{"className":2157},[1893,1894],[1830,2159,2161,2212],{"className":2160},[1898],[1830,2162,2165,2187,2200],{"className":2163,"style":2164},[1902],"height:1.6985em;",[1830,2166,2168,2172],{"style":2167},"top:-1.8723em;margin-left:0em;",[1830,2169],{"className":2170,"style":2171},[1910],"height:3.05em;",[1830,2173,2175],{"className":2174},[1915,1916,1917,1918],[1830,2176,2178,2181,2184],{"className":2177},[1880,1918],[1830,2179,1980],{"className":2180},[1880,1884,1918],[1830,2182,1963],{"className":2183},[2118,1918],[1830,2185,1986],{"className":2186},[1880,1918],[1830,2188,2190,2193],{"style":2189},"top:-3.05em;",[1830,2191],{"className":2192,"style":2171},[1910],[1830,2194,2195],{},[1830,2196,1975],{"className":2197},[2153,2198,2199],"op-symbol","large-op",[1830,2201,2203,2206],{"style":2202},"top:-4.3471em;margin-left:0em;",[1830,2204],{"className":2205,"style":2171},[1910],[1830,2207,2209],{"className":2208},[1915,1916,1917,1918],[1830,2210,1792],{"className":2211},[1880,1884,1918],[1830,2213,1926],{"className":2214},[1925],[1830,2216,2218],{"className":2217},[1898],[1830,2219,2222],{"className":2220,"style":2221},[1902],"height:1.2777em;",[1830,2223],{},[1830,2225],{"className":2226,"style":2227},[2113],"margin-right:0.1667em;",[1830,2229,2231,2234],{"className":2230},[1880],[1830,2232,1993],{"className":2233},[1880,1884],[1830,2235,2237],{"className":2236},[1889],[1830,2238,2240,2262],{"className":2239},[1893,1894],[1830,2241,2243,2259],{"className":2242},[1898],[1830,2244,2247],{"className":2245,"style":2246},[1902],"height:0.3117em;",[1830,2248,2250,2253],{"style":2249},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[1830,2251],{"className":2252,"style":1911},[1910],[1830,2254,2256],{"className":2255},[1915,1916,1917,1918],[1830,2257,1980],{"className":2258},[1880,1884,1918],[1830,2260,1926],{"className":2261},[1925],[1830,2263,2265],{"className":2264},[1898],[1830,2266,2268],{"className":2267,"style":1933},[1902],[1830,2269],{},[1830,2271,2273,2276],{"className":2272},[1880],[1830,2274,1854],{"className":2275,"style":1885},[1880,1884],[1830,2277,2279],{"className":2278},[1889],[1830,2280,2282,2311],{"className":2281},[1893,1894],[1830,2283,2285,2308],{"className":2284},[1898],[1830,2286,2288],{"className":2287,"style":2246},[1902],[1830,2289,2290,2293],{"style":1906},[1830,2291],{"className":2292,"style":1911},[1910],[1830,2294,2296],{"className":2295},[1915,1916,1917,1918],[1830,2297,2299,2302,2305],{"className":2298},[1880,1918],[1830,2300,1857],{"className":2301},[1880,1884,1918],[1830,2303,2006],{"className":2304},[2139,1918],[1830,2306,1980],{"className":2307},[1880,1884,1918],[1830,2309,1926],{"className":2310},[1925],[1830,2312,2314],{"className":2313},[1898],[1830,2315,2318],{"className":2316,"style":2317},[1902],"height:0.2083em;",[1830,2319],{},[1830,2321],{"className":2322,"style":2135},[2113],[1830,2324,1969],{"className":2325},[2139],[1830,2327],{"className":2328,"style":2135},[2113],[1830,2330,2332,2336,2403,2406,2447,2496,2499,2502],{"className":2331},[1871],[1830,2333],{"className":2334,"style":2335},[1875],"height:3.1123em;vertical-align:-1.4138em;",[1830,2337,2339],{"className":2338},[2153,2154],[1830,2340,2342,2394],{"className":2341},[1893,1894],[1830,2343,2345,2391],{"className":2344},[1898],[1830,2346,2348,2369,2379],{"className":2347,"style":2164},[1902],[1830,2349,2350,2353],{"style":2167},[1830,2351],{"className":2352,"style":2171},[1910],[1830,2354,2356],{"className":2355},[1915,1916,1917,1918],[1830,2357,2359,2363,2366],{"className":2358},[1880,1918],[1830,2360,2019],{"className":2361,"style":2362},[1880,1884,1918],"margin-right:0.0572em;",[1830,2364,1963],{"className":2365},[2118,1918],[1830,2367,1986],{"className":2368},[1880,1918],[1830,2370,2371,2374],{"style":2189},[1830,2372],{"className":2373,"style":2171},[1910],[1830,2375,2376],{},[1830,2377,1975],{"className":2378},[2153,2198,2199],[1830,2380,2381,2384],{"style":2202},[1830,2382],{"className":2383,"style":2171},[1910],[1830,2385,2387],{"className":2386},[1915,1916,1917,1918],[1830,2388,2026],{"className":2389,"style":2390},[1880,1884,1918],"margin-right:0.0359em;",[1830,2392,1926],{"className":2393},[1925],[1830,2395,2397],{"className":2396},[1898],[1830,2398,2401],{"className":2399,"style":2400},[1902],"height:1.4138em;",[1830,2402],{},[1830,2404],{"className":2405,"style":2227},[2113],[1830,2407,2409,2412],{"className":2408},[1880],[1830,2410,2031],{"className":2411,"style":1885},[1880,1884],[1830,2413,2415],{"className":2414},[1889],[1830,2416,2418,2438],{"className":2417},[1893,1894],[1830,2419,2421,2435],{"className":2420},[1898],[1830,2422,2424],{"className":2423,"style":2246},[1902],[1830,2425,2426,2429],{"style":1906},[1830,2427],{"className":2428,"style":1911},[1910],[1830,2430,2432],{"className":2431},[1915,1916,1917,1918],[1830,2433,2019],{"className":2434,"style":2362},[1880,1884,1918],[1830,2436,1926],{"className":2437},[1925],[1830,2439,2441],{"className":2440},[1898],[1830,2442,2445],{"className":2443,"style":2444},[1902],"height:0.2861em;",[1830,2446],{},[1830,2448,2450,2453],{"className":2449},[1880],[1830,2451,2038],{"className":2452},[1880,1884],[1830,2454,2456],{"className":2455},[1889],[1830,2457,2459,2488],{"className":2458},[1893,1894],[1830,2460,2462,2485],{"className":2461},[1898],[1830,2463,2465],{"className":2464,"style":2246},[1902],[1830,2466,2467,2470],{"style":2249},[1830,2468],{"className":2469,"style":1911},[1910],[1830,2471,2473],{"className":2472},[1915,1916,1917,1918],[1830,2474,2476,2479,2482],{"className":2475},[1880,1918],[1830,2477,1857],{"className":2478},[1880,1884,1918],[1830,2480,2006],{"className":2481},[2139,1918],[1830,2483,2019],{"className":2484,"style":2362},[1880,1884,1918],[1830,2486,1926],{"className":2487},[1925],[1830,2489,2491],{"className":2490},[1898],[1830,2492,2494],{"className":2493,"style":2444},[1902],[1830,2495],{},[1830,2497],{"className":2498,"style":2135},[2113],[1830,2500,1969],{"className":2501},[2139],[1830,2503],{"className":2504,"style":2135},[2113],[1830,2506,2508,2512,2552],{"className":2507},[1871],[1830,2509],{"className":2510,"style":2511},[1875],"height:0.625em;vertical-align:-0.1944em;",[1830,2513,2515,2518],{"className":2514},[1880],[1830,2516,2038],{"className":2517},[1880,1884],[1830,2519,2521],{"className":2520},[1889],[1830,2522,2524,2544],{"className":2523},[1893,1894],[1830,2525,2527,2541],{"className":2526},[1898],[1830,2528,2530],{"className":2529,"style":1903},[1902],[1830,2531,2532,2535],{"style":2249},[1830,2533],{"className":2534,"style":1911},[1910],[1830,2536,2538],{"className":2537},[1915,1916,1917,1918],[1830,2539,1857],{"className":2540},[1880,1884,1918],[1830,2542,1926],{"className":2543},[1925],[1830,2545,2547],{"className":2546},[1898],[1830,2548,2550],{"className":2549,"style":1933},[1902],[1830,2551],{},[1830,2553,2057],{"className":2554},[2555],"mpunct",[1792,2557,2558,2559,2629],{},"其中 ",[1830,2560,2562,2580],{"className":2561},[1833],[1830,2563,2565],{"className":2564},[1837],[1839,2566,2567],{"xmlns":1841},[1843,2568,2569,2577],{},[1846,2570,2571],{},[1849,2572,2573,2575],{},[1852,2574,2038],{},[1852,2576,1857],{},[1859,2578,2579],{"encoding":1861},"\\epsilon_t",[1830,2581,2583],{"className":2582,"ariaHidden":1867},[1866],[1830,2584,2586,2589],{"className":2585},[1871],[1830,2587],{"className":2588,"style":1876},[1875],[1830,2590,2592,2595],{"className":2591},[1880],[1830,2593,2038],{"className":2594},[1880,1884],[1830,2596,2598],{"className":2597},[1889],[1830,2599,2601,2621],{"className":2600},[1893,1894],[1830,2602,2604,2618],{"className":2603},[1898],[1830,2605,2607],{"className":2606,"style":1903},[1902],[1830,2608,2609,2612],{"style":2249},[1830,2610],{"className":2611,"style":1911},[1910],[1830,2613,2615],{"className":2614},[1915,1916,1917,1918],[1830,2616,1857],{"className":2617},[1880,1884,1918],[1830,2619,1926],{"className":2620},[1925],[1830,2622,2624],{"className":2623},[1898],[1830,2625,2627],{"className":2626,"style":1933},[1902],[1830,2628],{}," 为白噪声。对于大多数中长期资产定价问题，收益率本身通常被视为“近似不可预测”，即 AR 部分系数较小或不显著；",[1796,2631,2632,2635],{},[1799,2633,2634],{},"但在高频或某些特定资产上，短期自相关仍然可能存在；",[1799,2636,2637,2638,2642],{},"在风险建模中，更重要的是对",[2639,2640,2641],"strong",{},"波动","而非水平的建模。",[1822,2644,2646],{"id":2645},"_12-条件异方差与-garch","1.2 条件异方差与 GARCH",[1792,2648,2649],{},"Engle (1982) 提出的 ARCH 模型以及 Bollerslev (1986) 的 GARCH 模型刻画了金融时间序列中常见的“波动聚集”现象：",[1796,2651,2652,2789],{},[1799,2653,2654,2655,2788],{},"条件均值为 0（或小量）：",[1830,2656,2658,2684],{"className":2657},[1833],[1830,2659,2661],{"className":2660},[1837],[1839,2662,2663],{"xmlns":1841},[1843,2664,2665,2681],{},[1846,2666,2667,2673,2675],{},[1849,2668,2669,2671],{},[1852,2670,1854],{},[1852,2672,1857],{},[1961,2674,1963],{},[1849,2676,2677,2679],{},[1852,2678,2038],{},[1852,2680,1857],{},[1859,2682,2683],{"encoding":1861},"r_t = \\epsilon_t",[1830,2685,2687,2742],{"className":2686,"ariaHidden":1867},[1866],[1830,2688,2690,2693,2733,2736,2739],{"className":2689},[1871],[1830,2691],{"className":2692,"style":1876},[1875],[1830,2694,2696,2699],{"className":2695},[1880],[1830,2697,1854],{"className":2698,"style":1885},[1880,1884],[1830,2700,2702],{"className":2701},[1889],[1830,2703,2705,2725],{"className":2704},[1893,1894],[1830,2706,2708,2722],{"className":2707},[1898],[1830,2709,2711],{"className":2710,"style":1903},[1902],[1830,2712,2713,2716],{"style":1906},[1830,2714],{"className":2715,"style":1911},[1910],[1830,2717,2719],{"className":2718},[1915,1916,1917,1918],[1830,2720,1857],{"className":2721},[1880,1884,1918],[1830,2723,1926],{"className":2724},[1925],[1830,2726,2728],{"className":2727},[1898],[1830,2729,2731],{"className":2730,"style":1933},[1902],[1830,2732],{},[1830,2734],{"className":2735,"style":2114},[2113],[1830,2737,1963],{"className":2738},[2118],[1830,2740],{"className":2741,"style":2114},[2113],[1830,2743,2745,2748],{"className":2744},[1871],[1830,2746],{"className":2747,"style":1876},[1875],[1830,2749,2751,2754],{"className":2750},[1880],[1830,2752,2038],{"className":2753},[1880,1884],[1830,2755,2757],{"className":2756},[1889],[1830,2758,2760,2780],{"className":2759},[1893,1894],[1830,2761,2763,2777],{"className":2762},[1898],[1830,2764,2766],{"className":2765,"style":1903},[1902],[1830,2767,2768,2771],{"style":2249},[1830,2769],{"className":2770,"style":1911},[1910],[1830,2772,2774],{"className":2773},[1915,1916,1917,1918],[1830,2775,1857],{"className":2776},[1880,1884,1918],[1830,2778,1926],{"className":2779},[1925],[1830,2781,2783],{"className":2782},[1898],[1830,2784,2786],{"className":2785,"style":1933},[1902],[1830,2787],{},"；",[1799,2790,2791,2792,3138,2558,3141,3231,3232],{},"条件方差随时间动态变化：",[1830,2793,2795],{"className":2794},[1940],[1830,2796,2798,2881],{"className":2797},[1833],[1830,2799,2801],{"className":2800},[1837],[1839,2802,2803],{"xmlns":1841,"display":1949},[1843,2804,2805,2878],{},[1846,2806,2807,2813,2815,2822,2829,2831,2834,2840,2843,2845,2849,2851,2853,2856,2858,2862,2866,2869,2871,2873,2876],{},[1849,2808,2809,2811],{},[1852,2810,2038],{},[1852,2812,1857],{},[1961,2814,1963],{},[1849,2816,2817,2820],{},[1852,2818,2819],{},"σ",[1852,2821,1857],{},[1849,2823,2824,2827],{},[1852,2825,2826],{},"z",[1852,2828,1857],{},[1961,2830,2057],{"separator":1867},[2113,2832],{"width":2833},"1em",[1849,2835,2836,2838],{},[1852,2837,2826],{},[1852,2839,1857],{},[1961,2841,2842],{},"∼",[1852,2844,1980],{},[1852,2846,2848],{"mathvariant":2847},"normal",".",[1852,2850,1980],{},[1852,2852,2848],{"mathvariant":2847},[1852,2854,2855],{},"d",[1852,2857,2848],{"mathvariant":2847},[2859,2860,2861],"mtext",{}," ",[1961,2863,2865],{"stretchy":2864},"false","(",[1984,2867,2868],{},"0",[1961,2870,2057],{"separator":1867},[1984,2872,1986],{},[1961,2874,2875],{"stretchy":2864},")",[1961,2877,2057],{"separator":1867},[1859,2879,2880],{"encoding":1861},"\\epsilon_t = \\sigma_t z_t, \\quad z_t \\sim i.i.d.\\ (0,1),",[1830,2882,2884,2939,3087],{"className":2883,"ariaHidden":1867},[1866],[1830,2885,2887,2890,2930,2933,2936],{"className":2886},[1871],[1830,2888],{"className":2889,"style":1876},[1875],[1830,2891,2893,2896],{"className":2892},[1880],[1830,2894,2038],{"className":2895},[1880,1884],[1830,2897,2899],{"className":2898},[1889],[1830,2900,2902,2922],{"className":2901},[1893,1894],[1830,2903,2905,2919],{"className":2904},[1898],[1830,2906,2908],{"className":2907,"style":1903},[1902],[1830,2909,2910,2913],{"style":2249},[1830,2911],{"className":2912,"style":1911},[1910],[1830,2914,2916],{"className":2915},[1915,1916,1917,1918],[1830,2917,1857],{"className":2918},[1880,1884,1918],[1830,2920,1926],{"className":2921},[1925],[1830,2923,2925],{"className":2924},[1898],[1830,2926,2928],{"className":2927,"style":1933},[1902],[1830,2929],{},[1830,2931],{"className":2932,"style":2114},[2113],[1830,2934,1963],{"className":2935},[2118],[1830,2937],{"className":2938,"style":2114},[2113],[1830,2940,2942,2945,2986,3028,3031,3035,3038,3078,3081,3084],{"className":2941},[1871],[1830,2943],{"className":2944,"style":2511},[1875],[1830,2946,2948,2951],{"className":2947},[1880],[1830,2949,2819],{"className":2950,"style":2390},[1880,1884],[1830,2952,2954],{"className":2953},[1889],[1830,2955,2957,2978],{"className":2956},[1893,1894],[1830,2958,2960,2975],{"className":2959},[1898],[1830,2961,2963],{"className":2962,"style":1903},[1902],[1830,2964,2966,2969],{"style":2965},"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;",[1830,2967],{"className":2968,"style":1911},[1910],[1830,2970,2972],{"className":2971},[1915,1916,1917,1918],[1830,2973,1857],{"className":2974},[1880,1884,1918],[1830,2976,1926],{"className":2977},[1925],[1830,2979,2981],{"className":2980},[1898],[1830,2982,2984],{"className":2983,"style":1933},[1902],[1830,2985],{},[1830,2987,2989,2993],{"className":2988},[1880],[1830,2990,2826],{"className":2991,"style":2992},[1880,1884],"margin-right:0.044em;",[1830,2994,2996],{"className":2995},[1889],[1830,2997,2999,3020],{"className":2998},[1893,1894],[1830,3000,3002,3017],{"className":3001},[1898],[1830,3003,3005],{"className":3004,"style":1903},[1902],[1830,3006,3008,3011],{"style":3007},"top:-2.55em;margin-left:-0.044em;margin-right:0.05em;",[1830,3009],{"className":3010,"style":1911},[1910],[1830,3012,3014],{"className":3013},[1915,1916,1917,1918],[1830,3015,1857],{"className":3016},[1880,1884,1918],[1830,3018,1926],{"className":3019},[1925],[1830,3021,3023],{"className":3022},[1898],[1830,3024,3026],{"className":3025,"style":1933},[1902],[1830,3027],{},[1830,3029,2057],{"className":3030},[2555],[1830,3032],{"className":3033,"style":3034},[2113],"margin-right:1em;",[1830,3036],{"className":3037,"style":2227},[2113],[1830,3039,3041,3044],{"className":3040},[1880],[1830,3042,2826],{"className":3043,"style":2992},[1880,1884],[1830,3045,3047],{"className":3046},[1889],[1830,3048,3050,3070],{"className":3049},[1893,1894],[1830,3051,3053,3067],{"className":3052},[1898],[1830,3054,3056],{"className":3055,"style":1903},[1902],[1830,3057,3058,3061],{"style":3007},[1830,3059],{"className":3060,"style":1911},[1910],[1830,3062,3064],{"className":3063},[1915,1916,1917,1918],[1830,3065,1857],{"className":3066},[1880,1884,1918],[1830,3068,1926],{"className":3069},[1925],[1830,3071,3073],{"className":3072},[1898],[1830,3074,3076],{"className":3075,"style":1933},[1902],[1830,3077],{},[1830,3079],{"className":3080,"style":2114},[2113],[1830,3082,2842],{"className":3083},[2118],[1830,3085],{"className":3086,"style":2114},[2113],[1830,3088,3090,3094,3097,3100,3103,3106,3109,3112,3115,3119,3122,3125,3128,3131,3135],{"className":3089},[1871],[1830,3091],{"className":3092,"style":3093},[1875],"height:1em;vertical-align:-0.25em;",[1830,3095,1980],{"className":3096},[1880,1884],[1830,3098,2848],{"className":3099},[1880],[1830,3101,1980],{"className":3102},[1880,1884],[1830,3104,2848],{"className":3105},[1880],[1830,3107,2855],{"className":3108},[1880,1884],[1830,3110,2848],{"className":3111},[1880],[1830,3113,2861],{"className":3114},[2113],[1830,3116,2865],{"className":3117},[3118],"mopen",[1830,3120,2868],{"className":3121},[1880],[1830,3123,2057],{"className":3124},[2555],[1830,3126],{"className":3127,"style":2227},[2113],[1830,3129,1986],{"className":3130},[1880],[1830,3132,2875],{"className":3133},[3134],"mclose",[1830,3136,2057],{"className":3137},[2555],[3139,3140],"br",{},[1830,3142,3144,3166],{"className":3143},[1833],[1830,3145,3147],{"className":3146},[1837],[1839,3148,3149],{"xmlns":1841},[1843,3150,3151,3163],{},[1846,3152,3153],{},[3154,3155,3156,3158,3160],"msubsup",{},[1852,3157,2819],{},[1852,3159,1857],{},[1984,3161,3162],{},"2",[1859,3164,3165],{"encoding":1861},"\\sigma_t^2",[1830,3167,3169],{"className":3168,"ariaHidden":1867},[1866],[1830,3170,3172,3176],{"className":3171},[1871],[1830,3173],{"className":3174,"style":3175},[1875],"height:1.0611em;vertical-align:-0.247em;",[1830,3177,3179,3182],{"className":3178},[1880],[1830,3180,2819],{"className":3181,"style":2390},[1880,1884],[1830,3183,3185],{"className":3184},[1889],[1830,3186,3188,3222],{"className":3187},[1893,1894],[1830,3189,3191,3219],{"className":3190},[1898],[1830,3192,3195,3207],{"className":3193,"style":3194},[1902],"height:0.8141em;",[1830,3196,3198,3201],{"style":3197},"top:-2.453em;margin-left:-0.0359em;margin-right:0.05em;",[1830,3199],{"className":3200,"style":1911},[1910],[1830,3202,3204],{"className":3203},[1915,1916,1917,1918],[1830,3205,1857],{"className":3206},[1880,1884,1918],[1830,3208,3210,3213],{"style":3209},"top:-3.063em;margin-right:0.05em;",[1830,3211],{"className":3212,"style":1911},[1910],[1830,3214,3216],{"className":3215},[1915,1916,1917,1918],[1830,3217,3162],{"className":3218},[1880,1918],[1830,3220,1926],{"className":3221},[1925],[1830,3223,3225],{"className":3224},[1898],[1830,3226,3229],{"className":3227,"style":3228},[1902],"height:0.247em;",[1830,3230],{}," 的演化由 GARCH(1,1) 指定：",[1830,3233,3235],{"className":3234},[1940],[1830,3236,3238,3303],{"className":3237},[1833],[1830,3239,3241],{"className":3240},[1837],[1839,3242,3243],{"xmlns":1841,"display":1949},[1843,3244,3245,3300],{},[1846,3246,3247,3255,3257,3260,3262,3265,3279,3281,3284,3298],{},[3154,3248,3249,3251,3253],{},[1852,3250,2819],{},[1852,3252,1857],{},[1984,3254,3162],{},[1961,3256,1963],{},[1852,3258,3259],{},"ω",[1961,3261,1969],{},[1852,3263,3264],{},"α",[3154,3266,3267,3269,3277],{},[1852,3268,2038],{},[1846,3270,3271,3273,3275],{},[1852,3272,1857],{},[1961,3274,2006],{},[1984,3276,1986],{},[1984,3278,3162],{},[1961,3280,1969],{},[1852,3282,3283],{},"β",[3154,3285,3286,3288,3296],{},[1852,3287,2819],{},[1846,3289,3290,3292,3294],{},[1852,3291,1857],{},[1961,3293,2006],{},[1984,3295,1986],{},[1984,3297,3162],{},[1852,3299,2848],{"mathvariant":2847},[1859,3301,3302],{"encoding":1861},"\\sigma_t^2 = \\omega + \\alpha \\epsilon_{t-1}^2 + \\beta \\sigma_{t-1}^2.",[1830,3304,3306,3375,3393,3475],{"className":3305,"ariaHidden":1867},[1866],[1830,3307,3309,3313,3366,3369,3372],{"className":3308},[1871],[1830,3310],{"className":3311,"style":3312},[1875],"height:1.1111em;vertical-align:-0.247em;",[1830,3314,3316,3319],{"className":3315},[1880],[1830,3317,2819],{"className":3318,"style":2390},[1880,1884],[1830,3320,3322],{"className":3321},[1889],[1830,3323,3325,3358],{"className":3324},[1893,1894],[1830,3326,3328,3355],{"className":3327},[1898],[1830,3329,3332,3343],{"className":3330,"style":3331},[1902],"height:0.8641em;",[1830,3333,3334,3337],{"style":3197},[1830,3335],{"className":3336,"style":1911},[1910],[1830,3338,3340],{"className":3339},[1915,1916,1917,1918],[1830,3341,1857],{"className":3342},[1880,1884,1918],[1830,3344,3346,3349],{"style":3345},"top:-3.113em;margin-right:0.05em;",[1830,3347],{"className":3348,"style":1911},[1910],[1830,3350,3352],{"className":3351},[1915,1916,1917,1918],[1830,3353,3162],{"className":3354},[1880,1918],[1830,3356,1926],{"className":3357},[1925],[1830,3359,3361],{"className":3360},[1898],[1830,3362,3364],{"className":3363,"style":3228},[1902],[1830,3365],{},[1830,3367],{"className":3368,"style":2114},[2113],[1830,3370,1963],{"className":3371},[2118],[1830,3373],{"className":3374,"style":2114},[2113],[1830,3376,3378,3381,3384,3387,3390],{"className":3377},[1871],[1830,3379],{"className":3380,"style":2128},[1875],[1830,3382,3259],{"className":3383,"style":2390},[1880,1884],[1830,3385],{"className":3386,"style":2135},[2113],[1830,3388,1969],{"className":3389},[2139],[1830,3391],{"className":3392,"style":2135},[2113],[1830,3394,3396,3400,3404,3466,3469,3472],{"className":3395},[1871],[1830,3397],{"className":3398,"style":3399},[1875],"height:1.1694em;vertical-align:-0.3053em;",[1830,3401,3264],{"className":3402,"style":3403},[1880,1884],"margin-right:0.0037em;",[1830,3405,3407,3410],{"className":3406},[1880],[1830,3408,2038],{"className":3409},[1880,1884],[1830,3411,3413],{"className":3412},[1889],[1830,3414,3416,3457],{"className":3415},[1893,1894],[1830,3417,3419,3454],{"className":3418},[1898],[1830,3420,3422,3443],{"className":3421,"style":3331},[1902],[1830,3423,3425,3428],{"style":3424},"top:-2.453em;margin-left:0em;margin-right:0.05em;",[1830,3426],{"className":3427,"style":1911},[1910],[1830,3429,3431],{"className":3430},[1915,1916,1917,1918],[1830,3432,3434,3437,3440],{"className":3433},[1880,1918],[1830,3435,1857],{"className":3436},[1880,1884,1918],[1830,3438,2006],{"className":3439},[2139,1918],[1830,3441,1986],{"className":3442},[1880,1918],[1830,3444,3445,3448],{"style":3345},[1830,3446],{"className":3447,"style":1911},[1910],[1830,3449,3451],{"className":3450},[1915,1916,1917,1918],[1830,3452,3162],{"className":3453},[1880,1918],[1830,3455,1926],{"className":3456},[1925],[1830,3458,3460],{"className":3459},[1898],[1830,3461,3464],{"className":3462,"style":3463},[1902],"height:0.3053em;",[1830,3465],{},[1830,3467],{"className":3468,"style":2135},[2113],[1830,3470,1969],{"className":3471},[2139],[1830,3473],{"className":3474,"style":2135},[2113],[1830,3476,3478,3481,3485,3545],{"className":3477},[1871],[1830,3479],{"className":3480,"style":3399},[1875],[1830,3482,3283],{"className":3483,"style":3484},[1880,1884],"margin-right:0.0528em;",[1830,3486,3488,3491],{"className":3487},[1880],[1830,3489,2819],{"className":3490,"style":2390},[1880,1884],[1830,3492,3494],{"className":3493},[1889],[1830,3495,3497,3537],{"className":3496},[1893,1894],[1830,3498,3500,3534],{"className":3499},[1898],[1830,3501,3503,3523],{"className":3502,"style":3331},[1902],[1830,3504,3505,3508],{"style":3197},[1830,3506],{"className":3507,"style":1911},[1910],[1830,3509,3511],{"className":3510},[1915,1916,1917,1918],[1830,3512,3514,3517,3520],{"className":3513},[1880,1918],[1830,3515,1857],{"className":3516},[1880,1884,1918],[1830,3518,2006],{"className":3519},[2139,1918],[1830,3521,1986],{"className":3522},[1880,1918],[1830,3524,3525,3528],{"style":3345},[1830,3526],{"className":3527,"style":1911},[1910],[1830,3529,3531],{"className":3530},[1915,1916,1917,1918],[1830,3532,3162],{"className":3533},[1880,1918],[1830,3535,1926],{"className":3536},[1925],[1830,3538,3540],{"className":3539},[1898],[1830,3541,3543],{"className":3542,"style":3463},[1902],[1830,3544],{},[1830,3546,2848],{"className":3547},[1880],[1792,3549,3550],{},"典型实证结论是：",[1796,3552,3553,3556,3559],{},[1799,3554,3555],{},"对日度或更高频率的收益率数据，GARCH(1,1) 往往能捕捉到波动的聚集；",[1799,3557,3558],{},"在风险管理中，GARCH 型模型可以用于估计滚动 VaR\u002FCVaR；",[1799,3560,3561],{},"在计量资产定价中，波动模型有助于构造条件异方差稳健的标准误差。",[1822,3563,3565],{"id":3564},"_13-对量化研究的启示","1.3 对量化研究的启示",[1796,3567,3568,3571,3574],{},[1799,3569,3570],{},"简单策略回测中若只用样本方差估计风险，可能忽略波动聚集和时间变动；",[1799,3572,3573],{},"对高杠杆或卖出期权类策略，精细的波动建模尤为关键；",[1799,3575,3576],{},"但在多资产组合层面的因子模型中，GARCH 的高维扩展将变得复杂，研究中往往采用更简化的协方差估计方法（如 EWMA、滚动窗口）。",[1817,3578,3580],{"id":3579},"_2-截面与面板回归从因子到收益","2. 截面与面板回归：从因子到收益",[1822,3582,3584],{"id":3583},"_21-经典横截面回归与-famamacbeth","2.1 经典横截面回归与 Fama–MacBeth",[1792,3586,3587],{},"在第 03~04 章中，我们已经使用过 Fama–MacBeth (1973) 型横截面回归来估计因子溢价。这里稍作形式整理：",[3589,3590,3591,4319],"ol",{},[1799,3592,3593,3596,3597,3626,3627,4143,4145,4146,4318],{},[2639,3594,3595],{},"第一步（截面回归）","：对每个时点 ",[1830,3598,3600,3613],{"className":3599},[1833],[1830,3601,3603],{"className":3602},[1837],[1839,3604,3605],{"xmlns":1841},[1843,3606,3607,3611],{},[1846,3608,3609],{},[1852,3610,1857],{},[1859,3612,1857],{"encoding":1861},[1830,3614,3616],{"className":3615,"ariaHidden":1867},[1866],[1830,3617,3619,3623],{"className":3618},[1871],[1830,3620],{"className":3621,"style":3622},[1875],"height:0.6151em;",[1830,3624,1857],{"className":3625},[1880,1884],"，在截面上回归：",[1830,3628,3630],{"className":3629},[1940],[1830,3631,3633,3743],{"className":3632},[1833],[1830,3634,3636],{"className":3635},[1837],[1839,3637,3638],{"xmlns":1841,"display":1949},[1843,3639,3640,3740],{},[1846,3641,3642,3658,3660,3673,3675,3691,3703,3720,3722,3738],{},[1849,3643,3644,3646],{},[1852,3645,1854],{},[1846,3647,3648,3650,3652,3654,3656],{},[1852,3649,1980],{},[1961,3651,2057],{"separator":1867},[1852,3653,1857],{},[1961,3655,1969],{},[1984,3657,1986],{},[1961,3659,1963],{},[1849,3661,3662,3665],{},[1852,3663,3664],{},"λ",[1846,3666,3667,3669,3671],{},[1984,3668,2868],{},[1961,3670,2057],{"separator":1867},[1852,3672,1857],{},[1961,3674,1969],{},[1971,3676,3677,3679,3688],{},[1961,3678,1975],{},[1846,3680,3681,3684,3686],{},[1852,3682,3683],{},"k",[1961,3685,1963],{},[1984,3687,1986],{},[1852,3689,3690],{},"K",[1849,3692,3693,3695],{},[1852,3694,3664],{},[1846,3696,3697,3699,3701],{},[1852,3698,3683],{},[1961,3700,2057],{"separator":1867},[1852,3702,1857],{},[1849,3704,3705,3708],{},[1852,3706,3707],{},"f",[1846,3709,3710,3712,3714,3716,3718],{},[1852,3711,3683],{},[1961,3713,2057],{"separator":1867},[1852,3715,1980],{},[1961,3717,2057],{"separator":1867},[1852,3719,1857],{},[1961,3721,1969],{},[1849,3723,3724,3726],{},[1852,3725,2038],{},[1846,3727,3728,3730,3732,3734,3736],{},[1852,3729,1980],{},[1961,3731,2057],{"separator":1867},[1852,3733,1857],{},[1961,3735,1969],{},[1984,3737,1986],{},[1852,3739,2848],{"mathvariant":2847},[1859,3741,3742],{"encoding":1861},"r_{i,t+1} = \\lambda_{0,t} + \\sum_{k=1}^K \\lambda_{k,t} f_{k,i,t} + \\epsilon_{i,t+1}.",[1830,3744,3746,3817,3883,4079],{"className":3745,"ariaHidden":1867},[1866],[1830,3747,3749,3753,3808,3811,3814],{"className":3748},[1871],[1830,3750],{"className":3751,"style":3752},[1875],"height:0.7167em;vertical-align:-0.2861em;",[1830,3754,3756,3759],{"className":3755},[1880],[1830,3757,1854],{"className":3758,"style":1885},[1880,1884],[1830,3760,3762],{"className":3761},[1889],[1830,3763,3765,3800],{"className":3764},[1893,1894],[1830,3766,3768,3797],{"className":3767},[1898],[1830,3769,3771],{"className":3770,"style":2246},[1902],[1830,3772,3773,3776],{"style":1906},[1830,3774],{"className":3775,"style":1911},[1910],[1830,3777,3779],{"className":3778},[1915,1916,1917,1918],[1830,3780,3782,3785,3788,3791,3794],{"className":3781},[1880,1918],[1830,3783,1980],{"className":3784},[1880,1884,1918],[1830,3786,2057],{"className":3787},[2555,1918],[1830,3789,1857],{"className":3790},[1880,1884,1918],[1830,3792,1969],{"className":3793},[2139,1918],[1830,3795,1986],{"className":3796},[1880,1918],[1830,3798,1926],{"className":3799},[1925],[1830,3801,3803],{"className":3802},[1898],[1830,3804,3806],{"className":3805,"style":2444},[1902],[1830,3807],{},[1830,3809],{"className":3810,"style":2114},[2113],[1830,3812,1963],{"className":3813},[2118],[1830,3815],{"className":3816,"style":2114},[2113],[1830,3818,3820,3824,3874,3877,3880],{"className":3819},[1871],[1830,3821],{"className":3822,"style":3823},[1875],"height:0.9805em;vertical-align:-0.2861em;",[1830,3825,3827,3830],{"className":3826},[1880],[1830,3828,3664],{"className":3829},[1880,1884],[1830,3831,3833],{"className":3832},[1889],[1830,3834,3836,3866],{"className":3835},[1893,1894],[1830,3837,3839,3863],{"className":3838},[1898],[1830,3840,3843],{"className":3841,"style":3842},[1902],"height:0.3011em;",[1830,3844,3845,3848],{"style":2249},[1830,3846],{"className":3847,"style":1911},[1910],[1830,3849,3851],{"className":3850},[1915,1916,1917,1918],[1830,3852,3854,3857,3860],{"className":3853},[1880,1918],[1830,3855,2868],{"className":3856},[1880,1918],[1830,3858,2057],{"className":3859},[2555,1918],[1830,3861,1857],{"className":3862},[1880,1884,1918],[1830,3864,1926],{"className":3865},[1925],[1830,3867,3869],{"className":3868},[1898],[1830,3870,3872],{"className":3871,"style":2444},[1902],[1830,3873],{},[1830,3875],{"className":3876,"style":2135},[2113],[1830,3878,1969],{"className":3879},[2139],[1830,3881],{"className":3882,"style":2135},[2113],[1830,3884,3886,3890,3960,3963,4013,4070,4073,4076],{"className":3885},[1871],[1830,3887],{"className":3888,"style":3889},[1875],"height:3.1304em;vertical-align:-1.3021em;",[1830,3891,3893],{"className":3892},[2153,2154],[1830,3894,3896,3951],{"className":3895},[1893,1894],[1830,3897,3899,3948],{"className":3898},[1898],[1830,3900,3903,3925,3935],{"className":3901,"style":3902},[1902],"height:1.8283em;",[1830,3904,3906,3909],{"style":3905},"top:-1.8479em;margin-left:0em;",[1830,3907],{"className":3908,"style":2171},[1910],[1830,3910,3912],{"className":3911},[1915,1916,1917,1918],[1830,3913,3915,3919,3922],{"className":3914},[1880,1918],[1830,3916,3683],{"className":3917,"style":3918},[1880,1884,1918],"margin-right:0.0315em;",[1830,3920,1963],{"className":3921},[2118,1918],[1830,3923,1986],{"className":3924},[1880,1918],[1830,3926,3927,3930],{"style":2189},[1830,3928],{"className":3929,"style":2171},[1910],[1830,3931,3932],{},[1830,3933,1975],{"className":3934},[2153,2198,2199],[1830,3936,3938,3941],{"style":3937},"top:-4.3em;margin-left:0em;",[1830,3939],{"className":3940,"style":2171},[1910],[1830,3942,3944],{"className":3943},[1915,1916,1917,1918],[1830,3945,3690],{"className":3946,"style":3947},[1880,1884,1918],"margin-right:0.0715em;",[1830,3949,1926],{"className":3950},[1925],[1830,3952,3954],{"className":3953},[1898],[1830,3955,3958],{"className":3956,"style":3957},[1902],"height:1.3021em;",[1830,3959],{},[1830,3961],{"className":3962,"style":2227},[2113],[1830,3964,3966,3969],{"className":3965},[1880],[1830,3967,3664],{"className":3968},[1880,1884],[1830,3970,3972],{"className":3971},[1889],[1830,3973,3975,4005],{"className":3974},[1893,1894],[1830,3976,3978,4002],{"className":3977},[1898],[1830,3979,3982],{"className":3980,"style":3981},[1902],"height:0.3361em;",[1830,3983,3984,3987],{"style":2249},[1830,3985],{"className":3986,"style":1911},[1910],[1830,3988,3990],{"className":3989},[1915,1916,1917,1918],[1830,3991,3993,3996,3999],{"className":3992},[1880,1918],[1830,3994,3683],{"className":3995,"style":3918},[1880,1884,1918],[1830,3997,2057],{"className":3998},[2555,1918],[1830,4000,1857],{"className":4001},[1880,1884,1918],[1830,4003,1926],{"className":4004},[1925],[1830,4006,4008],{"className":4007},[1898],[1830,4009,4011],{"className":4010,"style":2444},[1902],[1830,4012],{},[1830,4014,4016,4020],{"className":4015},[1880],[1830,4017,3707],{"className":4018,"style":4019},[1880,1884],"margin-right:0.1076em;",[1830,4021,4023],{"className":4022},[1889],[1830,4024,4026,4062],{"className":4025},[1893,1894],[1830,4027,4029,4059],{"className":4028},[1898],[1830,4030,4032],{"className":4031,"style":3981},[1902],[1830,4033,4035,4038],{"style":4034},"top:-2.55em;margin-left:-0.1076em;margin-right:0.05em;",[1830,4036],{"className":4037,"style":1911},[1910],[1830,4039,4041],{"className":4040},[1915,1916,1917,1918],[1830,4042,4044,4047,4050,4053,4056],{"className":4043},[1880,1918],[1830,4045,3683],{"className":4046,"style":3918},[1880,1884,1918],[1830,4048,2057],{"className":4049},[2555,1918],[1830,4051,1980],{"className":4052},[1880,1884,1918],[1830,4054,2057],{"className":4055},[2555,1918],[1830,4057,1857],{"className":4058},[1880,1884,1918],[1830,4060,1926],{"className":4061},[1925],[1830,4063,4065],{"className":4064},[1898],[1830,4066,4068],{"className":4067,"style":2444},[1902],[1830,4069],{},[1830,4071],{"className":4072,"style":2135},[2113],[1830,4074,1969],{"className":4075},[2139],[1830,4077],{"className":4078,"style":2135},[2113],[1830,4080,4082,4085,4140],{"className":4081},[1871],[1830,4083],{"className":4084,"style":3752},[1875],[1830,4086,4088,4091],{"className":4087},[1880],[1830,4089,2038],{"className":4090},[1880,1884],[1830,4092,4094],{"className":4093},[1889],[1830,4095,4097,4132],{"className":4096},[1893,1894],[1830,4098,4100,4129],{"className":4099},[1898],[1830,4101,4103],{"className":4102,"style":2246},[1902],[1830,4104,4105,4108],{"style":2249},[1830,4106],{"className":4107,"style":1911},[1910],[1830,4109,4111],{"className":4110},[1915,1916,1917,1918],[1830,4112,4114,4117,4120,4123,4126],{"className":4113},[1880,1918],[1830,4115,1980],{"className":4116},[1880,1884,1918],[1830,4118,2057],{"className":4119},[2555,1918],[1830,4121,1857],{"className":4122},[1880,1884,1918],[1830,4124,1969],{"className":4125},[2139,1918],[1830,4127,1986],{"className":4128},[1880,1918],[1830,4130,1926],{"className":4131},[1925],[1830,4133,4135],{"className":4134},[1898],[1830,4136,4138],{"className":4137,"style":2444},[1902],[1830,4139],{},[1830,4141,2848],{"className":4142},[1880],[3139,4144],{},"得到一组时间序列系数 ",[1830,4147,4149,4192],{"className":4148},[1833],[1830,4150,4152],{"className":4151},[1837],[1839,4153,4154],{"xmlns":1841},[1843,4155,4156,4189],{},[1846,4157,4158,4161,4173],{},[1961,4159,4160],{"stretchy":2864},"{",[1849,4162,4163,4165],{},[1852,4164,3664],{},[1846,4166,4167,4169,4171],{},[1852,4168,3683],{},[1961,4170,2057],{"separator":1867},[1852,4172,1857],{},[3154,4174,4175,4178,4186],{},[1961,4176,4177],{"stretchy":2864},"}",[1846,4179,4180,4182,4184],{},[1852,4181,1857],{},[1961,4183,1963],{},[1984,4185,1986],{},[1852,4187,4188],{},"T",[1859,4190,4191],{"encoding":1861},"\\{\\lambda_{k,t}\\}_{t=1}^T",[1830,4193,4195],{"className":4194,"ariaHidden":1867},[1866],[1830,4196,4198,4202,4205,4254],{"className":4197},[1871],[1830,4199],{"className":4200,"style":4201},[1875],"height:1.1274em;vertical-align:-0.2861em;",[1830,4203,4160],{"className":4204},[3118],[1830,4206,4208,4211],{"className":4207},[1880],[1830,4209,3664],{"className":4210},[1880,1884],[1830,4212,4214],{"className":4213},[1889],[1830,4215,4217,4246],{"className":4216},[1893,1894],[1830,4218,4220,4243],{"className":4219},[1898],[1830,4221,4223],{"className":4222,"style":3981},[1902],[1830,4224,4225,4228],{"style":2249},[1830,4226],{"className":4227,"style":1911},[1910],[1830,4229,4231],{"className":4230},[1915,1916,1917,1918],[1830,4232,4234,4237,4240],{"className":4233},[1880,1918],[1830,4235,3683],{"className":4236,"style":3918},[1880,1884,1918],[1830,4238,2057],{"className":4239},[2555,1918],[1830,4241,1857],{"className":4242},[1880,1884,1918],[1830,4244,1926],{"className":4245},[1925],[1830,4247,4249],{"className":4248},[1898],[1830,4250,4252],{"className":4251,"style":2444},[1902],[1830,4253],{},[1830,4255,4257,4260],{"className":4256},[3134],[1830,4258,4177],{"className":4259},[3134],[1830,4261,4263],{"className":4262},[1889],[1830,4264,4266,4309],{"className":4265},[1893,1894],[1830,4267,4269,4306],{"className":4268},[1898],[1830,4270,4273,4294],{"className":4271,"style":4272},[1902],"height:0.8413em;",[1830,4274,4276,4279],{"style":4275},"top:-2.4519em;margin-left:0em;margin-right:0.05em;",[1830,4277],{"className":4278,"style":1911},[1910],[1830,4280,4282],{"className":4281},[1915,1916,1917,1918],[1830,4283,4285,4288,4291],{"className":4284},[1880,1918],[1830,4286,1857],{"className":4287},[1880,1884,1918],[1830,4289,1963],{"className":4290},[2118,1918],[1830,4292,1986],{"className":4293},[1880,1918],[1830,4295,4296,4299],{"style":3209},[1830,4297],{"className":4298,"style":1911},[1910],[1830,4300,4302],{"className":4301},[1915,1916,1917,1918],[1830,4303,4188],{"className":4304,"style":4305},[1880,1884,1918],"margin-right:0.1389em;",[1830,4307,1926],{"className":4308},[1925],[1830,4310,4312],{"className":4311},[1898],[1830,4313,4316],{"className":4314,"style":4315},[1902],"height:0.2481em;",[1830,4317],{},"。",[1799,4320,4321,4324,4325,4354,4355,4717,4719],{},[2639,4322,4323],{},"第二步（时间序列平均）","：对每个因子 ",[1830,4326,4328,4341],{"className":4327},[1833],[1830,4329,4331],{"className":4330},[1837],[1839,4332,4333],{"xmlns":1841},[1843,4334,4335,4339],{},[1846,4336,4337],{},[1852,4338,3683],{},[1859,4340,3683],{"encoding":1861},[1830,4342,4344],{"className":4343,"ariaHidden":1867},[1866],[1830,4345,4347,4351],{"className":4346},[1871],[1830,4348],{"className":4349,"style":4350},[1875],"height:0.6944em;",[1830,4352,3683],{"className":4353,"style":3918},[1880,1884],"，计算平均溢价：",[1830,4356,4358],{"className":4357},[1940],[1830,4359,4361,4422],{"className":4360},[1833],[1830,4362,4364],{"className":4363},[1837],[1839,4365,4366],{"xmlns":1841,"display":1949},[1843,4367,4368,4419],{},[1846,4369,4370,4382,4384,4391,4405,4417],{},[1849,4371,4372,4380],{},[4373,4374,4375,4377],"mover",{"accent":1867},[1852,4376,3664],{},[1961,4378,4379],{},"ˉ",[1852,4381,3683],{},[1961,4383,1963],{},[4385,4386,4387,4389],"mfrac",{},[1984,4388,1986],{},[1852,4390,4188],{},[1971,4392,4393,4395,4403],{},[1961,4394,1975],{},[1846,4396,4397,4399,4401],{},[1852,4398,1857],{},[1961,4400,1963],{},[1984,4402,1986],{},[1852,4404,4188],{},[1849,4406,4407,4409],{},[1852,4408,3664],{},[1846,4410,4411,4413,4415],{},[1852,4412,3683],{},[1961,4414,2057],{"separator":1867},[1852,4416,1857],{},[1961,4418,2057],{"separator":1867},[1859,4420,4421],{"encoding":1861},"\\bar{\\lambda}_k = \\frac{1}{T} \\sum_{t=1}^T \\lambda_{k,t},",[1830,4423,4425,4516],{"className":4424,"ariaHidden":1867},[1866],[1830,4426,4428,4432,4507,4510,4513],{"className":4427},[1871],[1830,4429],{"className":4430,"style":4431},[1875],"height:0.9812em;vertical-align:-0.15em;",[1830,4433,4435,4473],{"className":4434},[1880],[1830,4436,4439],{"className":4437},[1880,4438],"accent",[1830,4440,4442],{"className":4441},[1893],[1830,4443,4445],{"className":4444},[1898],[1830,4446,4449,4459],{"className":4447,"style":4448},[1902],"height:0.8312em;",[1830,4450,4452,4456],{"style":4451},"top:-3em;",[1830,4453],{"className":4454,"style":4455},[1910],"height:3em;",[1830,4457,3664],{"className":4458},[1880,1884],[1830,4460,4462,4465],{"style":4461},"top:-3.2634em;",[1830,4463],{"className":4464,"style":4455},[1910],[1830,4466,4470],{"className":4467,"style":4469},[4468],"accent-body","left:-0.25em;",[1830,4471,4379],{"className":4472},[1880],[1830,4474,4476],{"className":4475},[1889],[1830,4477,4479,4499],{"className":4478},[1893,1894],[1830,4480,4482,4496],{"className":4481},[1898],[1830,4483,4485],{"className":4484,"style":3981},[1902],[1830,4486,4487,4490],{"style":2249},[1830,4488],{"className":4489,"style":1911},[1910],[1830,4491,4493],{"className":4492},[1915,1916,1917,1918],[1830,4494,3683],{"className":4495,"style":3918},[1880,1884,1918],[1830,4497,1926],{"className":4498},[1925],[1830,4500,4502],{"className":4501},[1898],[1830,4503,4505],{"className":4504,"style":1933},[1902],[1830,4506],{},[1830,4508],{"className":4509,"style":2114},[2113],[1830,4511,1963],{"className":4512},[2118],[1830,4514],{"className":4515,"style":2114},[2113],[1830,4517,4519,4523,4593,4596,4662,4665,4714],{"className":4518},[1871],[1830,4520],{"className":4521,"style":4522},[1875],"height:3.0954em;vertical-align:-1.2671em;",[1830,4524,4526,4530,4590],{"className":4525},[1880],[1830,4527],{"className":4528},[3118,4529],"nulldelimiter",[1830,4531,4533],{"className":4532},[4385],[1830,4534,4536,4581],{"className":4535},[1893,1894],[1830,4537,4539,4578],{"className":4538},[1898],[1830,4540,4543,4555,4566],{"className":4541,"style":4542},[1902],"height:1.3214em;",[1830,4544,4546,4549],{"style":4545},"top:-2.314em;",[1830,4547],{"className":4548,"style":4455},[1910],[1830,4550,4552],{"className":4551},[1880],[1830,4553,4188],{"className":4554,"style":4305},[1880,1884],[1830,4556,4558,4561],{"style":4557},"top:-3.23em;",[1830,4559],{"className":4560,"style":4455},[1910],[1830,4562],{"className":4563,"style":4565},[4564],"frac-line","border-bottom-width:0.04em;",[1830,4567,4569,4572],{"style":4568},"top:-3.677em;",[1830,4570],{"className":4571,"style":4455},[1910],[1830,4573,4575],{"className":4574},[1880],[1830,4576,1986],{"className":4577},[1880],[1830,4579,1926],{"className":4580},[1925],[1830,4582,4584],{"className":4583},[1898],[1830,4585,4588],{"className":4586,"style":4587},[1902],"height:0.686em;",[1830,4589],{},[1830,4591],{"className":4592},[3134,4529],[1830,4594],{"className":4595,"style":2227},[2113],[1830,4597,4599],{"className":4598},[2153,2154],[1830,4600,4602,4653],{"className":4601},[1893,1894],[1830,4603,4605,4650],{"className":4604},[1898],[1830,4606,4608,4629,4639],{"className":4607,"style":3902},[1902],[1830,4609,4611,4614],{"style":4610},"top:-1.8829em;margin-left:0em;",[1830,4612],{"className":4613,"style":2171},[1910],[1830,4615,4617],{"className":4616},[1915,1916,1917,1918],[1830,4618,4620,4623,4626],{"className":4619},[1880,1918],[1830,4621,1857],{"className":4622},[1880,1884,1918],[1830,4624,1963],{"className":4625},[2118,1918],[1830,4627,1986],{"className":4628},[1880,1918],[1830,4630,4631,4634],{"style":2189},[1830,4632],{"className":4633,"style":2171},[1910],[1830,4635,4636],{},[1830,4637,1975],{"className":4638},[2153,2198,2199],[1830,4640,4641,4644],{"style":3937},[1830,4642],{"className":4643,"style":2171},[1910],[1830,4645,4647],{"className":4646},[1915,1916,1917,1918],[1830,4648,4188],{"className":4649,"style":4305},[1880,1884,1918],[1830,4651,1926],{"className":4652},[1925],[1830,4654,4656],{"className":4655},[1898],[1830,4657,4660],{"className":4658,"style":4659},[1902],"height:1.2671em;",[1830,4661],{},[1830,4663],{"className":4664,"style":2227},[2113],[1830,4666,4668,4671],{"className":4667},[1880],[1830,4669,3664],{"className":4670},[1880,1884],[1830,4672,4674],{"className":4673},[1889],[1830,4675,4677,4706],{"className":4676},[1893,1894],[1830,4678,4680,4703],{"className":4679},[1898],[1830,4681,4683],{"className":4682,"style":3981},[1902],[1830,4684,4685,4688],{"style":2249},[1830,4686],{"className":4687,"style":1911},[1910],[1830,4689,4691],{"className":4690},[1915,1916,1917,1918],[1830,4692,4694,4697,4700],{"className":4693},[1880,1918],[1830,4695,3683],{"className":4696,"style":3918},[1880,1884,1918],[1830,4698,2057],{"className":4699},[2555,1918],[1830,4701,1857],{"className":4702},[1880,1884,1918],[1830,4704,1926],{"className":4705},[1925],[1830,4707,4709],{"className":4708},[1898],[1830,4710,4712],{"className":4711,"style":2444},[1902],[1830,4713],{},[1830,4715,2057],{"className":4716},[2555],[3139,4718],{},"并对其进行 t 检验评估显著性。",[1792,4721,4722],{},"Fama–MacBeth 的优点是：",[1796,4724,4725,4728],{},[1799,4726,4727],{},"自然兼顾时间序列和横截面的信息；",[1799,4729,4730],{},"在截面相关和时间序列依赖的弱条件下，平均系数的 t 统计具有近似正态分布。",[1792,4732,4733],{},"在实际操作中需注意：",[1796,4735,4736,4739],{},[1799,4737,4738],{},"对残差的序列相关和异方差做出稳健调整（如 Newey–West 标准误）；",[1799,4740,4741],{},"对样本内的极端值和异常收益进行处理，以避免单期极端事件主导结果。",[1822,4743,4745],{"id":4744},"_22-面板数据回归","2.2 面板数据回归",[1792,4747,4748],{},"对于含有大量资产和长时间序列的数据，可以视为面板数据：",[1796,4750,4751,4784],{},[1799,4752,4753,4754,4783],{},"资产 ",[1830,4755,4757,4770],{"className":4756},[1833],[1830,4758,4760],{"className":4759},[1837],[1839,4761,4762],{"xmlns":1841},[1843,4763,4764,4768],{},[1846,4765,4766],{},[1852,4767,1980],{},[1859,4769,1980],{"encoding":1861},[1830,4771,4773],{"className":4772,"ariaHidden":1867},[1866],[1830,4774,4776,4780],{"className":4775},[1871],[1830,4777],{"className":4778,"style":4779},[1875],"height:0.6595em;",[1830,4781,1980],{"className":4782},[1880,1884]," 为横截面维度；",[1799,4785,4786,4787,4815],{},"时间 ",[1830,4788,4790,4803],{"className":4789},[1833],[1830,4791,4793],{"className":4792},[1837],[1839,4794,4795],{"xmlns":1841},[1843,4796,4797,4801],{},[1846,4798,4799],{},[1852,4800,1857],{},[1859,4802,1857],{"encoding":1861},[1830,4804,4806],{"className":4805,"ariaHidden":1867},[1866],[1830,4807,4809,4812],{"className":4808},[1871],[1830,4810],{"className":4811,"style":3622},[1875],[1830,4813,1857],{"className":4814},[1880,1884]," 为时间维度。",[1792,4817,4818],{},"标准的线性面板模型形式为：",[1830,4820,4822],{"className":4821},[1940],[1830,4823,4825,4887],{"className":4824},[1833],[1830,4826,4828],{"className":4827},[1837],[1839,4829,4830],{"xmlns":1841,"display":1949},[1843,4831,4832,4884],{},[1846,4833,4834,4846,4848,4850,4852,4854,4867,4869,4882],{},[1849,4835,4836,4838],{},[1852,4837,1854],{},[1846,4839,4840,4842,4844],{},[1852,4841,1980],{},[1961,4843,2057],{"separator":1867},[1852,4845,1857],{},[1961,4847,1963],{},[1852,4849,3264],{},[1961,4851,1969],{},[1852,4853,3283],{},[1849,4855,4856,4859],{},[1852,4857,4858],{},"x",[1846,4860,4861,4863,4865],{},[1852,4862,1980],{},[1961,4864,2057],{"separator":1867},[1852,4866,1857],{},[1961,4868,1969],{},[1849,4870,4871,4874],{},[1852,4872,4873],{},"u",[1846,4875,4876,4878,4880],{},[1852,4877,1980],{},[1961,4879,2057],{"separator":1867},[1852,4881,1857],{},[1961,4883,2057],{"separator":1867},[1859,4885,4886],{"encoding":1861}," r_{i,t} = \\alpha + \\beta x_{i,t} + u_{i,t},",[1830,4888,4890,4954,4972,5039],{"className":4889,"ariaHidden":1867},[1866],[1830,4891,4893,4896,4945,4948,4951],{"className":4892},[1871],[1830,4894],{"className":4895,"style":3752},[1875],[1830,4897,4899,4902],{"className":4898},[1880],[1830,4900,1854],{"className":4901,"style":1885},[1880,1884],[1830,4903,4905],{"className":4904},[1889],[1830,4906,4908,4937],{"className":4907},[1893,1894],[1830,4909,4911,4934],{"className":4910},[1898],[1830,4912,4914],{"className":4913,"style":2246},[1902],[1830,4915,4916,4919],{"style":1906},[1830,4917],{"className":4918,"style":1911},[1910],[1830,4920,4922],{"className":4921},[1915,1916,1917,1918],[1830,4923,4925,4928,4931],{"className":4924},[1880,1918],[1830,4926,1980],{"className":4927},[1880,1884,1918],[1830,4929,2057],{"className":4930},[2555,1918],[1830,4932,1857],{"className":4933},[1880,1884,1918],[1830,4935,1926],{"className":4936},[1925],[1830,4938,4940],{"className":4939},[1898],[1830,4941,4943],{"className":4942,"style":2444},[1902],[1830,4944],{},[1830,4946],{"className":4947,"style":2114},[2113],[1830,4949,1963],{"className":4950},[2118],[1830,4952],{"className":4953,"style":2114},[2113],[1830,4955,4957,4960,4963,4966,4969],{"className":4956},[1871],[1830,4958],{"className":4959,"style":2128},[1875],[1830,4961,3264],{"className":4962,"style":3403},[1880,1884],[1830,4964],{"className":4965,"style":2135},[2113],[1830,4967,1969],{"className":4968},[2139],[1830,4970],{"className":4971,"style":2135},[2113],[1830,4973,4975,4978,4981,5030,5033,5036],{"className":4974},[1871],[1830,4976],{"className":4977,"style":3823},[1875],[1830,4979,3283],{"className":4980,"style":3484},[1880,1884],[1830,4982,4984,4987],{"className":4983},[1880],[1830,4985,4858],{"className":4986},[1880,1884],[1830,4988,4990],{"className":4989},[1889],[1830,4991,4993,5022],{"className":4992},[1893,1894],[1830,4994,4996,5019],{"className":4995},[1898],[1830,4997,4999],{"className":4998,"style":2246},[1902],[1830,5000,5001,5004],{"style":2249},[1830,5002],{"className":5003,"style":1911},[1910],[1830,5005,5007],{"className":5006},[1915,1916,1917,1918],[1830,5008,5010,5013,5016],{"className":5009},[1880,1918],[1830,5011,1980],{"className":5012},[1880,1884,1918],[1830,5014,2057],{"className":5015},[2555,1918],[1830,5017,1857],{"className":5018},[1880,1884,1918],[1830,5020,1926],{"className":5021},[1925],[1830,5023,5025],{"className":5024},[1898],[1830,5026,5028],{"className":5027,"style":2444},[1902],[1830,5029],{},[1830,5031],{"className":5032,"style":2135},[2113],[1830,5034,1969],{"className":5035},[2139],[1830,5037],{"className":5038,"style":2135},[2113],[1830,5040,5042,5045,5094],{"className":5041},[1871],[1830,5043],{"className":5044,"style":3752},[1875],[1830,5046,5048,5051],{"className":5047},[1880],[1830,5049,4873],{"className":5050},[1880,1884],[1830,5052,5054],{"className":5053},[1889],[1830,5055,5057,5086],{"className":5056},[1893,1894],[1830,5058,5060,5083],{"className":5059},[1898],[1830,5061,5063],{"className":5062,"style":2246},[1902],[1830,5064,5065,5068],{"style":2249},[1830,5066],{"className":5067,"style":1911},[1910],[1830,5069,5071],{"className":5070},[1915,1916,1917,1918],[1830,5072,5074,5077,5080],{"className":5073},[1880,1918],[1830,5075,1980],{"className":5076},[1880,1884,1918],[1830,5078,2057],{"className":5079},[2555,1918],[1830,5081,1857],{"className":5082},[1880,1884,1918],[1830,5084,1926],{"className":5085},[1925],[1830,5087,5089],{"className":5088},[1898],[1830,5090,5092],{"className":5091,"style":2444},[1902],[1830,5093],{},[1830,5095,2057],{"className":5096},[2555],[1792,5098,2558,5099,5184],{},[1830,5100,5102,5126],{"className":5101},[1833],[1830,5103,5105],{"className":5104},[1837],[1839,5106,5107],{"xmlns":1841},[1843,5108,5109,5123],{},[1846,5110,5111],{},[1849,5112,5113,5115],{},[1852,5114,4858],{},[1846,5116,5117,5119,5121],{},[1852,5118,1980],{},[1961,5120,2057],{"separator":1867},[1852,5122,1857],{},[1859,5124,5125],{"encoding":1861},"x_{i,t}",[1830,5127,5129],{"className":5128,"ariaHidden":1867},[1866],[1830,5130,5132,5135],{"className":5131},[1871],[1830,5133],{"className":5134,"style":3752},[1875],[1830,5136,5138,5141],{"className":5137},[1880],[1830,5139,4858],{"className":5140},[1880,1884],[1830,5142,5144],{"className":5143},[1889],[1830,5145,5147,5176],{"className":5146},[1893,1894],[1830,5148,5150,5173],{"className":5149},[1898],[1830,5151,5153],{"className":5152,"style":2246},[1902],[1830,5154,5155,5158],{"style":2249},[1830,5156],{"className":5157,"style":1911},[1910],[1830,5159,5161],{"className":5160},[1915,1916,1917,1918],[1830,5162,5164,5167,5170],{"className":5163},[1880,1918],[1830,5165,1980],{"className":5166},[1880,1884,1918],[1830,5168,2057],{"className":5169},[2555,1918],[1830,5171,1857],{"className":5172},[1880,1884,1918],[1830,5174,1926],{"className":5175},[1925],[1830,5177,5179],{"className":5178},[1898],[1830,5180,5182],{"className":5181,"style":2444},[1902],[1830,5183],{}," 可以是因子暴露、公司特征或宏观变量。根据是否控制个体效应和时间效应，可以扩展为：",[1796,5186,5187,5509],{},[1799,5188,5189,5190],{},"固定效应模型（FE）：",[1830,5191,5193],{"className":5192},[1940],[1830,5194,5196,5260],{"className":5195},[1833],[1830,5197,5199],{"className":5198},[1837],[1839,5200,5201],{"xmlns":1841,"display":1949},[1843,5202,5203,5257],{},[1846,5204,5205,5217,5219,5225,5227,5229,5241,5243,5255],{},[1849,5206,5207,5209],{},[1852,5208,1854],{},[1846,5210,5211,5213,5215],{},[1852,5212,1980],{},[1961,5214,2057],{"separator":1867},[1852,5216,1857],{},[1961,5218,1963],{},[1849,5220,5221,5223],{},[1852,5222,3264],{},[1852,5224,1980],{},[1961,5226,1969],{},[1852,5228,3283],{},[1849,5230,5231,5233],{},[1852,5232,4858],{},[1846,5234,5235,5237,5239],{},[1852,5236,1980],{},[1961,5238,2057],{"separator":1867},[1852,5240,1857],{},[1961,5242,1969],{},[1849,5244,5245,5247],{},[1852,5246,4873],{},[1846,5248,5249,5251,5253],{},[1852,5250,1980],{},[1961,5252,2057],{"separator":1867},[1852,5254,1857],{},[1852,5256,2848],{"mathvariant":2847},[1859,5258,5259],{"encoding":1861},"r_{i,t} = \\alpha_i + \\beta x_{i,t} + u_{i,t}.",[1830,5261,5263,5327,5384,5451],{"className":5262,"ariaHidden":1867},[1866],[1830,5264,5266,5269,5318,5321,5324],{"className":5265},[1871],[1830,5267],{"className":5268,"style":3752},[1875],[1830,5270,5272,5275],{"className":5271},[1880],[1830,5273,1854],{"className":5274,"style":1885},[1880,1884],[1830,5276,5278],{"className":5277},[1889],[1830,5279,5281,5310],{"className":5280},[1893,1894],[1830,5282,5284,5307],{"className":5283},[1898],[1830,5285,5287],{"className":5286,"style":2246},[1902],[1830,5288,5289,5292],{"style":1906},[1830,5290],{"className":5291,"style":1911},[1910],[1830,5293,5295],{"className":5294},[1915,1916,1917,1918],[1830,5296,5298,5301,5304],{"className":5297},[1880,1918],[1830,5299,1980],{"className":5300},[1880,1884,1918],[1830,5302,2057],{"className":5303},[2555,1918],[1830,5305,1857],{"className":5306},[1880,1884,1918],[1830,5308,1926],{"className":5309},[1925],[1830,5311,5313],{"className":5312},[1898],[1830,5314,5316],{"className":5315,"style":2444},[1902],[1830,5317],{},[1830,5319],{"className":5320,"style":2114},[2113],[1830,5322,1963],{"className":5323},[2118],[1830,5325],{"className":5326,"style":2114},[2113],[1830,5328,5330,5334,5375,5378,5381],{"className":5329},[1871],[1830,5331],{"className":5332,"style":5333},[1875],"height:0.7333em;vertical-align:-0.15em;",[1830,5335,5337,5340],{"className":5336},[1880],[1830,5338,3264],{"className":5339,"style":3403},[1880,1884],[1830,5341,5343],{"className":5342},[1889],[1830,5344,5346,5367],{"className":5345},[1893,1894],[1830,5347,5349,5364],{"className":5348},[1898],[1830,5350,5352],{"className":5351,"style":2246},[1902],[1830,5353,5355,5358],{"style":5354},"top:-2.55em;margin-left:-0.0037em;margin-right:0.05em;",[1830,5356],{"className":5357,"style":1911},[1910],[1830,5359,5361],{"className":5360},[1915,1916,1917,1918],[1830,5362,1980],{"className":5363},[1880,1884,1918],[1830,5365,1926],{"className":5366},[1925],[1830,5368,5370],{"className":5369},[1898],[1830,5371,5373],{"className":5372,"style":1933},[1902],[1830,5374],{},[1830,5376],{"className":5377,"style":2135},[2113],[1830,5379,1969],{"className":5380},[2139],[1830,5382],{"className":5383,"style":2135},[2113],[1830,5385,5387,5390,5393,5442,5445,5448],{"className":5386},[1871],[1830,5388],{"className":5389,"style":3823},[1875],[1830,5391,3283],{"className":5392,"style":3484},[1880,1884],[1830,5394,5396,5399],{"className":5395},[1880],[1830,5397,4858],{"className":5398},[1880,1884],[1830,5400,5402],{"className":5401},[1889],[1830,5403,5405,5434],{"className":5404},[1893,1894],[1830,5406,5408,5431],{"className":5407},[1898],[1830,5409,5411],{"className":5410,"style":2246},[1902],[1830,5412,5413,5416],{"style":2249},[1830,5414],{"className":5415,"style":1911},[1910],[1830,5417,5419],{"className":5418},[1915,1916,1917,1918],[1830,5420,5422,5425,5428],{"className":5421},[1880,1918],[1830,5423,1980],{"className":5424},[1880,1884,1918],[1830,5426,2057],{"className":5427},[2555,1918],[1830,5429,1857],{"className":5430},[1880,1884,1918],[1830,5432,1926],{"className":5433},[1925],[1830,5435,5437],{"className":5436},[1898],[1830,5438,5440],{"className":5439,"style":2444},[1902],[1830,5441],{},[1830,5443],{"className":5444,"style":2135},[2113],[1830,5446,1969],{"className":5447},[2139],[1830,5449],{"className":5450,"style":2135},[2113],[1830,5452,5454,5457,5506],{"className":5453},[1871],[1830,5455],{"className":5456,"style":3752},[1875],[1830,5458,5460,5463],{"className":5459},[1880],[1830,5461,4873],{"className":5462},[1880,1884],[1830,5464,5466],{"className":5465},[1889],[1830,5467,5469,5498],{"className":5468},[1893,1894],[1830,5470,5472,5495],{"className":5471},[1898],[1830,5473,5475],{"className":5474,"style":2246},[1902],[1830,5476,5477,5480],{"style":2249},[1830,5478],{"className":5479,"style":1911},[1910],[1830,5481,5483],{"className":5482},[1915,1916,1917,1918],[1830,5484,5486,5489,5492],{"className":5485},[1880,1918],[1830,5487,1980],{"className":5488},[1880,1884,1918],[1830,5490,2057],{"className":5491},[2555,1918],[1830,5493,1857],{"className":5494},[1880,1884,1918],[1830,5496,1926],{"className":5497},[1925],[1830,5499,5501],{"className":5500},[1898],[1830,5502,5504],{"className":5503,"style":2444},[1902],[1830,5505],{},[1830,5507,2848],{"className":5508},[1880],[1799,5510,5511,5512],{},"双向固定效应：",[1830,5513,5515],{"className":5514},[1940],[1830,5516,5518,5591],{"className":5517},[1833],[1830,5519,5521],{"className":5520},[1837],[1839,5522,5523],{"xmlns":1841,"display":1949},[1843,5524,5525,5588],{},[1846,5526,5527,5539,5541,5547,5549,5556,5558,5560,5572,5574,5586],{},[1849,5528,5529,5531],{},[1852,5530,1854],{},[1846,5532,5533,5535,5537],{},[1852,5534,1980],{},[1961,5536,2057],{"separator":1867},[1852,5538,1857],{},[1961,5540,1963],{},[1849,5542,5543,5545],{},[1852,5544,3264],{},[1852,5546,1980],{},[1961,5548,1969],{},[1849,5550,5551,5554],{},[1852,5552,5553],{},"γ",[1852,5555,1857],{},[1961,5557,1969],{},[1852,5559,3283],{},[1849,5561,5562,5564],{},[1852,5563,4858],{},[1846,5565,5566,5568,5570],{},[1852,5567,1980],{},[1961,5569,2057],{"separator":1867},[1852,5571,1857],{},[1961,5573,1969],{},[1849,5575,5576,5578],{},[1852,5577,4873],{},[1846,5579,5580,5582,5584],{},[1852,5581,1980],{},[1961,5583,2057],{"separator":1867},[1852,5585,1857],{},[1852,5587,2848],{"mathvariant":2847},[1859,5589,5590],{"encoding":1861},"r_{i,t} = \\alpha_i + \\gamma_t + \\beta x_{i,t} + u_{i,t}.",[1830,5592,5594,5658,5713,5771,5838],{"className":5593,"ariaHidden":1867},[1866],[1830,5595,5597,5600,5649,5652,5655],{"className":5596},[1871],[1830,5598],{"className":5599,"style":3752},[1875],[1830,5601,5603,5606],{"className":5602},[1880],[1830,5604,1854],{"className":5605,"style":1885},[1880,1884],[1830,5607,5609],{"className":5608},[1889],[1830,5610,5612,5641],{"className":5611},[1893,1894],[1830,5613,5615,5638],{"className":5614},[1898],[1830,5616,5618],{"className":5617,"style":2246},[1902],[1830,5619,5620,5623],{"style":1906},[1830,5621],{"className":5622,"style":1911},[1910],[1830,5624,5626],{"className":5625},[1915,1916,1917,1918],[1830,5627,5629,5632,5635],{"className":5628},[1880,1918],[1830,5630,1980],{"className":5631},[1880,1884,1918],[1830,5633,2057],{"className":5634},[2555,1918],[1830,5636,1857],{"className":5637},[1880,1884,1918],[1830,5639,1926],{"className":5640},[1925],[1830,5642,5644],{"className":5643},[1898],[1830,5645,5647],{"className":5646,"style":2444},[1902],[1830,5648],{},[1830,5650],{"className":5651,"style":2114},[2113],[1830,5653,1963],{"className":5654},[2118],[1830,5656],{"className":5657,"style":2114},[2113],[1830,5659,5661,5664,5704,5707,5710],{"className":5660},[1871],[1830,5662],{"className":5663,"style":5333},[1875],[1830,5665,5667,5670],{"className":5666},[1880],[1830,5668,3264],{"className":5669,"style":3403},[1880,1884],[1830,5671,5673],{"className":5672},[1889],[1830,5674,5676,5696],{"className":5675},[1893,1894],[1830,5677,5679,5693],{"className":5678},[1898],[1830,5680,5682],{"className":5681,"style":2246},[1902],[1830,5683,5684,5687],{"style":5354},[1830,5685],{"className":5686,"style":1911},[1910],[1830,5688,5690],{"className":5689},[1915,1916,1917,1918],[1830,5691,1980],{"className":5692},[1880,1884,1918],[1830,5694,1926],{"className":5695},[1925],[1830,5697,5699],{"className":5698},[1898],[1830,5700,5702],{"className":5701,"style":1933},[1902],[1830,5703],{},[1830,5705],{"className":5706,"style":2135},[2113],[1830,5708,1969],{"className":5709},[2139],[1830,5711],{"className":5712,"style":2135},[2113],[1830,5714,5716,5720,5762,5765,5768],{"className":5715},[1871],[1830,5717],{"className":5718,"style":5719},[1875],"height:0.7778em;vertical-align:-0.1944em;",[1830,5721,5723,5727],{"className":5722},[1880],[1830,5724,5553],{"className":5725,"style":5726},[1880,1884],"margin-right:0.0556em;",[1830,5728,5730],{"className":5729},[1889],[1830,5731,5733,5754],{"className":5732},[1893,1894],[1830,5734,5736,5751],{"className":5735},[1898],[1830,5737,5739],{"className":5738,"style":1903},[1902],[1830,5740,5742,5745],{"style":5741},"top:-2.55em;margin-left:-0.0556em;margin-right:0.05em;",[1830,5743],{"className":5744,"style":1911},[1910],[1830,5746,5748],{"className":5747},[1915,1916,1917,1918],[1830,5749,1857],{"className":5750},[1880,1884,1918],[1830,5752,1926],{"className":5753},[1925],[1830,5755,5757],{"className":5756},[1898],[1830,5758,5760],{"className":5759,"style":1933},[1902],[1830,5761],{},[1830,5763],{"className":5764,"style":2135},[2113],[1830,5766,1969],{"className":5767},[2139],[1830,5769],{"className":5770,"style":2135},[2113],[1830,5772,5774,5777,5780,5829,5832,5835],{"className":5773},[1871],[1830,5775],{"className":5776,"style":3823},[1875],[1830,5778,3283],{"className":5779,"style":3484},[1880,1884],[1830,5781,5783,5786],{"className":5782},[1880],[1830,5784,4858],{"className":5785},[1880,1884],[1830,5787,5789],{"className":5788},[1889],[1830,5790,5792,5821],{"className":5791},[1893,1894],[1830,5793,5795,5818],{"className":5794},[1898],[1830,5796,5798],{"className":5797,"style":2246},[1902],[1830,5799,5800,5803],{"style":2249},[1830,5801],{"className":5802,"style":1911},[1910],[1830,5804,5806],{"className":5805},[1915,1916,1917,1918],[1830,5807,5809,5812,5815],{"className":5808},[1880,1918],[1830,5810,1980],{"className":5811},[1880,1884,1918],[1830,5813,2057],{"className":5814},[2555,1918],[1830,5816,1857],{"className":5817},[1880,1884,1918],[1830,5819,1926],{"className":5820},[1925],[1830,5822,5824],{"className":5823},[1898],[1830,5825,5827],{"className":5826,"style":2444},[1902],[1830,5828],{},[1830,5830],{"className":5831,"style":2135},[2113],[1830,5833,1969],{"className":5834},[2139],[1830,5836],{"className":5837,"style":2135},[2113],[1830,5839,5841,5844,5893],{"className":5840},[1871],[1830,5842],{"className":5843,"style":3752},[1875],[1830,5845,5847,5850],{"className":5846},[1880],[1830,5848,4873],{"className":5849},[1880,1884],[1830,5851,5853],{"className":5852},[1889],[1830,5854,5856,5885],{"className":5855},[1893,1894],[1830,5857,5859,5882],{"className":5858},[1898],[1830,5860,5862],{"className":5861,"style":2246},[1902],[1830,5863,5864,5867],{"style":2249},[1830,5865],{"className":5866,"style":1911},[1910],[1830,5868,5870],{"className":5869},[1915,1916,1917,1918],[1830,5871,5873,5876,5879],{"className":5872},[1880,1918],[1830,5874,1980],{"className":5875},[1880,1884,1918],[1830,5877,2057],{"className":5878},[2555,1918],[1830,5880,1857],{"className":5881},[1880,1884,1918],[1830,5883,1926],{"className":5884},[1925],[1830,5886,5888],{"className":5887},[1898],[1830,5889,5891],{"className":5890,"style":2444},[1902],[1830,5892],{},[1830,5894,2848],{"className":5895},[1880],[1792,5897,5898],{},"在资产定价实证中，固定效应用于控制：",[1796,5900,5901,5904],{},[1799,5902,5903],{},"不可观测的资产\u002F公司特定特征；",[1799,5905,5906],{},"时间特定的宏观冲击。",[1792,5908,5909],{},"面板回归的挑战在于：",[1796,5911,5912,5973],{},[1799,5913,5914,5915,5943,5944,5972],{},"误差项在 ",[1830,5916,5918,5931],{"className":5917},[1833],[1830,5919,5921],{"className":5920},[1837],[1839,5922,5923],{"xmlns":1841},[1843,5924,5925,5929],{},[1846,5926,5927],{},[1852,5928,1980],{},[1859,5930,1980],{"encoding":1861},[1830,5932,5934],{"className":5933,"ariaHidden":1867},[1866],[1830,5935,5937,5940],{"className":5936},[1871],[1830,5938],{"className":5939,"style":4779},[1875],[1830,5941,1980],{"className":5942},[1880,1884]," 和 ",[1830,5945,5947,5960],{"className":5946},[1833],[1830,5948,5950],{"className":5949},[1837],[1839,5951,5952],{"xmlns":1841},[1843,5953,5954,5958],{},[1846,5955,5956],{},[1852,5957,1857],{},[1859,5959,1857],{"encoding":1861},[1830,5961,5963],{"className":5962,"ariaHidden":1867},[1866],[1830,5964,5966,5969],{"className":5965},[1871],[1830,5967],{"className":5968,"style":3622},[1875],[1830,5970,1857],{"className":5971},[1880,1884]," 上往往同时存在相关性；",[1799,5974,5975],{},"需要采用聚类标准误差（clustered standard errors）或多维稳健估计（如 Driscoll–Kraay）。",[1817,5977,5979],{"id":5978},"_3-数据挖掘偏差与-reality-check","3. 数据挖掘偏差与 Reality Check",[1822,5981,5983],{"id":5982},"_31-多重检验问题","3.1 多重检验问题",[1792,5985,5986],{},"在量化研究中，经常会在同一份数据上测试大量策略或因子：",[1796,5988,5989,5992],{},[1799,5990,5991],{},"不同因子定义、参数组合、筛选规则；",[1799,5993,5994],{},"多只资产、多市场、多频率。",[1792,5996,5997],{},"如果使用传统的 t 检验或 p 值判断“显著性”，将严重低估“偶然好结果”的概率。这就是多重检验问题。",[1792,5999,6000],{},"简单例子：",[1796,6002,6003,6006],{},[1799,6004,6005],{},"若对 100 个独立无效策略分别进行 5% 显著性检验，期望会有约 5 个策略“看起来显著”；",[1799,6007,6008],{},"实际上它们只是噪声中的幸运儿。",[1822,6010,6012],{"id":6011},"_32-whites-reality-check","3.2 White's Reality Check",[1792,6014,6015],{},"White (2000) 提出的 Reality Check 框架，用于检验：在一组候选模型\u002F策略中，是否存在真正优于基准的策略，还是“最好的那个”也只是数据挖掘的结果。",[1792,6017,6018],{},"基本思路（略化）：",[3589,6020,6021,6169,6458,6692,6757],{},[1799,6022,6023,6024,6054,6055,6083,6084,2788],{},"定义每个策略 ",[1830,6025,6027,6041],{"className":6026},[1833],[1830,6028,6030],{"className":6029},[1837],[1839,6031,6032],{"xmlns":1841},[1843,6033,6034,6039],{},[1846,6035,6036],{},[1852,6037,6038],{},"m",[1859,6040,6038],{"encoding":1861},[1830,6042,6044],{"className":6043,"ariaHidden":1867},[1866],[1830,6045,6047,6051],{"className":6046},[1871],[1830,6048],{"className":6049,"style":6050},[1875],"height:0.4306em;",[1830,6052,6038],{"className":6053},[1880,1884]," 在时间 ",[1830,6056,6058,6071],{"className":6057},[1833],[1830,6059,6061],{"className":6060},[1837],[1839,6062,6063],{"xmlns":1841},[1843,6064,6065,6069],{},[1846,6066,6067],{},[1852,6068,1857],{},[1859,6070,1857],{"encoding":1861},[1830,6072,6074],{"className":6073,"ariaHidden":1867},[1866],[1830,6075,6077,6080],{"className":6076},[1871],[1830,6078],{"className":6079,"style":3622},[1875],[1830,6081,1857],{"className":6082},[1880,1884]," 的绩效差异（相对于基准）为 ",[1830,6085,6087,6111],{"className":6086},[1833],[1830,6088,6090],{"className":6089},[1837],[1839,6091,6092],{"xmlns":1841},[1843,6093,6094,6108],{},[1846,6095,6096],{},[1849,6097,6098,6100],{},[1852,6099,2855],{},[1846,6101,6102,6104,6106],{},[1852,6103,6038],{},[1961,6105,2057],{"separator":1867},[1852,6107,1857],{},[1859,6109,6110],{"encoding":1861},"d_{m,t}",[1830,6112,6114],{"className":6113,"ariaHidden":1867},[1866],[1830,6115,6117,6120],{"className":6116},[1871],[1830,6118],{"className":6119,"style":3823},[1875],[1830,6121,6123,6126],{"className":6122},[1880],[1830,6124,2855],{"className":6125},[1880,1884],[1830,6127,6129],{"className":6128},[1889],[1830,6130,6132,6161],{"className":6131},[1893,1894],[1830,6133,6135,6158],{"className":6134},[1898],[1830,6136,6138],{"className":6137,"style":1903},[1902],[1830,6139,6140,6143],{"style":2249},[1830,6141],{"className":6142,"style":1911},[1910],[1830,6144,6146],{"className":6145},[1915,1916,1917,1918],[1830,6147,6149,6152,6155],{"className":6148},[1880,1918],[1830,6150,6038],{"className":6151},[1880,1884,1918],[1830,6153,2057],{"className":6154},[2555,1918],[1830,6156,1857],{"className":6157},[1880,1884,1918],[1830,6159,1926],{"className":6160},[1925],[1830,6162,6164],{"className":6163},[1898],[1830,6165,6167],{"className":6166,"style":2444},[1902],[1830,6168],{},[1799,6170,6171,6172,2788],{},"对每个策略计算样本平均绩效：",[1830,6173,6175,6228],{"className":6174},[1833],[1830,6176,6178],{"className":6177},[1837],[1839,6179,6180],{"xmlns":1841},[1843,6181,6182,6225],{},[1846,6183,6184,6194,6196,6207,6213],{},[1849,6185,6186,6192],{},[4373,6187,6188,6190],{"accent":1867},[1852,6189,2855],{},[1961,6191,4379],{},[1852,6193,6038],{},[1961,6195,1963],{},[6197,6198,6199,6201],"msup",{},[1852,6200,4188],{},[1846,6202,6203,6205],{},[1961,6204,2006],{},[1984,6206,1986],{},[1849,6208,6209,6211],{},[1961,6210,1975],{},[1852,6212,1857],{},[1849,6214,6215,6217],{},[1852,6216,2855],{},[1846,6218,6219,6221,6223],{},[1852,6220,6038],{},[1961,6222,2057],{"separator":1867},[1852,6224,1857],{},[1859,6226,6227],{"encoding":1861},"\\bar{d}_m = T^{-1} \\sum_t d_{m,t}",[1830,6229,6231,6316],{"className":6230,"ariaHidden":1867},[1866],[1830,6232,6234,6237,6307,6310,6313],{"className":6233},[1871],[1830,6235],{"className":6236,"style":4431},[1875],[1830,6238,6240,6272],{"className":6239},[1880],[1830,6241,6243],{"className":6242},[1880,4438],[1830,6244,6246],{"className":6245},[1893],[1830,6247,6249],{"className":6248},[1898],[1830,6250,6252,6260],{"className":6251,"style":4448},[1902],[1830,6253,6254,6257],{"style":4451},[1830,6255],{"className":6256,"style":4455},[1910],[1830,6258,2855],{"className":6259},[1880,1884],[1830,6261,6262,6265],{"style":4461},[1830,6263],{"className":6264,"style":4455},[1910],[1830,6266,6269],{"className":6267,"style":6268},[4468],"left:-0.0833em;",[1830,6270,4379],{"className":6271},[1880],[1830,6273,6275],{"className":6274},[1889],[1830,6276,6278,6299],{"className":6277},[1893,1894],[1830,6279,6281,6296],{"className":6280},[1898],[1830,6282,6285],{"className":6283,"style":6284},[1902],"height:0.1514em;",[1830,6286,6287,6290],{"style":2249},[1830,6288],{"className":6289,"style":1911},[1910],[1830,6291,6293],{"className":6292},[1915,1916,1917,1918],[1830,6294,6038],{"className":6295},[1880,1884,1918],[1830,6297,1926],{"className":6298},[1925],[1830,6300,6302],{"className":6301},[1898],[1830,6303,6305],{"className":6304,"style":1933},[1902],[1830,6306],{},[1830,6308],{"className":6309,"style":2114},[2113],[1830,6311,1963],{"className":6312},[2118],[1830,6314],{"className":6315,"style":2114},[2113],[1830,6317,6319,6323,6358,6361,6406,6409],{"className":6318},[1871],[1830,6320],{"className":6321,"style":6322},[1875],"height:1.1138em;vertical-align:-0.2997em;",[1830,6324,6326,6329],{"className":6325},[1880],[1830,6327,4188],{"className":6328,"style":4305},[1880,1884],[1830,6330,6332],{"className":6331},[1889],[1830,6333,6335],{"className":6334},[1893],[1830,6336,6338],{"className":6337},[1898],[1830,6339,6341],{"className":6340,"style":3194},[1902],[1830,6342,6343,6346],{"style":3209},[1830,6344],{"className":6345,"style":1911},[1910],[1830,6347,6349],{"className":6348},[1915,1916,1917,1918],[1830,6350,6352,6355],{"className":6351},[1880,1918],[1830,6353,2006],{"className":6354},[1880,1918],[1830,6356,1986],{"className":6357},[1880,1918],[1830,6359],{"className":6360,"style":2227},[2113],[1830,6362,6364,6369],{"className":6363},[2153],[1830,6365,1975],{"className":6366,"style":6368},[2153,2198,6367],"small-op","position:relative;top:0em;",[1830,6370,6372],{"className":6371},[1889],[1830,6373,6375,6397],{"className":6374},[1893,1894],[1830,6376,6378,6394],{"className":6377},[1898],[1830,6379,6382],{"className":6380,"style":6381},[1902],"height:0.1308em;",[1830,6383,6385,6388],{"style":6384},"top:-2.4003em;margin-left:0em;margin-right:0.05em;",[1830,6386],{"className":6387,"style":1911},[1910],[1830,6389,6391],{"className":6390},[1915,1916,1917,1918],[1830,6392,1857],{"className":6393},[1880,1884,1918],[1830,6395,1926],{"className":6396},[1925],[1830,6398,6400],{"className":6399},[1898],[1830,6401,6404],{"className":6402,"style":6403},[1902],"height:0.2997em;",[1830,6405],{},[1830,6407],{"className":6408,"style":2227},[2113],[1830,6410,6412,6415],{"className":6411},[1880],[1830,6413,2855],{"className":6414},[1880,1884],[1830,6416,6418],{"className":6417},[1889],[1830,6419,6421,6450],{"className":6420},[1893,1894],[1830,6422,6424,6447],{"className":6423},[1898],[1830,6425,6427],{"className":6426,"style":1903},[1902],[1830,6428,6429,6432],{"style":2249},[1830,6430],{"className":6431,"style":1911},[1910],[1830,6433,6435],{"className":6434},[1915,1916,1917,1918],[1830,6436,6438,6441,6444],{"className":6437},[1880,1918],[1830,6439,6038],{"className":6440},[1880,1884,1918],[1830,6442,2057],{"className":6443},[2555,1918],[1830,6445,1857],{"className":6446},[1880,1884,1918],[1830,6448,1926],{"className":6449},[1925],[1830,6451,6453],{"className":6452},[1898],[1830,6454,6456],{"className":6455,"style":2444},[1902],[1830,6457],{},[1799,6459,6460,6461],{},"构造统计量：",[1830,6462,6464],{"className":6463},[1940],[1830,6465,6467,6514],{"className":6466},[1833],[1830,6468,6470],{"className":6469},[1837],[1839,6471,6472],{"xmlns":1841,"display":1949},[1843,6473,6474,6511],{},[1846,6475,6476,6483,6485,6498,6508],{},[4373,6477,6478,6480],{"accent":1867},[1852,6479,2031],{},[1961,6481,6482],{},"^",[1961,6484,1963],{},[6486,6487,6488,6496],"munder",{},[1846,6489,6490,6493],{},[1852,6491,6492],{},"max",[1961,6494,6495],{},"⁡",[1852,6497,6038],{},[1849,6499,6500,6506],{},[4373,6501,6502,6504],{"accent":1867},[1852,6503,2855],{},[1961,6505,4379],{},[1852,6507,6038],{},[1961,6509,6510],{"separator":1867},";",[1859,6512,6513],{"encoding":1861},"\\hat{\\theta} = \\max_m \\bar{d}_m;",[1830,6515,6517,6565],{"className":6516,"ariaHidden":1867},[1866],[1830,6518,6520,6524,6556,6559,6562],{"className":6519},[1871],[1830,6521],{"className":6522,"style":6523},[1875],"height:0.9579em;",[1830,6525,6527],{"className":6526},[1880,4438],[1830,6528,6530],{"className":6529},[1893],[1830,6531,6533],{"className":6532},[1898],[1830,6534,6536,6544],{"className":6535,"style":6523},[1902],[1830,6537,6538,6541],{"style":4451},[1830,6539],{"className":6540,"style":4455},[1910],[1830,6542,2031],{"className":6543,"style":1885},[1880,1884],[1830,6545,6546,6549],{"style":4461},[1830,6547],{"className":6548,"style":4455},[1910],[1830,6550,6553],{"className":6551,"style":6552},[4468],"left:-0.1667em;",[1830,6554,6482],{"className":6555},[1880],[1830,6557],{"className":6558,"style":2114},[2113],[1830,6560,1963],{"className":6561},[2118],[1830,6563],{"className":6564,"style":2114},[2113],[1830,6566,6568,6572,6618,6621,6689],{"className":6567},[1871],[1830,6569],{"className":6570,"style":6571},[1875],"height:1.5312em;vertical-align:-0.7em;",[1830,6573,6575],{"className":6574},[2153,2154],[1830,6576,6578,6609],{"className":6577},[1893,1894],[1830,6579,6581,6606],{"className":6580},[1898],[1830,6582,6584,6596],{"className":6583,"style":6050},[1902],[1830,6585,6587,6590],{"style":6586},"top:-2.4em;margin-left:0em;",[1830,6588],{"className":6589,"style":4455},[1910],[1830,6591,6593],{"className":6592},[1915,1916,1917,1918],[1830,6594,6038],{"className":6595},[1880,1884,1918],[1830,6597,6598,6601],{"style":4451},[1830,6599],{"className":6600,"style":4455},[1910],[1830,6602,6603],{},[1830,6604,6492],{"className":6605},[2153],[1830,6607,1926],{"className":6608},[1925],[1830,6610,6612],{"className":6611},[1898],[1830,6613,6616],{"className":6614,"style":6615},[1902],"height:0.7em;",[1830,6617],{},[1830,6619],{"className":6620,"style":2227},[2113],[1830,6622,6624,6655],{"className":6623},[1880],[1830,6625,6627],{"className":6626},[1880,4438],[1830,6628,6630],{"className":6629},[1893],[1830,6631,6633],{"className":6632},[1898],[1830,6634,6636,6644],{"className":6635,"style":4448},[1902],[1830,6637,6638,6641],{"style":4451},[1830,6639],{"className":6640,"style":4455},[1910],[1830,6642,2855],{"className":6643},[1880,1884],[1830,6645,6646,6649],{"style":4461},[1830,6647],{"className":6648,"style":4455},[1910],[1830,6650,6652],{"className":6651,"style":6268},[4468],[1830,6653,4379],{"className":6654},[1880],[1830,6656,6658],{"className":6657},[1889],[1830,6659,6661,6681],{"className":6660},[1893,1894],[1830,6662,6664,6678],{"className":6663},[1898],[1830,6665,6667],{"className":6666,"style":6284},[1902],[1830,6668,6669,6672],{"style":2249},[1830,6670],{"className":6671,"style":1911},[1910],[1830,6673,6675],{"className":6674},[1915,1916,1917,1918],[1830,6676,6038],{"className":6677},[1880,1884,1918],[1830,6679,1926],{"className":6680},[1925],[1830,6682,6684],{"className":6683},[1898],[1830,6685,6687],{"className":6686,"style":1933},[1902],[1830,6688],{},[1830,6690,6510],{"className":6691},[2555],[1799,6693,6694,6695,6756],{},"使用自助法（bootstrap）在“所有策略都无效”的原假设下模拟 ",[1830,6696,6698,6716],{"className":6697},[1833],[1830,6699,6701],{"className":6700},[1837],[1839,6702,6703],{"xmlns":1841},[1843,6704,6705,6713],{},[1846,6706,6707],{},[4373,6708,6709,6711],{"accent":1867},[1852,6710,2031],{},[1961,6712,6482],{},[1859,6714,6715],{"encoding":1861},"\\hat{\\theta}",[1830,6717,6719],{"className":6718,"ariaHidden":1867},[1866],[1830,6720,6722,6725],{"className":6721},[1871],[1830,6723],{"className":6724,"style":6523},[1875],[1830,6726,6728],{"className":6727},[1880,4438],[1830,6729,6731],{"className":6730},[1893],[1830,6732,6734],{"className":6733},[1898],[1830,6735,6737,6745],{"className":6736,"style":6523},[1902],[1830,6738,6739,6742],{"style":4451},[1830,6740],{"className":6741,"style":4455},[1910],[1830,6743,2031],{"className":6744,"style":1885},[1880,1884],[1830,6746,6747,6750],{"style":4461},[1830,6748],{"className":6749,"style":4455},[1910],[1830,6751,6753],{"className":6752,"style":6552},[4468],[1830,6754,6482],{"className":6755},[1880]," 的分布；",[1799,6758,6759,6760,6820],{},"将实际观测的 ",[1830,6761,6763,6780],{"className":6762},[1833],[1830,6764,6766],{"className":6765},[1837],[1839,6767,6768],{"xmlns":1841},[1843,6769,6770,6778],{},[1846,6771,6772],{},[4373,6773,6774,6776],{"accent":1867},[1852,6775,2031],{},[1961,6777,6482],{},[1859,6779,6715],{"encoding":1861},[1830,6781,6783],{"className":6782,"ariaHidden":1867},[1866],[1830,6784,6786,6789],{"className":6785},[1871],[1830,6787],{"className":6788,"style":6523},[1875],[1830,6790,6792],{"className":6791},[1880,4438],[1830,6793,6795],{"className":6794},[1893],[1830,6796,6798],{"className":6797},[1898],[1830,6799,6801,6809],{"className":6800,"style":6523},[1902],[1830,6802,6803,6806],{"style":4451},[1830,6804],{"className":6805,"style":4455},[1910],[1830,6807,2031],{"className":6808,"style":1885},[1880,1884],[1830,6810,6811,6814],{"style":4461},[1830,6812],{"className":6813,"style":4455},[1910],[1830,6815,6817],{"className":6816,"style":6552},[4468],[1830,6818,6482],{"className":6819},[1880]," 与模拟分布比较，得到 p 值。",[1792,6822,6823],{},"该方法在理论上考虑了“在很多模型中挑最大值”的偏差，但在实践中：",[1796,6825,6826,6829,6832],{},[1799,6827,6828],{},"计算成本较高（需要大量 bootstrap 重抽样）；",[1799,6830,6831],{},"对依赖结构和重抽样方案敏感；",[1799,6833,6834],{},"对策略集很大时仍可能偏保守。",[1822,6836,6838],{"id":6837},"_33-spa-检验","3.3 SPA 检验",[1792,6840,6841],{},"Hansen (2005) 提出的 Superior Predictive Ability (SPA) 检验是对 Reality Check 的改进，旨在提高检验的功效：",[1796,6843,6844,6847],{},[1799,6845,6846],{},"通过对不同模型的绩效差异进行截断处理，减弱“差得很差的模型”对检验结果的干扰；",[1799,6848,6849],{},"更适合包含大量弱策略和少数潜在强策略的情境。",[1792,6851,6852],{},"在量化 Alpha 研究中，Reality Check 与 SPA 可以作为“策略池筛选”的最后一层防线，用于判断：",[1796,6854,6855,6858],{},[1799,6856,6857],{},"在大量候选策略中，是否至少存在一部分在统计上确实优于基准；",[1799,6859,6860],{},"或者所有“好表现”都可以解释为数据挖掘偏差。",[1817,6862,6864],{"id":6863},"_4-稳健标准误与依赖结构","4. 稳健标准误与依赖结构",[1822,6866,6868],{"id":6867},"_41-neweywest-与-hac-协方差","4.1 Newey–West 与 HAC 协方差",[1792,6870,6871,6872,6942],{},"在时间序列回归中，残差 ",[1830,6873,6875,6893],{"className":6874},[1833],[1830,6876,6878],{"className":6877},[1837],[1839,6879,6880],{"xmlns":1841},[1843,6881,6882,6890],{},[1846,6883,6884],{},[1849,6885,6886,6888],{},[1852,6887,4873],{},[1852,6889,1857],{},[1859,6891,6892],{"encoding":1861},"u_t",[1830,6894,6896],{"className":6895,"ariaHidden":1867},[1866],[1830,6897,6899,6902],{"className":6898},[1871],[1830,6900],{"className":6901,"style":1876},[1875],[1830,6903,6905,6908],{"className":6904},[1880],[1830,6906,4873],{"className":6907},[1880,1884],[1830,6909,6911],{"className":6910},[1889],[1830,6912,6914,6934],{"className":6913},[1893,1894],[1830,6915,6917,6931],{"className":6916},[1898],[1830,6918,6920],{"className":6919,"style":1903},[1902],[1830,6921,6922,6925],{"style":2249},[1830,6923],{"className":6924,"style":1911},[1910],[1830,6926,6928],{"className":6927},[1915,1916,1917,1918],[1830,6929,1857],{"className":6930},[1880,1884,1918],[1830,6932,1926],{"className":6933},[1925],[1830,6935,6937],{"className":6936},[1898],[1830,6938,6940],{"className":6939,"style":1933},[1902],[1830,6941],{}," 往往存在自相关和异方差。若直接使用 OLS 标准误，会低估不确定性。Newey & West (1987) 提出了一类 HAC（heteroskedasticity and autocorrelation consistent）协方差估计：",[1796,6944,6945,6948],{},[1799,6946,6947],{},"通过对残差的自协方差进行加权求和，构造对真实协方差矩阵的一致估计；",[1799,6949,6950],{},"常用于时间序列回归中 t 统计和 F 统计的稳健估计。",[1792,6952,6953],{},"在资产定价实证中：",[1796,6955,6956,6959],{},[1799,6957,6958],{},"对 Fama–MacBeth 平均系数的 t 统计，经常会使用 Newey–West 修正；",[1799,6960,6961],{},"对多因子回归中的参数置信区间也会使用 HAC 协方差。",[1822,6963,6965],{"id":6964},"_42-聚类标准误差","4.2 聚类标准误差",[1792,6967,6968],{},"在横截面或面板回归中，误差项在资产之间或时间上可能相关：",[1796,6970,6971,6974],{},[1799,6972,6973],{},"同一时间的不同资产共享某些宏观冲击；",[1799,6975,6976],{},"同一资产在不同时间段受到公司特定冲击。",[1792,6978,6979],{},"聚类标准误差（clustered standard errors）通过按某一维度（如资产或时间）聚类来调整标准误：",[1796,6981,6982,6985],{},[1799,6983,6984],{},"单维聚类：按资产或按时间聚类；",[1799,6986,6987],{},"多维聚类：同时按资产和时间聚类（参见 Cameron, Gelbach & Miller, 2011）。",[1792,6989,6990],{},"在量化研究中，一个简单但常用的经验规则是：",[1796,6992,6993,6996,6999],{},[1799,6994,6995],{},"若怀疑误差在截面上高度相关，则对时间维度聚类；",[1799,6997,6998],{},"若怀疑误差在时间上高度相关，则对资产维度聚类；",[1799,7000,7001],{},"在高要求场景下使用双向聚类。",[1817,7003,7005],{"id":7004},"_5-实证工作流的计量-checklist","5. 实证工作流的计量 Checklist",[1792,7007,7008],{},"在量化\u002F资产定价研究中，一个相对规范的计量工作流通常包括：",[3589,7010,7011,7025,7041,7054,7070],{},[1799,7012,7013,7016,7017],{},[2639,7014,7015],{},"明确假设与对象","：",[1796,7018,7019,7022],{},[1799,7020,7021],{},"例如某因子是否具有显著正溢价；",[1799,7023,7024],{},"某策略是否显著优于基准。",[1799,7026,7027,7016,7030],{},[2639,7028,7029],{},"选择合适的模型与检验方法",[1796,7031,7032,7035,7038],{},[1799,7033,7034],{},"时间序列回归、横截面\u002F面板回归、Fama–MacBeth；",[1799,7036,7037],{},"是否需要 GARCH 或其他波动模型；",[1799,7039,7040],{},"是否需要 Reality Check\u002FSPA 等多重检验修正。",[1799,7042,7043,7016,7046],{},[2639,7044,7045],{},"检查模型假设与残差特性",[1796,7047,7048,7051],{},[1799,7049,7050],{},"自相关、异方差、重尾分布；",[1799,7052,7053],{},"根据需要选择 HAC 或聚类标准误差。",[1799,7055,7056,7016,7059],{},[2639,7057,7058],{},"进行稳健性分析",[1796,7060,7061,7064,7067],{},[1799,7062,7063],{},"更换样本区间、子样本划分；",[1799,7065,7066],{},"更换因子定义或参数；",[1799,7068,7069],{},"更换估计方法（如 OLS vs LAD、不同权重）。",[1799,7071,7072,7016,7075],{},[2639,7073,7074],{},"记录与复现",[1796,7076,7077,7080],{},[1799,7078,7079],{},"清晰记录数据源、样本区间、模型设定、估计方法和所有超参数；",[1799,7081,7082],{},"保证他人或未来的自己可以在相同条件下复现实证结果。",[7084,7085],"hr",{},[1817,7087,7089],{"id":7088},"_6-自学手册为策略研究选择合适的检验","6. 自学手册：为策略研究选择合适的检验",[1822,7091,7093],{"id":7092},"_61-学习目标","6.1 学习目标",[1792,7095,7096],{},"学完本章后，你应当能够：",[3589,7098,7099,7102,7105,7108,7111],{},[1799,7100,7101],{},"判断研究问题属于时间序列、横截面还是面板检验；",[1799,7103,7104],{},"解释普通 OLS 标准误在自相关、异方差和聚类相关下为什么会失真；",[1799,7106,7107],{},"为 Fama–MacBeth、面板回归和策略收益检验选择合适的稳健标准误；",[1799,7109,7110],{},"说明多重检验和数据挖掘偏差如何夸大策略显著性；",[1799,7112,7113],{},"把计量检验结果写成可复查的研究结论，而不是只报告一个 p 值。",[1822,7115,7117],{"id":7116},"_62-研究场景","6.2 研究场景",[1792,7119,7120],{},"你测试了 60 个候选因子，其中 8 个在普通 t 检验下显著。PM 问：“这些因子真的有效，还是只是试得太多？”风控问：“标准误是否考虑了截面相关和时间序列自相关？”这时，你需要把统计问题拆开：",[1796,7122,7123,7126,7129,7132],{},[1799,7124,7125],{},"每个因子的收益序列是否有自相关？",[1799,7127,7128],{},"横截面资产是否受同一市场冲击影响？",[1799,7130,7131],{},"这些候选因子是否是在同一数据集上反复筛出来的？",[1799,7133,7134],{},"显著性是否在子样本和替代规格下保持？",[1792,7136,7137],{},"本章的核心是：计量方法不是装饰，而是决定研究结论可信度的证据系统。",[1822,7139,7141],{"id":7140},"_63-定义与工作流逻辑","6.3 定义与工作流逻辑",[7143,7144,7145,7161],"table",{},[7146,7147,7148],"thead",{},[7149,7150,7151,7155,7158],"tr",{},[7152,7153,7154],"th",{},"研究问题",[7152,7156,7157],{},"常用方法",[7152,7159,7160],{},"关键风险",[7162,7163,7164,7176,7187,7198,7209],"tbody",{},[7149,7165,7166,7170,7173],{},[7167,7168,7169],"td",{},"策略收益均值是否为正",[7167,7171,7172],{},"时间序列 t 检验、HAC\u002FNewey–West",[7167,7174,7175],{},"收益自相关、异方差、厚尾",[7149,7177,7178,7181,7184],{},[7167,7179,7180],{},"因子是否解释截面收益",[7167,7182,7183],{},"Fama–MacBeth、横截面回归",[7167,7185,7186],{},"截面相关、极端收益",[7149,7188,7189,7192,7195],{},[7167,7190,7191],{},"面板特征是否有预测力",[7167,7193,7194],{},"固定效应、双向固定效应",[7167,7196,7197],{},"个体效应、时间效应、聚类相关",[7149,7199,7200,7203,7206],{},[7167,7201,7202],{},"多个策略中是否真有赢家",[7167,7204,7205],{},"Reality Check、SPA、bootstrap",[7167,7207,7208],{},"多重检验、数据挖掘",[7149,7210,7211,7214,7217],{},[7167,7212,7213],{},"风险是否随时间变化",[7167,7215,7216],{},"GARCH、EWMA、滚动窗口",[7167,7218,7219],{},"参数不稳定、尾部风险",[1792,7221,7222],{},"一个规范实证流程是：",[3589,7224,7225,7228,7231,7234,7237,7240],{},[1799,7226,7227],{},"先写出可检验假设和原假设；",[1799,7229,7230],{},"明确样本、频率、资产池和变量定义；",[1799,7232,7233],{},"选择模型，并说明误差结构的可能问题；",[1799,7235,7236],{},"使用匹配的稳健标准误或重抽样方法；",[1799,7238,7239],{},"做子样本、替代变量、替代窗口和异常期稳健性检查；",[1799,7241,7242],{},"报告经济显著性与统计显著性，而不是只报告显著星号。",[1822,7244,7246],{"id":7245},"_64-迷你案例rank-ic-的显著性","6.4 迷你案例：Rank IC 的显著性",[1792,7248,7249],{},"某因子月度 Rank IC 均值为 0.045，样本 120 个月，普通标准误给出 t=2.4。你不能立即宣布因子有效，还要检查：",[3589,7251,7252,7255,7258,7261,7264,7267],{},[1799,7253,7254],{},"IC 时间序列是否存在自相关，尤其是因子持仓和收益重叠时；",[1799,7256,7257],{},"是否有少数极端月份贡献了大部分均值；",[1799,7259,7260],{},"使用 Newey–West 标准误后 t 值是否仍然显著；",[1799,7262,7263],{},"在 2008-2012、2013-2018、2019-2024 等子样本中符号是否一致；",[1799,7265,7266],{},"该因子是否来自大量候选因子筛选，是否需要多重检验修正；",[1799,7268,7269],{},"即便统计显著，扣除成本后的经济收益是否足够。",[1822,7271,7273],{"id":7272},"_65-常见错误与研究陷阱","6.5 常见错误与研究陷阱",[1796,7275,7276,7282,7288,7294,7300],{},[1799,7277,7278,7281],{},[2639,7279,7280],{},"把普通 t 值当最终证据","：金融收益很少满足 iid 正态，普通标准误常常过于乐观。",[1799,7283,7284,7287],{},[2639,7285,7286],{},"只报告统计显著性","：t 值显著但收益极小、换手极高，仍可能没有投资价值。",[1799,7289,7290,7293],{},[2639,7291,7292],{},"忽略多重检验路径","：报告最终 3 个显著因子，却不说明试过 300 个候选因子。",[1799,7295,7296,7299],{},[2639,7297,7298],{},"样本切分事后化","：看到某段表现差后才重新定义子样本，会让稳健性检验失去意义。",[1799,7301,7302,7305],{},[2639,7303,7304],{},"把复杂模型当作稳健性","：更复杂的模型不一定更可信；关键是误差结构和假设是否匹配。",[1822,7307,7309],{"id":7308},"_66-自测题与答案提示","6.6 自测题与答案提示",[3589,7311,7312,7315,7318,7321],{},[1799,7313,7314],{},"Newey–West 标准误主要修正什么问题？\n答案提示：修正时间序列残差的异方差和自相关，使参数显著性评估更稳健。",[1799,7316,7317],{},"Fama–MacBeth 回归为什么常用于因子研究？\n答案提示：它先在每期截面估计因子价格，再对时间序列均值做检验，适合横截面收益预测问题。",[1799,7319,7320],{},"为什么测试很多策略后不能直接使用普通 p 值？\n答案提示：多重检验会提高偶然显著的概率，需要 Reality Check、SPA 或其他修正。",[1799,7322,7323],{},"统计显著和经济显著有什么区别？\n答案提示：统计显著说明估计值相对标准误较大；经济显著要求收益幅度在成本、风险和容量约束后仍有实际价值。",[1822,7325,7327],{"id":7326},"_67-小结与过渡","6.7 小结与过渡",[1792,7329,7330],{},"计量方法帮助你回答“我看到的策略表现是否可信”。它不能替代经济逻辑、数据审计和真实交易约束，但能显著降低被噪声误导的概率。下一章会把数据、因子、回测、组合、执行、生产和计量全部串成一个完整案例，展示一份研究复盘应如何组织。",[7084,7332],{},[1792,7334,7335,7016],{},[2639,7336,7337],{},"参考文献（节选）",[1796,7339,7340,7347,7353,7359,7364,7370,7375],{},[1799,7341,7342,7343],{},"Engle, R. F. (1982). \"Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation.\" ",[7344,7345,7346],"em",{},"Econometrica.",[1799,7348,7349,7350],{},"Bollerslev, T. (1986). \"Generalized autoregressive conditional heteroskedasticity.\" ",[7344,7351,7352],{},"Journal of Econometrics.",[1799,7354,7355,7356],{},"Fama, E. F., & MacBeth, J. D. (1973). \"Risk, return, and equilibrium: Empirical tests.\" ",[7344,7357,7358],{},"Journal of Political Economy.",[1799,7360,7361,7362],{},"White, H. (2000). \"A reality check for data snooping.\" ",[7344,7363,7346],{},[1799,7365,7366,7367],{},"Hansen, P. R. (2005). \"A test for superior predictive ability.\" ",[7344,7368,7369],{},"Journal of Business & Economic Statistics.",[1799,7371,7372,7373],{},"Newey, W. K., & West, K. D. (1987). \"A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix.\" ",[7344,7374,7346],{},[1799,7376,7377,7378],{},"Cameron, A. C., Gelbach, J. B., & Miller, D. L. (2011). \"Robust inference with multiway clustering.\" ",[7344,7379,7369],{},{"title":10,"searchDepth":7381,"depth":7381,"links":7382},2,[7383,7389,7393,7398,7402,7403],{"id":1819,"depth":7381,"text":1820,"children":7384},[7385,7387,7388],{"id":1824,"depth":7386,"text":1825},3,{"id":2645,"depth":7386,"text":2646},{"id":3564,"depth":7386,"text":3565},{"id":3579,"depth":7381,"text":3580,"children":7390},[7391,7392],{"id":3583,"depth":7386,"text":3584},{"id":4744,"depth":7386,"text":4745},{"id":5978,"depth":7381,"text":5979,"children":7394},[7395,7396,7397],{"id":5982,"depth":7386,"text":5983},{"id":6011,"depth":7386,"text":6012},{"id":6837,"depth":7386,"text":6838},{"id":6863,"depth":7381,"text":6864,"children":7399},[7400,7401],{"id":6867,"depth":7386,"text":6868},{"id":6964,"depth":7386,"text":6965},{"id":7004,"depth":7381,"text":7005},{"id":7088,"depth":7381,"text":7089,"children":7404},[7405,7406,7407,7408,7409,7410,7411],{"id":7092,"depth":7386,"text":7093},{"id":7116,"depth":7386,"text":7117},{"id":7140,"depth":7386,"text":7141},{"id":7245,"depth":7386,"text":7246},{"id":7272,"depth":7386,"text":7273},{"id":7308,"depth":7386,"text":7309},{"id":7326,"depth":7386,"text":7327},"为收益、因子和策略绩效选择与时间和横截面依赖、多重检验相匹配的推断方法。","md",{"sidebar":7415},{"order":7416},8,true,{"title":1771,"description":7412},"Y1K2dwQ56fKIiMGeh1cDyeIrts2xd3YIX_2DNTNScxc",[7421,7423],{"title":1767,"path":1768,"stem":1769,"description":7422,"children":-1},"设计从版本化数据、研究任务和模型制品到订单、监控和复现的工程依赖链。",{"title":1775,"path":1776,"stem":1777,"description":7424,"children":-1},"用一份端到端案例整合时点数据、因子、样本外回测、组合、执行和上线监控。",1785754759627]