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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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are separate modelling problems. An unconditional ARMA model can describe ",[1802,2834,2836,2874],{"className":2835},[1809],[1802,2837,2839],{"className":2838},[1813],[1815,2840,2841],{"xmlns":1817},[1820,2842,2843,2871],{},[1823,2844,2845,2847,2849,2855,2857,2869],{},[1829,2846,1895],{},[1836,2848,1899],{"stretchy":1898},[1826,2850,2851,2853],{},[1829,2852,1831],{},[1829,2854,1834],{},[1836,2856,1908],{},[1826,2858,2859,2861],{},[1829,2860,1914],{"mathvariant":1913},[1823,2862,2863,2865,2867],{},[1829,2864,1834],{},[1836,2866,1921],{},[1923,2868,1925],{},[1836,2870,1928],{"stretchy":1898},[1975,2872,2873],{"encoding":1977},"E(r_t\\mid\\mathcal F_{t-1})",[1802,2875,2877,2938],{"className":2876,"ariaHidden":1858},[1982],[1802,2878,2880,2883,2886,2889,2929,2932,2935],{"className":2879},[1986],[1802,2881],{"className":2882,"style":2452},[1990],[1802,2884,1895],{"className":2885,"style":2392},[1995,1999],[1802,2887,1899],{"className":2888},[2396],[1802,2890,2892,2895],{"className":2891},[1995],[1802,2893,1831],{"className":2894,"style":2000},[1995,1999],[1802,2896,2898],{"className":2897},[2004],[1802,2899,2901,2921],{"className":2900},[2008,2009],[1802,2902,2904,2918],{"className":2903},[2013],[1802,2905,2907],{"className":2906,"style":2018},[2017],[1802,2908,2909,2912],{"style":2021},[1802,2910],{"className":2911,"style":2026},[2025],[1802,2913,2915],{"className":2914},[2030,2031,2032,2033],[1802,2916,1834],{"className":2917},[1995,1999,2033],[1802,2919,2041],{"className":2920},[2040],[1802,2922,2924],{"className":2923},[2013],[1802,2925,2927],{"className":2926,"style":2048},[2017],[1802,2928],{},[1802,2930],{"className":2931,"style":2054},[1861],[1802,2933,1908],{"className":2934},[2058],[1802,2936],{"className":2937,"style":2054},[1861],[1802,2939,2941,2944,2993],{"className":2940},[1986],[1802,2942],{"className":2943,"style":2452},[1990],[1802,2945,2947,2950],{"className":2946},[1995],[1802,2948,1914],{"className":2949,"style":2460},[1995,2459],[1802,2951,2953],{"className":2952},[2004],[1802,2954,2956,2985],{"className":2955},[2008,2009],[1802,2957,2959,2982],{"className":2958},[2013],[1802,2960,2962],{"className":2961,"style":2473},[2017],[1802,2963,2964,2967],{"style":2476},[1802,2965],{"className":2966,"style":2026},[2025],[1802,2968,2970],{"className":2969},[2030,2031,2032,2033],[1802,2971,2973,2976,2979],{"className":2972},[1995,2033],[1802,2974,1834],{"className":2975},[1995,1999,2033],[1802,2977,1921],{"className":2978},[2117,2033],[1802,2980,1925],{"className":2981},[1995,2033],[1802,2983,2041],{"className":2984},[2040],[1802,2986,2988],{"className":2987},[2013],[1802,2989,2991],{"className":2990,"style":2504},[2017],[1802,2992],{},[1802,2994,1928],{"className":2995},[2510]," while missing the risk clustering in ",[1802,2998,3000,3017],{"className":2999},[1809],[1802,3001,3003],{"className":3002},[1813],[1815,3004,3005],{"xmlns":1817},[1820,3006,3007,3015],{},[1823,3008,3009],{},[1826,3010,3011,3013],{},[1829,3012,1879],{},[1829,3014,1834],{},[1975,3016,2781],{"encoding":1977},[1802,3018,3020],{"className":3019,"ariaHidden":1858},[1982],[1802,3021,3023,3026],{"className":3022},[1986],[1802,3024],{"className":3025,"style":2791},[1990],[1802,3027,3029,3032],{"className":3028},[1995],[1802,3030,1879],{"className":3031},[1995,1999],[1802,3033,3035],{"className":3034},[2004],[1802,3036,3038,3058],{"className":3037},[2008,2009],[1802,3039,3041,3055],{"className":3040},[2013],[1802,3042,3044],{"className":3043,"style":2018},[2017],[1802,3045,3046,3049],{"style":2089},[1802,3047],{"className":3048,"style":2026},[2025],[1802,3050,3052],{"className":3051},[2030,2031,2032,2033],[1802,3053,1834],{"className":3054},[1995,1999,2033],[1802,3056,2041],{"className":3057},[2040],[1802,3059,3061],{"className":3060},[2013],[1802,3062,3064],{"className":3063,"style":2048},[2017],[1802,3065],{},".",[1793,3068,3070],{"id":3069},"from-arch-to-garch","From ARCH to GARCH",[1798,3072,3073,3080,3081,3086],{},[3074,3075,3079],"a",{"href":3076,"rel":3077},"https:\u002F\u002Fdoi.org\u002F10.2307\u002F1912773",[3078],"nofollow","Engle's ARCH model"," lets recent squared shocks drive variance. ",[3074,3082,3085],{"href":3083,"rel":3084},"https:\u002F\u002Fdoi.org\u002F10.1016\u002F0304-4076(86)90063-1",[3078],"Bollerslev's GARCH model"," adds lagged variance:",[1802,3088,3090],{"className":3089},[1805],[1802,3091,3093,3179],{"className":3092},[1809],[1802,3094,3096],{"className":3095},[1813],[1815,3097,3098],{"xmlns":1817,"display":1818},[1820,3099,3100,3176],{},[1823,3101,3102,3108,3110,3113,3115,3118,3132,3134,3137,3149,3151,3153,3155,3158,3160,3162,3164,3166,3168,3170,3173],{},[1826,3103,3104,3106],{},[1829,3105,1879],{},[1829,3107,1834],{},[1836,3109,1838],{},[1829,3111,3112],{},"ω",[1836,3114,1848],{},[1829,3116,3117],{},"α",[1944,3119,3120,3122,3130],{},[1829,3121,1853],{},[1823,3123,3124,3126,3128],{},[1829,3125,1834],{},[1836,3127,1921],{},[1923,3129,1925],{},[1923,3131,1952],{},[1836,3133,1848],{},[1829,3135,3136],{},"β",[1826,3138,3139,3141],{},[1829,3140,1879],{},[1823,3142,3143,3145,3147],{},[1829,3144,1834],{},[1836,3146,1921],{},[1923,3148,1925],{},[1836,3150,1859],{"separator":1858},[1861,3152],{"width":1863},[1829,3154,3112],{},[1836,3156,3157],{},">",[1923,3159,1933],{},[1836,3161,1859],{"separator":1858},[1861,3163],{"width":1938},[1829,3165,3117],{},[1836,3167,1859],{"separator":1858},[1829,3169,3136],{},[1836,3171,3172],{},"≥",[1923,3174,3175],{},"0.",[1975,3177,3178],{"encoding":1977},"h_t=\\omega+\\alpha\\varepsilon_{t-1}^2+\\beta h_{t-1},\n\\qquad\n\\omega>0,\\quad\\alpha,\\beta\\ge0.",[1802,3180,3182,3237,3257,3339,3420,3460],{"className":3181,"ariaHidden":1858},[1982],[1802,3183,3185,3188,3228,3231,3234],{"className":3184},[1986],[1802,3186],{"className":3187,"style":2791},[1990],[1802,3189,3191,3194],{"className":3190},[1995],[1802,3192,1879],{"className":3193},[1995,1999],[1802,3195,3197],{"className":3196},[2004],[1802,3198,3200,3220],{"className":3199},[2008,2009],[1802,3201,3203,3217],{"className":3202},[2013],[1802,3204,3206],{"className":3205,"style":2018},[2017],[1802,3207,3208,3211],{"style":2089},[1802,3209],{"className":3210,"style":2026},[2025],[1802,3212,3214],{"className":3213},[2030,2031,2032,2033],[1802,3215,1834],{"className":3216},[1995,1999,2033],[1802,3218,2041],{"className":3219},[2040],[1802,3221,3223],{"className":3222},[2013],[1802,3224,3226],{"className":3225,"style":2048},[2017],[1802,3227],{},[1802,3229],{"className":3230,"style":2054},[1861],[1802,3232,1838],{"className":3233},[2058],[1802,3235],{"className":3236,"style":2054},[1861],[1802,3238,3240,3244,3248,3251,3254],{"className":3239},[1986],[1802,3241],{"className":3242,"style":3243},[1990],"height:0.6667em;vertical-align:-0.0833em;",[1802,3245,3112],{"className":3246,"style":3247},[1995,1999],"margin-right:0.0359em;",[1802,3249],{"className":3250,"style":2113},[1861],[1802,3252,1848],{"className":3253},[2117],[1802,3255],{"className":3256,"style":2113},[1861],[1802,3258,3260,3264,3268,3330,3333,3336],{"className":3259},[1986],[1802,3261],{"className":3262,"style":3263},[1990],"height:1.1694em;vertical-align:-0.3053em;",[1802,3265,3117],{"className":3266,"style":3267},[1995,1999],"margin-right:0.0037em;",[1802,3269,3271,3274],{"className":3270},[1995],[1802,3272,1853],{"className":3273},[1995,1999],[1802,3275,3277],{"className":3276},[2004],[1802,3278,3280,3321],{"className":3279},[2008,2009],[1802,3281,3283,3318],{"className":3282},[2013],[1802,3284,3286,3307],{"className":3285,"style":2564},[2017],[1802,3287,3289,3292],{"style":3288},"top:-2.453em;margin-left:0em;margin-right:0.05em;",[1802,3290],{"className":3291,"style":2026},[2025],[1802,3293,3295],{"className":3294},[2030,2031,2032,2033],[1802,3296,3298,3301,3304],{"className":3297},[1995,2033],[1802,3299,1834],{"className":3300},[1995,1999,2033],[1802,3302,1921],{"className":3303},[2117,2033],[1802,3305,1925],{"className":3306},[1995,2033],[1802,3308,3309,3312],{"style":2579},[1802,3310],{"className":3311,"style":2026},[2025],[1802,3313,3315],{"className":3314},[2030,2031,2032,2033],[1802,3316,1952],{"className":3317},[1995,2033],[1802,3319,2041],{"className":3320},[2040],[1802,3322,3324],{"className":3323},[2013],[1802,3325,3328],{"className":3326,"style":3327},[2017],"height:0.3053em;",[1802,3329],{},[1802,3331],{"className":3332,"style":2113},[1861],[1802,3334,1848],{"className":3335},[2117],[1802,3337],{"className":3338,"style":2113},[1861],[1802,3340,3342,3346,3350,3399,3402,3405,3408,3411,3414,3417],{"className":3341},[1986],[1802,3343],{"className":3344,"style":3345},[1990],"height:0.9028em;vertical-align:-0.2083em;",[1802,3347,3136],{"className":3348,"style":3349},[1995,1999],"margin-right:0.0528em;",[1802,3351,3353,3356],{"className":3352},[1995],[1802,3354,1879],{"className":3355},[1995,1999],[1802,3357,3359],{"className":3358},[2004],[1802,3360,3362,3391],{"className":3361},[2008,2009],[1802,3363,3365,3388],{"className":3364},[2013],[1802,3366,3368],{"className":3367,"style":2473},[2017],[1802,3369,3370,3373],{"style":2089},[1802,3371],{"className":3372,"style":2026},[2025],[1802,3374,3376],{"className":3375},[2030,2031,2032,2033],[1802,3377,3379,3382,3385],{"className":3378},[1995,2033],[1802,3380,1834],{"className":3381},[1995,1999,2033],[1802,3383,1921],{"className":3384},[2117,2033],[1802,3386,1925],{"className":3387},[1995,2033],[1802,3389,2041],{"className":3390},[2040],[1802,3392,3394],{"className":3393},[2013],[1802,3395,3397],{"className":3396,"style":2504},[2017],[1802,3398],{},[1802,3400,1859],{"className":3401},[2171],[1802,3403],{"className":3404,"style":2175},[1861],[1802,3406],{"className":3407,"style":2179},[1861],[1802,3409,3112],{"className":3410,"style":3247},[1995,1999],[1802,3412],{"className":3413,"style":2054},[1861],[1802,3415,3157],{"className":3416},[2058],[1802,3418],{"className":3419,"style":2054},[1861],[1802,3421,3423,3427,3430,3433,3436,3439,3442,3445,3448,3451,3454,3457],{"className":3422},[1986],[1802,3424],{"className":3425,"style":3426},[1990],"height:0.8889em;vertical-align:-0.1944em;",[1802,3428,1933],{"className":3429},[1995],[1802,3431,1859],{"className":3432},[2171],[1802,3434],{"className":3435,"style":2536},[1861],[1802,3437],{"className":3438,"style":2179},[1861],[1802,3440,3117],{"className":3441,"style":3267},[1995,1999],[1802,3443,1859],{"className":3444},[2171],[1802,3446],{"className":3447,"style":2179},[1861],[1802,3449,3136],{"className":3450,"style":3349},[1995,1999],[1802,3452],{"className":3453,"style":2054},[1861],[1802,3455,31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",[1802,3473,3475,3498],{"className":3474},[1809],[1802,3476,3478],{"className":3477},[1813],[1815,3479,3480],{"xmlns":1817},[1820,3481,3482,3495],{},[1823,3483,3484,3486,3488,3490,3493],{},[1829,3485,3117],{},[1836,3487,1848],{},[1829,3489,3136],{},[1836,3491,3492],{},"\u003C",[1923,3494,1925],{},[1975,3496,3497],{"encoding":1977},"\\alpha+\\beta\u003C1",[1802,3499,3501,3519,3537],{"className":3500,"ariaHidden":1858},[1982],[1802,3502,3504,3507,3510,3513,3516],{"className":3503},[1986],[1802,3505],{"className":3506,"style":3243},[1990],[1802,3508,3117],{"className":3509,"style":3267},[1995,1999],[1802,3511],{"className":3512,"style":2113},[1861],[1802,3514,1848],{"className":3515},[2117],[1802,3517],{"className":3518,"style":2113},[1861],[1802,3520,3522,3525,3528,3531,3534],{"className":3521},[1986],[1802,3523],{"className":3524,"style":3426},[1990],[1802,3526,3136],{"className":3527,"style":3349},[1995,1999],[1802,3529],{"className":3530,"style":2054},[1861],[1802,3532,3492],{"className":3533},[2058],[1802,3535],{"className":3536,"style":2054},[1861],[1802,3538,3540,3543],{"className":3539},[1986],[1802,3541],{"className":3542,"style":2683},[1990],[1802,3544,1925],{"className":3545},[1995],", the unconditional variance is",[1802,3548,3550],{"className":3549},[1805],[1802,3551,3553,3599],{"className":3552},[1809],[1802,3554,3556],{"className":3555},[1813],[1815,3557,3558],{"xmlns":1817,"display":1818},[1820,3559,3560,3596],{},[1823,3561,3562,3564,3566,3572,3574,3576,3593],{},[1829,3563,1895],{},[1836,3565,1899],{"stretchy":1898},[1826,3567,3568,3570],{},[1829,3569,1879],{},[1829,3571,1834],{},[1836,3573,1928],{"stretchy":1898},[1836,3575,1838],{},[3577,3578,3579,3581],"mfrac",{},[1829,3580,3112],{},[1823,3582,3583,3585,3587,3589,3591],{},[1923,3584,1925],{},[1836,3586,1921],{},[1829,3588,3117],{},[1836,3590,1921],{},[1829,3592,3136],{},[1829,3594,3066],{"mathvariant":3595},"normal",[1975,3597,3598],{"encoding":1977},"E(h_t)=\\frac{\\omega}{1-\\alpha-\\beta}.",[1802,3600,3602,3666],{"className":3601,"ariaHidden":1858},[1982],[1802,3603,3605,3608,3611,3614,3654,3657,3660,3663],{"className":3604},[1986],[1802,3606],{"className":3607,"style":2452},[1990],[1802,3609,1895],{"className":3610,"style":2392},[1995,1999],[1802,3612,1899],{"className":3613},[2396],[1802,3615,3617,3620],{"className":3616},[1995],[1802,3618,1879],{"className":3619},[1995,1999],[1802,3621,3623],{"className":3622},[2004],[1802,3624,3626,3646],{"className":3625},[2008,2009],[1802,3627,3629,3643],{"className":3628},[2013],[1802,3630,3632],{"className":3631,"style":2018},[2017],[1802,3633,3634,3637],{"style":2089},[1802,3635],{"className":3636,"style":2026},[2025],[1802,3638,3640],{"className":3639},[2030,2031,2032,2033],[1802,3641,1834],{"className":3642},[1995,1999,2033],[1802,3644,2041],{"className":3645},[2040],[1802,3647,3649],{"className":3648},[2013],[1802,3650,3652],{"className":3651,"style":2048},[2017],[1802,3653],{},[1802,3655,1928],{"className":3656},[2510],[1802,3658],{"className":3659,"style":2054},[1861],[1802,3661,1838],{"className":3662},[2058],[1802,3664],{"className":3665,"style":2054},[1861],[1802,3667,3669,3673,3768],{"className":3668},[1986],[1802,3670],{"className":3671,"style":3672},[1990],"height:1.988em;vertical-align:-0.8804em;",[1802,3674,3676,3680,3765],{"className":3675},[1995],[1802,3677],{"className":3678},[2396,3679],"nulldelimiter",[1802,3681,3683],{"className":3682},[3577],[1802,3684,3686,3756],{"className":3685},[2008,2009],[1802,3687,3689,3753],{"className":3688},[2013],[1802,3690,3693,3730,3741],{"className":3691,"style":3692},[2017],"height:1.1076em;",[1802,3694,3696,3700],{"style":3695},"top:-2.314em;",[1802,3697],{"className":3698,"style":3699},[2025],"height:3em;",[1802,3701,3703,3706,3709,3712,3715,3718,3721,3724,3727],{"className":3702},[1995],[1802,3704,1925],{"className":3705},[1995],[1802,3707],{"className":3708,"style":2113},[1861],[1802,3710,1921],{"className":3711},[2117],[1802,3713],{"className":3714,"style":2113},[1861],[1802,3716,3117],{"className":3717,"style":3267},[1995,1999],[1802,3719],{"className":3720,"style":2113},[1861],[1802,3722,1921],{"className":3723},[2117],[1802,3725],{"className":3726,"style":2113},[1861],[1802,3728,3136],{"className":3729,"style":3349},[1995,1999],[1802,3731,3733,3736],{"style":3732},"top:-3.23em;",[1802,3734],{"className":3735,"style":3699},[2025],[1802,3737],{"className":3738,"style":3740},[3739],"frac-line","border-bottom-width:0.04em;",[1802,3742,3744,3747],{"style":3743},"top:-3.677em;",[1802,3745],{"className":3746,"style":3699},[2025],[1802,3748,3750],{"className":3749},[1995],[1802,3751,3112],{"className":3752,"style":3247},[1995,1999],[1802,3754,2041],{"className":3755},[2040],[1802,3757,3759],{"className":3758},[2013],[1802,3760,3763],{"className":3761,"style":3762},[2017],"height:0.8804em;",[1802,3764],{},[1802,3766],{"className":3767},[2510,3679],[1802,3769,3066],{"className":3770},[1995],[1798,3772,3773],{},"Interpretation:",[3775,3776,3777,3811,3843,3897],"ul",{},[3778,3779,3780,3810],"li",{},[1802,3781,3783,3797],{"className":3782},[1809],[1802,3784,3786],{"className":3785},[1813],[1815,3787,3788],{"xmlns":1817},[1820,3789,3790,3794],{},[1823,3791,3792],{},[1829,3793,3117],{},[1975,3795,3796],{"encoding":1977},"\\alpha",[1802,3798,3800],{"className":3799,"ariaHidden":1858},[1982],[1802,3801,3803,3807],{"className":3802},[1986],[1802,3804],{"className":3805,"style":3806},[1990],"height:0.4306em;",[1802,3808,3117],{"className":3809,"style":3267},[1995,1999]," is the immediate variance response to news;",[3778,3812,3813,3842],{},[1802,3814,3816,3830],{"className":3815},[1809],[1802,3817,3819],{"className":3818},[1813],[1815,3820,3821],{"xmlns":1817},[1820,3822,3823,3827],{},[1823,3824,3825],{},[1829,3826,3136],{},[1975,3828,3829],{"encoding":1977},"\\beta",[1802,3831,3833],{"className":3832,"ariaHidden":1858},[1982],[1802,3834,3836,3839],{"className":3835},[1986],[1802,3837],{"className":3838,"style":3426},[1990],[1802,3840,3136],{"className":3841,"style":3349},[1995,1999]," is persistence in the variance state;",[3778,3844,3845,3896],{},[1802,3846,3848,3866],{"className":3847},[1809],[1802,3849,3851],{"className":3850},[1813],[1815,3852,3853],{"xmlns":1817},[1820,3854,3855,3863],{},[1823,3856,3857,3859,3861],{},[1829,3858,3117],{},[1836,3860,1848],{},[1829,3862,3136],{},[1975,3864,3865],{"encoding":1977},"\\alpha+\\beta",[1802,3867,3869,3887],{"className":3868,"ariaHidden":1858},[1982],[1802,3870,3872,3875,3878,3881,3884],{"className":3871},[1986],[1802,3873],{"className":3874,"style":3243},[1990],[1802,3876,3117],{"className":3877,"style":3267},[1995,1999],[1802,3879],{"className":3880,"style":2113},[1861],[1802,3882,1848],{"className":3883},[2117],[1802,3885],{"className":3886,"style":2113},[1861],[1802,3888,3890,3893],{"className":3889},[1986],[1802,3891],{"className":3892,"style":3426},[1990],[1802,3894,3136],{"className":3895,"style":3349},[1995,1999]," controls the decay of a volatility shock;",[3778,3898,3899,3928],{},[1802,3900,3902,3916],{"className":3901},[1809],[1802,3903,3905],{"className":3904},[1813],[1815,3906,3907],{"xmlns":1817},[1820,3908,3909,3913],{},[1823,3910,3911],{},[1829,3912,3112],{},[1975,3914,3915],{"encoding":1977},"\\omega",[1802,3917,3919],{"className":3918,"ariaHidden":1858},[1982],[1802,3920,3922,3925],{"className":3921},[1986],[1802,3923],{"className":3924,"style":3806},[1990],[1802,3926,3112],{"className":3927,"style":3247},[1995,1999]," sets the long-run scale jointly with persistence.",[1798,3930,3931,3932,3982],{},"When ",[1802,3933,3935,3952],{"className":3934},[1809],[1802,3936,3938],{"className":3937},[1813],[1815,3939,3940],{"xmlns":1817},[1820,3941,3942,3950],{},[1823,3943,3944,3946,3948],{},[1829,3945,3117],{},[1836,3947,1848],{},[1829,3949,3136],{},[1975,3951,3865],{"encoding":1977},[1802,3953,3955,3973],{"className":3954,"ariaHidden":1858},[1982],[1802,3956,3958,3961,3964,3967,3970],{"className":3957},[1986],[1802,3959],{"className":3960,"style":3243},[1990],[1802,3962,3117],{"className":3963,"style":3267},[1995,1999],[1802,3965],{"className":3966,"style":2113},[1861],[1802,3968,1848],{"className":3969},[2117],[1802,3971],{"className":3972,"style":2113},[1861],[1802,3974,3976,3979],{"className":3975},[1986],[1802,3977],{"className":3978,"style":3426},[1990],[1802,3980,3136],{"className":3981,"style":3349},[1995,1999]," is close to one, volatility forecasts revert slowly. That is not the same as a unit root in the return level.",[1793,3984,3986],{"id":3985},"conditional-covariance-as-a-matrix","Conditional covariance as a matrix",[1798,3988,3989],{},"Given past information, a block of future shocks has covariance",[1802,3991,3993],{"className":3992},[1805],[1802,3994,3996,4081],{"className":3995},[1809],[1802,3997,3999],{"className":3998},[1813],[1815,4000,4001],{"xmlns":1817,"display":1818},[1820,4002,4003,4078],{},[1823,4004,4005,4027,4029,4032,4035,4037,4053,4055,4058,4060,4076],{},[1826,4006,4007,4010],{},[1829,4008,4009],{},"H",[1823,4011,4012,4014,4017,4019,4021,4023,4025],{},[1829,4013,1834],{},[1836,4015,4016],{},":",[1829,4018,1834],{},[1836,4020,1848],{},[1829,4022,1879],{},[1836,4024,1908],{},[1829,4026,1834],{},[1836,4028,1838],{},[1829,4030,4031],{"mathvariant":3595},"diag",[1836,4033,4034],{},"⁡",[1836,4036,1899],{"stretchy":1898},[1826,4038,4039,4041],{},[1829,4040,1879],{},[1823,4042,4043,4045,4047,4049,4051],{},[1829,4044,1834],{},[1836,4046,1848],{},[1923,4048,1925],{},[1836,4050,1908],{},[1829,4052,1834],{},[1836,4054,1859],{"separator":1858},[1836,4056,4057],{},"…",[1836,4059,1859],{"separator":1858},[1826,4061,4062,4064],{},[1829,4063,1879],{},[1823,4065,4066,4068,4070,4072,4074],{},[1829,4067,1834],{},[1836,4069,1848],{},[1829,4071,1879],{},[1836,4073,1908],{},[1829,4075,1834],{},[1836,4077,1928],{"stretchy":1898},[1975,4079,4080],{"encoding":1977},"H_{t:t+h\\mid t}\n=\\operatorname{diag}(h_{t+1\\mid t},\\ldots,h_{t+h\\mid t})",[1802,4082,4084,4165],{"className":4083,"ariaHidden":1858},[1982],[1802,4085,4087,4091,4156,4159,4162],{"className":4086},[1986],[1802,4088],{"className":4089,"style":4090},[1990],"height:1.0385em;vertical-align:-0.3552em;",[1802,4092,4094,4098],{"className":4093},[1995],[1802,4095,4009],{"className":4096,"style":4097},[1995,1999],"margin-right:0.0813em;",[1802,4099,4101],{"className":4100},[2004],[1802,4102,4104,4147],{"className":4103},[2008,2009],[1802,4105,4107,4144],{"className":4106},[2013],[1802,4108,4111],{"className":4109,"style":4110},[2017],"height:0.3448em;",[1802,4112,4114,4117],{"style":4113},"top:-2.5198em;margin-left:-0.0813em;margin-right:0.05em;",[1802,4115],{"className":4116,"style":2026},[2025],[1802,4118,4120],{"className":4119},[2030,2031,2032,2033],[1802,4121,4123,4126,4129,4132,4135,4138,4141],{"className":4122},[1995,2033],[1802,4124,1834],{"className":4125},[1995,1999,2033],[1802,4127,4016],{"className":4128},[2058,2033],[1802,4130,1834],{"className":4131},[1995,1999,2033],[1802,4133,1848],{"className":4134},[2117,2033],[1802,4136,1879],{"className":4137},[1995,1999,2033],[1802,4139,1908],{"className":4140},[2058,2033],[1802,4142,1834],{"className":4143},[1995,1999,2033],[1802,4145,2041],{"className":4146},[2040],[1802,4148,4150],{"className":4149},[2013],[1802,4151,4154],{"className":4152,"style":4153},[2017],"height:0.3552em;",[1802,4155],{},[1802,4157],{"className":4158,"style":2054},[1861],[1802,4160,1838],{"className":4161},[2058],[1802,4163],{"className":4164,"style":2054},[1861],[1802,4166,4168,4172,4181,4184,4240,4243,4246,4250,4253,4256,4259,4314],{"className":4167},[1986],[1802,4169],{"className":4170,"style":4171},[1990],"height:1.1052em;vertical-align:-0.3552em;",[1802,4173,4176],{"className":4174},[4175],"mop",[1802,4177,4031],{"className":4178,"style":4180},[1995,4179],"mathrm","margin-right:0.0139em;",[1802,4182,1899],{"className":4183},[2396],[1802,4185,4187,4190],{"className":4186},[1995],[1802,4188,1879],{"className":4189},[1995,1999],[1802,4191,4193],{"className":4192},[2004],[1802,4194,4196,4232],{"className":4195},[2008,2009],[1802,4197,4199,4229],{"className":4198},[2013],[1802,4200,4202],{"className":4201,"style":4110},[2017],[1802,4203,4205,4208],{"style":4204},"top:-2.5198em;margin-left:0em;margin-right:0.05em;",[1802,4206],{"className":4207,"style":2026},[2025],[1802,4209,4211],{"className":4210},[2030,2031,2032,2033],[1802,4212,4214,4217,4220,4223,4226],{"className":4213},[1995,2033],[1802,4215,1834],{"className":4216},[1995,1999,2033],[1802,4218,1848],{"className":4219},[2117,2033],[1802,4221,1925],{"className":4222},[1995,2033],[1802,4224,1908],{"className":4225},[2058,2033],[1802,4227,1834],{"className":4228},[1995,1999,2033],[1802,4230,2041],{"className":4231},[2040],[1802,4233,4235],{"className":4234},[2013],[1802,4236,4238],{"className":4237,"style":4153},[2017],[1802,4239],{},[1802,4241,1859],{"className":4242},[2171],[1802,4244],{"className":4245,"style":2179},[1861],[1802,4247,4057],{"className":4248},[4249],"minner",[1802,4251],{"className":4252,"style":2179},[1861],[1802,4254,1859],{"className":4255},[2171],[1802,4257],{"className":4258,"style":2179},[1861],[1802,4260,4262,4265],{"className":4261},[1995],[1802,4263,1879],{"className":4264},[1995,1999],[1802,4266,4268],{"className":4267},[2004],[1802,4269,4271,4306],{"className":4270},[2008,2009],[1802,4272,4274,4303],{"className":4273},[2013],[1802,4275,4277],{"className":4276,"style":4110},[2017],[1802,4278,4279,4282],{"style":4204},[1802,4280],{"className":4281,"style":2026},[2025],[1802,4283,4285],{"className":4284},[2030,2031,2032,2033],[1802,4286,4288,4291,4294,4297,4300],{"className":4287},[1995,2033],[1802,4289,1834],{"className":4290},[1995,1999,2033],[1802,4292,1848],{"className":4293},[2117,2033],[1802,4295,1879],{"className":4296},[1995,1999,2033],[1802,4298,1908],{"className":4299},[2058,2033],[1802,4301,1834],{"className":4302},[1995,1999,2033],[1802,4304,2041],{"className":4305},[2040],[1802,4307,4309],{"className":4308},[2013],[1802,4310,4312],{"className":4311,"style":4153},[2017],[1802,4313],{},[1802,4315,1928],{"className":4316},[2510],[1798,4318,4319,4320,4392],{},"only when future standardised innovations are conditionally uncorrelated. In a multivariate model, ",[1802,4321,4323,4341],{"className":4322},[1809],[1802,4324,4326],{"className":4325},[1813],[1815,4327,4328],{"xmlns":1817},[1820,4329,4330,4338],{},[1823,4331,4332],{},[1826,4333,4334,4336],{},[1829,4335,4009],{},[1829,4337,1834],{},[1975,4339,4340],{"encoding":1977},"H_t",[1802,4342,4344],{"className":4343,"ariaHidden":1858},[1982],[1802,4345,4347,4351],{"className":4346},[1986],[1802,4348],{"className":4349,"style":4350},[1990],"height:0.8333em;vertical-align:-0.15em;",[1802,4352,4354,4357],{"className":4353},[1995],[1802,4355,4009],{"className":4356,"style":4097},[1995,1999],[1802,4358,4360],{"className":4359},[2004],[1802,4361,4363,4384],{"className":4362},[2008,2009],[1802,4364,4366,4381],{"className":4365},[2013],[1802,4367,4369],{"className":4368,"style":2018},[2017],[1802,4370,4372,4375],{"style":4371},"top:-2.55em;margin-left:-0.0813em;margin-right:0.05em;",[1802,4373],{"className":4374,"style":2026},[2025],[1802,4376,4378],{"className":4377},[2030,2031,2032,2033],[1802,4379,1834],{"className":4380},[1995,1999,2033],[1802,4382,2041],{"className":4383},[2040],[1802,4385,4387],{"className":4386},[2013],[1802,4388,4390],{"className":4389,"style":2048},[2017],[1802,4391],{}," is a full positive-definite matrix and must simultaneously control variances and correlations.",[1798,4394,4395],{},"The one-step GARCH forecast is",[1802,4397,4399],{"className":4398},[1805],[1802,4400,4402,4458],{"className":4401},[1809],[1802,4403,4405],{"className":4404},[1813],[1815,4406,4407],{"xmlns":1817,"display":1818},[1820,4408,4409,4455],{},[1823,4410,4411,4427,4429,4431,4433,4435,4443,4445,4447,4453],{},[1826,4412,4413,4415],{},[1829,4414,1879],{},[1823,4416,4417,4419,4421,4423,4425],{},[1829,4418,1834],{},[1836,4420,1848],{},[1923,4422,1925],{},[1836,4424,1908],{},[1829,4426,1834],{},[1836,4428,1838],{},[1829,4430,3112],{},[1836,4432,1848],{},[1829,4434,3117],{},[1944,4436,4437,4439,4441],{},[1829,4438,1853],{},[1829,4440,1834],{},[1923,4442,1952],{},[1836,4444,1848],{},[1829,4446,3136],{},[1826,4448,4449,4451],{},[1829,4450,1879],{},[1829,4452,1834],{},[1829,4454,3066],{"mathvariant":3595},[1975,4456,4457],{"encoding":1977},"h_{t+1\\mid t}=\\omega+\\alpha\\varepsilon_t^2+\\beta h_t.",[1802,4459,4461,4532,4550,4620],{"className":4460,"ariaHidden":1858},[1982],[1802,4462,4464,4468,4523,4526,4529],{"className":4463},[1986],[1802,4465],{"className":4466,"style":4467},[1990],"height:1.0496em;vertical-align:-0.3552em;",[1802,4469,4471,4474],{"className":4470},[1995],[1802,4472,1879],{"className":4473},[1995,1999],[1802,4475,4477],{"className":4476},[2004],[1802,4478,4480,4515],{"className":4479},[2008,2009],[1802,4481,4483,4512],{"className":4482},[2013],[1802,4484,4486],{"className":4485,"style":4110},[2017],[1802,4487,4488,4491],{"style":4204},[1802,4489],{"className":4490,"style":2026},[2025],[1802,4492,4494],{"className":4493},[2030,2031,2032,2033],[1802,4495,4497,4500,4503,4506,4509],{"className":4496},[1995,2033],[1802,4498,1834],{"className":4499},[1995,1999,2033],[1802,4501,1848],{"className":4502},[2117,2033],[1802,4504,1925],{"className":4505},[1995,2033],[1802,4507,1908],{"className":4508},[2058,2033],[1802,4510,1834],{"className":4511},[1995,1999,2033],[1802,4513,2041],{"className":4514},[2040],[1802,4516,4518],{"className":4517},[2013],[1802,4519,4521],{"className":4520,"style":4153},[2017],[1802,4522],{},[1802,4524],{"className":4525,"style":2054},[1861],[1802,4527,1838],{"className":4528},[2058],[1802,4530],{"className":4531,"style":2054},[1861],[1802,4533,4535,4538,4541,4544,4547],{"className":4534},[1986],[1802,4536],{"className":4537,"style":3243},[1990],[1802,4539,3112],{"className":4540,"style":3247},[1995,1999],[1802,4542],{"className":4543,"style":2113},[1861],[1802,4545,1848],{"className":4546},[2117],[1802,4548],{"className":4549,"style":2113},[1861],[1802,4551,4553,4557,4560,4611,4614,4617],{"className":4552},[1986],[1802,4554],{"className":4555,"style":4556},[1990],"height:1.1111em;vertical-align:-0.247em;",[1802,4558,3117],{"className":4559,"style":3267},[1995,1999],[1802,4561,4563,4566],{"className":4562},[1995],[1802,4564,1853],{"className":4565},[1995,1999],[1802,4567,4569],{"className":4568},[2004],[1802,4570,4572,4603],{"className":4571},[2008,2009],[1802,4573,4575,4600],{"className":4574},[2013],[1802,4576,4578,4589],{"className":4577,"style":2564},[2017],[1802,4579,4580,4583],{"style":3288},[1802,4581],{"className":4582,"style":2026},[2025],[1802,4584,4586],{"className":4585},[2030,2031,2032,2033],[1802,4587,1834],{"className":4588},[1995,1999,2033],[1802,4590,4591,4594],{"style":2579},[1802,4592],{"className":4593,"style":2026},[2025],[1802,4595,4597],{"className":4596},[2030,2031,2032,2033],[1802,4598,1952],{"className":4599},[1995,2033],[1802,4601,2041],{"className":4602},[2040],[1802,4604,4606],{"className":4605},[2013],[1802,4607,4609],{"className":4608,"style":2598},[2017],[1802,4610],{},[1802,4612],{"className":4613,"style":2113},[1861],[1802,4615,1848],{"className":4616},[2117],[1802,4618],{"className":4619,"style":2113},[1861],[1802,4621,4623,4626,4629,4669],{"className":4622},[1986],[1802,4624],{"className":4625,"style":3426},[1990],[1802,4627,3136],{"className":4628,"style":3349},[1995,1999],[1802,4630,4632,4635],{"className":4631},[1995],[1802,4633,1879],{"className":4634},[1995,1999],[1802,4636,4638],{"className":4637},[2004],[1802,4639,4641,4661],{"className":4640},[2008,2009],[1802,4642,4644,4658],{"className":4643},[2013],[1802,4645,4647],{"className":4646,"style":2018},[2017],[1802,4648,4649,4652],{"style":2089},[1802,4650],{"className":4651,"style":2026},[2025],[1802,4653,4655],{"className":4654},[2030,2031,2032,2033],[1802,4656,1834],{"className":4657},[1995,1999,2033],[1802,4659,2041],{"className":4660},[2040],[1802,4662,4664],{"className":4663},[2013],[1802,4665,4667],{"className":4666,"style":2048},[2017],[1802,4668],{},[1802,4670,3066],{"className":4671},[1995],[1798,4673,4674,4675,1859],{},"For ",[1802,4676,4678,4697],{"className":4677},[1809],[1802,4679,4681],{"className":4680},[1813],[1815,4682,4683],{"xmlns":1817},[1820,4684,4685,4694],{},[1823,4686,4687,4690,4692],{},[1829,4688,4689],{},"k",[1836,4691,3172],{},[1923,4693,1952],{},[1975,4695,4696],{"encoding":1977},"k\\ge2",[1802,4698,4700,4720],{"className":4699,"ariaHidden":1858},[1982],[1802,4701,4703,4707,4711,4714,4717],{"className":4702},[1986],[1802,4704],{"className":4705,"style":4706},[1990],"height:0.8304em;vertical-align:-0.136em;",[1802,4708,4689],{"className":4709,"style":4710},[1995,1999],"margin-right:0.0315em;",[1802,4712],{"className":4713,"style":2054},[1861],[1802,4715,3172],{"className":4716},[2058],[1802,4718],{"className":4719,"style":2054},[1861],[1802,4721,4723,4726],{"className":4722},[1986],[1802,4724],{"className":4725,"style":2683},[1990],[1802,4727,1952],{"className":4728},[1995],[1802,4730,4732],{"className":4731},[1805],[1802,4733,4735,4801],{"className":4734},[1809],[1802,4736,4738],{"className":4737},[1813],[1815,4739,4740],{"xmlns":1817,"display":1818},[1820,4741,4742,4798],{},[1823,4743,4744,4760,4762,4764,4766,4768,4770,4772,4774,4776,4796],{},[1826,4745,4746,4748],{},[1829,4747,1879],{},[1823,4749,4750,4752,4754,4756,4758],{},[1829,4751,1834],{},[1836,4753,1848],{},[1829,4755,4689],{},[1836,4757,1908],{},[1829,4759,1834],{},[1836,4761,1838],{},[1829,4763,3112],{},[1836,4765,1848],{},[1836,4767,1899],{"stretchy":1898},[1829,4769,3117],{},[1836,4771,1848],{},[1829,4773,3136],{},[1836,4775,1928],{"stretchy":1898},[1826,4777,4778,4780],{},[1829,4779,1879],{},[1823,4781,4782,4784,4786,4788,4790,4792,4794],{},[1829,4783,1834],{},[1836,4785,1848],{},[1829,4787,4689],{},[1836,4789,1921],{},[1923,4791,1925],{},[1836,4793,1908],{},[1829,4795,1834],{},[1829,4797,3066],{"mathvariant":3595},[1975,4799,4800],{"encoding":1977},"h_{t+k\\mid t}=\\omega+(\\alpha+\\beta)h_{t+k-1\\mid t}.",[1802,4802,4804,4874,4892,4913],{"className":4803,"ariaHidden":1858},[1982],[1802,4805,4807,4810,4865,4868,4871],{"className":4806},[1986],[1802,4808],{"className":4809,"style":4467},[1990],[1802,4811,4813,4816],{"className":4812},[1995],[1802,4814,1879],{"className":4815},[1995,1999],[1802,4817,4819],{"className":4818},[2004],[1802,4820,4822,4857],{"className":4821},[2008,2009],[1802,4823,4825,4854],{"className":4824},[2013],[1802,4826,4828],{"className":4827,"style":4110},[2017],[1802,4829,4830,4833],{"style":4204},[1802,4831],{"className":4832,"style":2026},[2025],[1802,4834,4836],{"className":4835},[2030,2031,2032,2033],[1802,4837,4839,4842,4845,4848,4851],{"className":4838},[1995,2033],[1802,4840,1834],{"className":4841},[1995,1999,2033],[1802,4843,1848],{"className":4844},[2117,2033],[1802,4846,4689],{"className":4847,"style":4710},[1995,1999,2033],[1802,4849,1908],{"className":4850},[2058,2033],[1802,4852,1834],{"className":4853},[1995,1999,2033],[1802,4855,2041],{"className":4856},[2040],[1802,4858,4860],{"className":4859},[2013],[1802,4861,4863],{"className":4862,"style":4153},[2017],[1802,4864],{},[1802,4866],{"className":4867,"style":2054},[1861],[1802,4869,1838],{"className":4870},[2058],[1802,4872],{"className":4873,"style":2054},[1861],[1802,4875,4877,4880,4883,4886,4889],{"className":4876},[1986],[1802,4878],{"className":4879,"style":3243},[1990],[1802,4881,3112],{"className":4882,"style":3247},[1995,1999],[1802,4884],{"className":4885,"style":2113},[1861],[1802,4887,1848],{"className":4888},[2117],[1802,4890],{"className":4891,"style":2113},[1861],[1802,4893,4895,4898,4901,4904,4907,4910],{"className":4894},[1986],[1802,4896],{"className":4897,"style":2452},[1990],[1802,4899,1899],{"className":4900},[2396],[1802,4902,3117],{"className":4903,"style":3267},[1995,1999],[1802,4905],{"className":4906,"style":2113},[1861],[1802,4908,1848],{"className":4909},[2117],[1802,4911],{"className":4912,"style":2113},[1861],[1802,4914,4916,4919,4922,4925,4986],{"className":4915},[1986],[1802,4917],{"className":4918,"style":4171},[1990],[1802,4920,3136],{"className":4921,"style":3349},[1995,1999],[1802,4923,1928],{"className":4924},[2510],[1802,4926,4928,4931],{"className":4927},[1995],[1802,4929,1879],{"className":4930},[1995,1999],[1802,4932,4934],{"className":4933},[2004],[1802,4935,4937,4978],{"className":4936},[2008,2009],[1802,4938,4940,4975],{"className":4939},[2013],[1802,4941,4943],{"className":4942,"style":4110},[2017],[1802,4944,4945,4948],{"style":4204},[1802,4946],{"className":4947,"style":2026},[2025],[1802,4949,4951],{"className":4950},[2030,2031,2032,2033],[1802,4952,4954,4957,4960,4963,4966,4969,4972],{"className":4953},[1995,2033],[1802,4955,1834],{"className":4956},[1995,1999,2033],[1802,4958,1848],{"className":4959},[2117,2033],[1802,4961,4689],{"className":4962,"style":4710},[1995,1999,2033],[1802,4964,1921],{"className":4965},[2117,2033],[1802,4967,1925],{"className":4968},[1995,2033],[1802,4970,1908],{"className":4971},[2058,2033],[1802,4973,1834],{"className":4974},[1995,1999,2033],[1802,4976,2041],{"className":4977},[2040],[1802,4979,4981],{"className":4980},[2013],[1802,4982,4984],{"className":4983,"style":4153},[2017],[1802,4985],{},[1802,4987,3066],{"className":4988},[1995],[1793,4990,4992],{"id":4991},"gaussian-quasi-likelihood","Gaussian 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h_t(\\theta)+\\frac{\\varepsilon_t^2}{h_t(\\theta)}\\right].",[1802,5103,5105,5132],{"className":5104,"ariaHidden":1858},[1982],[1802,5106,5108,5111,5114,5117,5120,5123,5126,5129],{"className":5107},[1986],[1802,5109],{"className":5110,"style":2452},[1990],[1802,5112,5013],{"className":5113},[1995],[1802,5115,1899],{"className":5116},[2396],[1802,5118,5018],{"className":5119,"style":2000},[1995,1999],[1802,5121,1928],{"className":5122},[2510],[1802,5124],{"className":5125,"style":2054},[1861],[1802,5127,1838],{"className":5128},[2058],[1802,5130],{"className":5131,"style":2054},[1861],[1802,5133,5135,5139,5203,5206,5283,5286,5532,5535],{"className":5134},[1986],[1802,5136],{"className":5137,"style":5138},[1990],"height:3.0954em;vertical-align:-1.2671em;",[1802,5140,5142,5145,5200],{"className":5141},[1995],[1802,5143],{"className":5144},[2396,3679],[1802,5146,5148],{"className":5147},[3577],[1802,5149,5151,5191],{"className":5150},[2008,2009],[1802,5152,5154,5188],{"className":5153},[2013],[1802,5155,5158,5169,5177],{"className":5156,"style":5157},[2017],"height:1.3214em;",[1802,5159,5160,5163],{"style":3695},[1802,5161],{"className":5162,"style":3699},[2025],[1802,5164,5166],{"className":5165},[1995],[1802,5167,1952],{"className":5168},[1995],[1802,5170,5171,5174],{"style":3732},[1802,5172],{"className":5173,"style":3699},[2025],[1802,5175],{"className":5176,"style":3740},[3739],[1802,5178,5179,5182],{"style":3743},[1802,5180],{"className":5181,"style":3699},[2025],[1802,5183,5185],{"className":5184},[1995],[1802,5186,1925],{"className":5187},[1995],[1802,5189,2041],{"className":5190},[2040],[1802,5192,5194],{"className":5193},[2013],[1802,5195,5198],{"className":5196,"style":5197},[2017],"height:0.686em;",[1802,5199],{},[1802,5201],{"className":5202},[2510,3679],[1802,5204],{"className":5205,"style":2179},[1861],[1802,5207,5210],{"className":5208},[4175,5209],"op-limits",[1802,5211,5213,5274],{"className":5212},[2008,2009],[1802,5214,5216,5271],{"className":5215},[2013],[1802,5217,5220,5242,5255],{"className":5218,"style":5219},[2017],"height:1.8283em;",[1802,5221,5223,5227],{"style":5222},"top:-1.8829em;margin-left:0em;",[1802,5224],{"className":5225,"style":5226},[2025],"height:3.05em;",[1802,5228,5230],{"className":5229},[2030,2031,2032,2033],[1802,5231,5233,5236,5239],{"className":5232},[1995,2033],[1802,5234,1834],{"className":5235},[1995,1999,2033],[1802,5237,1838],{"className":5238},[2058,2033],[1802,5240,1925],{"className":5241},[1995,2033],[1802,5243,5245,5248],{"style":5244},"top:-3.05em;",[1802,5246],{"className":5247,"style":5226},[2025],[1802,5249,5250],{},[1802,5251,5034],{"className":5252},[4175,5253,5254],"op-symbol","large-op",[1802,5256,5258,5261],{"style":5257},"top:-4.3em;margin-left:0em;",[1802,5259],{"className":5260,"style":5226},[2025],[1802,5262,5264],{"className":5263},[2030,2031,2032,2033],[1802,5265,5267],{"className":5266},[1995,2033],[1802,5268,5045],{"className":5269,"style":5270},[1995,1999,2033],"margin-right:0.1389em;",[1802,5272,2041],{"className":5273},[2040],[1802,5275,5277],{"className":5276},[2013],[1802,5278,5281],{"className":5279,"style":5280},[2017],"height:1.2671em;",[1802,5282],{},[1802,5284],{"className":5285,"style":2179},[1861],[1802,5287,5289,5298,5305,5308,5348,5351,5354,5357,5360,5363,5366,5526],{"className":5288},[4249],[1802,5290,5294],{"className":5291,"style":5293},[2396,5292],"delimcenter","top:0em;",[1802,5295,5050],{"className":5296},[5297,2032],"delimsizing",[1802,5299,5301,5302],{"className":5300},[4175],"lo",[1802,5303,5304],{"style":4180},"g",[1802,5306],{"className":5307,"style":2179},[1861],[1802,5309,5311,5314],{"className":5310},[1995],[1802,5312,1879],{"className":5313},[1995,1999],[1802,5315,5317],{"className":5316},[2004],[1802,5318,5320,5340],{"className":5319},[2008,2009],[1802,5321,5323,5337],{"className":5322},[2013],[1802,5324,5326],{"className":5325,"style":2018},[2017],[1802,5327,5328,5331],{"style":2089},[1802,5329],{"className":5330,"style":2026},[2025],[1802,5332,5334],{"className":5333},[2030,2031,2032,2033],[1802,5335,1834],{"className":5336},[1995,1999,2033],[1802,5338,2041],{"className":5339},[2040],[1802,5341,5343],{"className":5342},[2013],[1802,5344,5346],{"className":5345,"style":2048},[2017],[1802,5347],{},[1802,5349,1899],{"className":5350},[2396],[1802,5352,5018],{"className":5353,"style":2000},[1995,1999],[1802,5355,1928],{"className":5356},[2510],[1802,5358],{"className":5359,"style":2113},[1861],[1802,5361,1848],{"className":5362},[2117],[1802,5364],{"className":5365,"style":2113},[1861],[1802,5367,5369,5372,5523],{"className":5368},[1995],[1802,5370],{"className":5371},[2396,3679],[1802,5373,5375],{"className":5374},[3577],[1802,5376,5378,5514],{"className":5377},[2008,2009],[1802,5379,5381,5511],{"className":5380},[2013],[1802,5382,5385,5442,5450],{"className":5383,"style":5384},[2017],"height:1.4911em;",[1802,5386,5387,5390],{"style":3695},[1802,5388],{"className":5389,"style":3699},[2025],[1802,5391,5393,5433,5436,5439],{"className":5392},[1995],[1802,5394,5396,5399],{"className":5395},[1995],[1802,5397,1879],{"className":5398},[1995,1999],[1802,5400,5402],{"className":5401},[2004],[1802,5403,5405,5425],{"className":5404},[2008,2009],[1802,5406,5408,5422],{"className":5407},[2013],[1802,5409,5411],{"className":5410,"style":2018},[2017],[1802,5412,5413,5416],{"style":2089},[1802,5414],{"className":5415,"style":2026},[2025],[1802,5417,5419],{"className":5418},[2030,2031,2032,2033],[1802,5420,1834],{"className":5421},[1995,1999,2033],[1802,5423,2041],{"className":5424},[2040],[1802,5426,5428],{"className":5427},[2013],[1802,5429,5431],{"className":5430,"style":2048},[2017],[1802,5432],{},[1802,5434,1899],{"className":5435},[2396],[1802,5437,5018],{"className":5438,"style":2000},[1995,1999],[1802,5440,1928],{"className":5441},[2510],[1802,5443,5444,5447],{"style":3732},[1802,5445],{"className":5446,"style":3699},[2025],[1802,5448],{"className":5449,"style":3740},[3739],[1802,5451,5452,5455],{"style":3743},[1802,5453],{"className":5454,"style":3699},[2025],[1802,5456,5458],{"className":5457},[1995],[1802,5459,5461,5464],{"className":5460},[1995],[1802,5462,1853],{"className":5463},[1995,1999],[1802,5465,5467],{"className":5466},[2004],[1802,5468,5470,5503],{"className":5469},[2008,2009],[1802,5471,5473,5500],{"className":5472},[2013],[1802,5474,5477,5488],{"className":5475,"style":5476},[2017],"height:0.8141em;",[1802,5478,5479,5482],{"style":3288},[1802,5480],{"className":5481,"style":2026},[2025],[1802,5483,5485],{"className":5484},[2030,2031,2032,2033],[1802,5486,1834],{"className":5487},[1995,1999,2033],[1802,5489,5491,5494],{"style":5490},"top:-3.063em;margin-right:0.05em;",[1802,5492],{"className":5493,"style":2026},[2025],[1802,5495,5497],{"className":5496},[2030,2031,2032,2033],[1802,5498,1952],{"className":5499},[1995,2033],[1802,5501,2041],{"className":5502},[2040],[1802,5504,5506],{"className":5505},[2013],[1802,5507,5509],{"className":5508,"style":2598},[2017],[1802,5510],{},[1802,5512,2041],{"className":5513},[2040],[1802,5515,5517],{"className":5516},[2013],[1802,5518,5521],{"className":5519,"style":5520},[2017],"height:0.936em;",[1802,5522],{},[1802,5524],{"className":5525},[2510,3679],[1802,5527,5529],{"className":5528,"style":5293},[2510,5292],[1802,5530,5096],{"className":5531},[5297,2032],[1802,5533],{"className":5534,"style":2179},[1861],[1802,5536,3066],{"className":5537},[1995],[1798,5539,5540,5541,5545,5546,5616],{},"It is a ",[5542,5543,5544],"strong",{},"quasi","-likelihood when ",[1802,5547,5549,5567],{"className":5548},[1809],[1802,5550,5552],{"className":5551},[1813],[1815,5553,5554],{"xmlns":1817},[1820,5555,5556,5564],{},[1823,5557,5558],{},[1826,5559,5560,5562],{},[1829,5561,1886],{},[1829,5563,1834],{},[1975,5565,5566],{"encoding":1977},"z_t",[1802,5568,5570],{"className":5569,"ariaHidden":1858},[1982],[1802,5571,5573,5576],{"className":5572},[1986],[1802,5574],{"className":5575,"style":1991},[1990],[1802,5577,5579,5582],{"className":5578},[1995],[1802,5580,1886],{"className":5581,"style":2344},[1995,1999],[1802,5583,5585],{"className":5584},[2004],[1802,5586,5588,5608],{"className":5587},[2008,2009],[1802,5589,5591,5605],{"className":5590},[2013],[1802,5592,5594],{"className":5593,"style":2018},[2017],[1802,5595,5596,5599],{"style":2359},[1802,5597],{"className":5598,"style":2026},[2025],[1802,5600,5602],{"className":5601},[2030,2031,2032,2033],[1802,5603,1834],{"className":5604},[1995,1999,2033],[1802,5606,2041],{"className":5607},[2040],[1802,5609,5611],{"className":5610},[2013],[1802,5612,5614],{"className":5613,"style":2048},[2017],[1802,5615],{}," is not Gaussian. Under suitable conditions it can still estimate the variance recursion consistently, but Gaussian tail probabilities and conventional standard errors need not be valid.",[1798,5618,5619],{},"Always inspect standardised residuals",[1802,5621,5623],{"className":5622},[1805],[1802,5624,5626,5679],{"className":5625},[1809],[1802,5627,5629],{"className":5628},[1813],[1815,5630,5631],{"xmlns":1817,"display":1818},[1820,5632,5633,5676],{},[1823,5634,5635,5647,5649,5659,5662,5674],{},[1826,5636,5637,5645],{},[5638,5639,5640,5642],"mover",{"accent":1858},[1829,5641,1886],{},[1836,5643,5644],{},"^",[1829,5646,1834],{},[1836,5648,1838],{},[1826,5650,5651,5657],{},[5638,5652,5653,5655],{"accent":1858},[1829,5654,1853],{},[1836,5656,5644],{},[1829,5658,1834],{},[1829,5660,5661],{"mathvariant":3595},"\u002F",[1873,5663,5664],{},[1826,5665,5666,5672],{},[5638,5667,5668,5670],{"accent":1858},[1829,5669,1879],{},[1836,5671,5644],{},[1829,5673,1834],{},[1829,5675,3066],{"mathvariant":3595},[1975,5677,5678],{"encoding":1977},"\\hat z_t=\\hat\\varepsilon_t\u002F\\sqrt{\\hat h_t}.",[1802,5680,5682,5770],{"className":5681,"ariaHidden":1858},[1982],[1802,5683,5685,5688,5761,5764,5767],{"className":5684},[1986],[1802,5686],{"className":5687,"style":2791},[1990],[1802,5689,5691,5727],{"className":5690},[1995],[1802,5692,5695],{"className":5693},[1995,5694],"accent",[1802,5696,5698],{"className":5697},[2008],[1802,5699,5701],{"className":5700},[2013],[1802,5702,5705,5714],{"className":5703,"style":5704},[2017],"height:0.6944em;",[1802,5706,5708,5711],{"style":5707},"top:-3em;",[1802,5709],{"className":5710,"style":3699},[2025],[1802,5712,1886],{"className":5713,"style":2344},[1995,1999],[1802,5715,5716,5719],{"style":5707},[1802,5717],{"className":5718,"style":3699},[2025],[1802,5720,5724],{"className":5721,"style":5723},[5722],"accent-body","left:-0.1944em;",[1802,5725,5644],{"className":5726},[1995],[1802,5728,5730],{"className":5729},[2004],[1802,5731,5733,5753],{"className":5732},[2008,2009],[1802,5734,5736,5750],{"className":5735},[2013],[1802,5737,5739],{"className":5738,"style":2018},[2017],[1802,5740,5741,5744],{"style":2359},[1802,5742],{"className":5743,"style":2026},[2025],[1802,5745,5747],{"className":5746},[2030,2031,2032,2033],[1802,5748,1834],{"className":5749},[1995,1999,2033],[1802,5751,2041],{"className":5752},[2040],[1802,5754,5756],{"className":5755},[2013],[1802,5757,5759],{"className":5758,"style":2048},[2017],[1802,5760],{},[1802,5762],{"className":5763,"style":2054},[1861],[1802,5765,1838],{"className":5766},[2058],[1802,5768],{"className":5769,"style":2054},[1861],[1802,5771,5773,5777,5846,5849,5973],{"className":5772},[1986],[1802,5774],{"className":5775,"style":5776},[1990],"height:1.84em;vertical-align:-0.4022em;",[1802,5778,5780,5812],{"className":5779},[1995],[1802,5781,5783],{"className":5782},[1995,5694],[1802,5784,5786],{"className":5785},[2008],[1802,5787,5789],{"className":5788},[2013],[1802,5790,5792,5800],{"className":5791,"style":5704},[2017],[1802,5793,5794,5797],{"style":5707},[1802,5795],{"className":5796,"style":3699},[2025],[1802,5798,1853],{"className":5799},[1995,1999],[1802,5801,5802,5805],{"style":5707},[1802,5803],{"className":5804,"style":3699},[2025],[1802,5806,5809],{"className":5807,"style":5808},[5722],"left:-0.1667em;",[1802,5810,5644],{"className":5811},[1995],[1802,5813,5815],{"className":5814},[2004],[1802,5816,5818,5838],{"className":5817},[2008,2009],[1802,5819,5821,5835],{"className":5820},[2013],[1802,5822,5824],{"className":5823,"style":2018},[2017],[1802,5825,5826,5829],{"style":2089},[1802,5827],{"className":5828,"style":2026},[2025],[1802,5830,5832],{"className":5831},[2030,2031,2032,2033],[1802,5833,1834],{"className":5834},[1995,1999,2033],[1802,5836,2041],{"className":5837},[2040],[1802,5839,5841],{"className":5840},[2013],[1802,5842,5844],{"className":5843,"style":2048},[2017],[1802,5845],{},[1802,5847,5661],{"className":5848},[1995],[1802,5850,5852],{"className":5851},[1995,2239],[1802,5853,5855,5964],{"className":5854},[2008,2009],[1802,5856,5858,5961],{"className":5857},[2013],[1802,5859,5862,5944],{"className":5860,"style":5861},[2017],"height:1.4378em;",[1802,5863,5866,5870],{"className":5864,"style":5865},[2253],"top:-3.8em;",[1802,5867],{"className":5868,"style":5869},[2025],"height:3.8em;",[1802,5871,5873],{"className":5872,"style":2262},[1995],[1802,5874,5876,5910],{"className":5875},[1995],[1802,5877,5879],{"className":5878},[1995,5694],[1802,5880,5882],{"className":5881},[2008],[1802,5883,5885],{"className":5884},[2013],[1802,5886,5889,5897],{"className":5887,"style":5888},[2017],"height:0.9579em;",[1802,5890,5891,5894],{"style":5707},[1802,5892],{"className":5893,"style":3699},[2025],[1802,5895,1879],{"className":5896},[1995,1999],[1802,5898,5900,5903],{"style":5899},"top:-3.2634em;",[1802,5901],{"className":5902,"style":3699},[2025],[1802,5904,5907],{"className":5905,"style":5906},[5722],"left:-0.25em;",[1802,5908,5644],{"className":5909},[1995],[1802,5911,5913],{"className":5912},[2004],[1802,5914,5916,5936],{"className":5915},[2008,2009],[1802,5917,5919,5933],{"className":5918},[2013],[1802,5920,5922],{"className":5921,"style":2018},[2017],[1802,5923,5924,5927],{"style":2089},[1802,5925],{"className":5926,"style":2026},[2025],[1802,5928,5930],{"className":5929},[2030,2031,2032,2033],[1802,5931,1834],{"className":5932},[1995,1999,2033],[1802,5934,2041],{"className":5935},[2040],[1802,5937,5939],{"className":5938},[2013],[1802,5940,5942],{"className":5941,"style":2048},[2017],[1802,5943],{},[1802,5945,5947,5950],{"style":5946},"top:-3.3978em;",[1802,5948],{"className":5949,"style":5869},[2025],[1802,5951,5954],{"className":5952,"style":5953},[2312],"min-width:1.02em;height:1.88em;",[2315,5955,5958],{"xmlns":2317,"width":2318,"height":5956,"viewBox":5957,"preserveAspectRatio":2321},"1.88em","0 0 400000 1944",[2323,5959],{"d":5960},"M983 90\nl0 -0\nc4,-6.7,10,-10,18,-10 H400000v40\nH1013.1s-83.4,268,-264.1,840c-180.7,572,-277,876.3,-289,913c-4.7,4.7,-12.7,7,-24,7\ns-12,0,-12,0c-1.3,-3.3,-3.7,-11.7,-7,-25c-35.3,-125.3,-106.7,-373.3,-214,-744\nc-10,12,-21,25,-33,39s-32,39,-32,39c-6,-5.3,-15,-14,-27,-26s25,-30,25,-30\nc26.7,-32.7,52,-63,76,-91s52,-60,52,-60s208,722,208,722\nc56,-175.3,126.3,-397.3,211,-666c84.7,-268.7,153.8,-488.2,207.5,-658.5\nc53.7,-170.3,84.5,-266.8,92.5,-289.5z\nM1001 80h400000v40h-400000z",[1802,5962,2041],{"className":5963},[2040],[1802,5965,5967],{"className":5966},[2013],[1802,5968,5971],{"className":5969,"style":5970},[2017],"height:0.4022em;",[1802,5972],{},[1802,5974,3066],{"className":5975},[1995],[1798,5977,5978,5979,6095,6096,6198],{},"Remaining dependence in ",[1802,5980,5982,6006],{"className":5981},[1809],[1802,5983,5985],{"className":5984},[1813],[1815,5986,5987],{"xmlns":1817},[1820,5988,5989,6003],{},[1823,5990,5991],{},[1944,5992,5993,5999,6001],{},[5638,5994,5995,5997],{"accent":1858},[1829,5996,1886],{},[1836,5998,5644],{},[1829,6000,1834],{},[1923,6002,1952],{},[1975,6004,6005],{"encoding":1977},"\\hat z_t^2",[1802,6007,6009],{"className":6008,"ariaHidden":1858},[1982],[1802,6010,6012,6016],{"className":6011},[1986],[1802,6013],{"className":6014,"style":6015},[1990],"height:1.0611em;vertical-align:-0.247em;",[1802,6017,6019,6050],{"className":6018},[1995],[1802,6020,6022],{"className":6021},[1995,5694],[1802,6023,6025],{"className":6024},[2008],[1802,6026,6028],{"className":6027},[2013],[1802,6029,6031,6039],{"className":6030,"style":5704},[2017],[1802,6032,6033,6036],{"style":5707},[1802,6034],{"className":6035,"style":3699},[2025],[1802,6037,1886],{"className":6038,"style":2344},[1995,1999],[1802,6040,6041,6044],{"style":5707},[1802,6042],{"className":6043,"style":3699},[2025],[1802,6045,6047],{"className":6046,"style":5723},[5722],[1802,6048,5644],{"className":6049},[1995],[1802,6051,6053],{"className":6052},[2004],[1802,6054,6056,6087],{"className":6055},[2008,2009],[1802,6057,6059,6084],{"className":6058},[2013],[1802,6060,6062,6073],{"className":6061,"style":5476},[2017],[1802,6063,6064,6067],{"style":2567},[1802,6065],{"className":6066,"style":2026},[2025],[1802,6068,6070],{"className":6069},[2030,2031,2032,2033],[1802,6071,1834],{"className":6072},[1995,1999,2033],[1802,6074,6075,6078],{"style":5490},[1802,6076],{"className":6077,"style":2026},[2025],[1802,6079,6081],{"className":6080},[2030,2031,2032,2033],[1802,6082,1952],{"className":6083},[1995,2033],[1802,6085,2041],{"className":6086},[2040],[1802,6088,6090],{"className":6089},[2013],[1802,6091,6093],{"className":6092,"style":2598},[2017],[1802,6094],{}," signals an inadequate variance recursion; heavy tails in ",[1802,6097,6099,6121],{"className":6098},[1809],[1802,6100,6102],{"className":6101},[1813],[1815,6103,6104],{"xmlns":1817},[1820,6105,6106,6118],{},[1823,6107,6108],{},[1826,6109,6110,6116],{},[5638,6111,6112,6114],{"accent":1858},[1829,6113,1886],{},[1836,6115,5644],{},[1829,6117,1834],{},[1975,6119,6120],{"encoding":1977},"\\hat z_t",[1802,6122,6124],{"className":6123,"ariaHidden":1858},[1982],[1802,6125,6127,6130],{"className":6126},[1986],[1802,6128],{"className":6129,"style":2791},[1990],[1802,6131,6133,6164],{"className":6132},[1995],[1802,6134,6136],{"className":6135},[1995,5694],[1802,6137,6139],{"className":6138},[2008],[1802,6140,6142],{"className":6141},[2013],[1802,6143,6145,6153],{"className":6144,"style":5704},[2017],[1802,6146,6147,6150],{"style":5707},[1802,6148],{"className":6149,"style":3699},[2025],[1802,6151,1886],{"className":6152,"style":2344},[1995,1999],[1802,6154,6155,6158],{"style":5707},[1802,6156],{"className":6157,"style":3699},[2025],[1802,6159,6161],{"className":6160,"style":5723},[5722],[1802,6162,5644],{"className":6163},[1995],[1802,6165,6167],{"className":6166},[2004],[1802,6168,6170,6190],{"className":6169},[2008,2009],[1802,6171,6173,6187],{"className":6172},[2013],[1802,6174,6176],{"className":6175,"style":2018},[2017],[1802,6177,6178,6181],{"style":2359},[1802,6179],{"className":6180,"style":2026},[2025],[1802,6182,6184],{"className":6183},[2030,2031,2032,2033],[1802,6185,1834],{"className":6186},[1995,1999,2033],[1802,6188,2041],{"className":6189},[2040],[1802,6191,6193],{"className":6192},[2013],[1802,6194,6196],{"className":6195,"style":2048},[2017],[1802,6197],{}," signal an inadequate innovation distribution.",[1793,6200,6202],{"id":6201},"r-laboratory-estimate-garch-by-recursion","R laboratory: estimate GARCH by recursion",[6204,6205],"web-r",{"code64":6206,"layout":6207,"locale":7,"title":6208},"c2V0LnNlZWQoMTk4NikKVG4gPC0gOTAwCnRydWUgPC0gYyhvbWVnYSA9IDAuMDUsIGFscGhhID0gMC4wOCwgYmV0YSA9IDAuODkpCgpoIDwtIG51bWVyaWMoVG4pCnIgPC0gbnVtZXJpYyhUbikKaFsxXSA8LSB0cnVlWyJvbWVnYSJdIC8gKDEgLSB0cnVlWyJhbHBoYSJdIC0gdHJ1ZVsiYmV0YSJdKQpmb3IgKHQgaW4gMjpUbikgewogIHJbdCAtIDFdIDwtIHNxcnQoaFt0IC0gMV0pICogcm5vcm0oMSkKICBoW3RdIDwtIHRydWVbIm9tZWdhIl0gKwogICAgdHJ1ZVsiYWxwaGEiXSAqIHJbdCAtIDFdXjIgKwogICAgdHJ1ZVsiYmV0YSJdICogaFt0IC0gMV0KfQpyW1RuXSA8LSBzcXJ0KGhbVG5dKSAqIHJub3JtKDEpCgojIE1hcCB1bnJlc3RyaWN0ZWQgcGFyYW1ldGVycyBpbnRvIG9tZWdhID4gMCwgYWxwaGEgPj0gMCwKIyBiZXRhID49IDAsIGFuZCBhbHBoYSArIGJldGEgPCAwLjk5NS4KdW5wYWNrIDwtIGZ1bmN0aW9uKHRoZXRhKSB7CiAgcmF3IDwtIGV4cCh0aGV0YVsyOjNdKQogIGMoCiAgICBvbWVnYSA9IGV4cCh0aGV0YVsxXSksCiAgICBhbHBoYSA9IDAuOTk1ICogcmF3WzFdIC8gKDEgKyBzdW0ocmF3KSksCiAgICBiZXRhID0gMC45OTUgKiByYXdbMl0gLyAoMSArIHN1bShyYXcpKQogICkKfQoKZmlsdGVyX3ZhcmlhbmNlIDwtIGZ1bmN0aW9uKHBhciwgeCkgewogIGh0IDwtIG51bWVyaWMobGVuZ3RoKHgpKQogIGh0WzFdIDwtIHZhcih4KQogIGZvciAodCBpbiAyOmxlbmd0aCh4KSkgewogICAgaHRbdF0gPC0gcGFyWyJvbWVnYSJdICsKICAgICAgcGFyWyJhbHBoYSJdICogeFt0IC0gMV1eMiArCiAgICAgIHBhclsiYmV0YSJdICogaHRbdCAtIDFdCiAgfQogIGh0Cn0KCm5sbCA8LSBmdW5jdGlvbih0aGV0YSwgeCkgewogIHBhciA8LSB1bnBhY2sodGhldGEpCiAgaHQgPC0gZmlsdGVyX3ZhcmlhbmNlKHBhciwgeCkKICAwLjUgKiBzdW0obG9nKGh0KSArIHheMiAvIGh0KQp9CgpmaXQgPC0gb3B0aW0oYyhsb2coMC4wNSksIGxvZygwLjA4IC8gMC4wMyksIGxvZygwLjg5IC8gMC4wMykpLAogICAgICAgICAgICAgbmxsLCB4ID0gciwgbWV0aG9kID0gIkJGR1MiKQplc3RpbWF0ZSA8LSB1bnBhY2soZml0JHBhcikKaF9oYXQgPC0gZmlsdGVyX3ZhcmlhbmNlKGVzdGltYXRlLCByKQoKaF9uZXh0IDwtIGVzdGltYXRlWyJvbWVnYSJdICsKICBlc3RpbWF0ZVsiYWxwaGEiXSAqIHRhaWwociwgMSleMiArCiAgZXN0aW1hdGVbImJldGEiXSAqIHRhaWwoaF9oYXQsIDEpCgojIE9uZS1kYXkgbG93ZXItdGFpbCBOb3JtYWwgVmFSIGFuZCBFUywgcmVwb3J0ZWQgYXMgcG9zaXRpdmUgbG9zc2VzCnAgPC0gMC4wMQpyZXR1cm5fcXVhbnRpbGUgPC0gcW5vcm0ocCkgKiBzcXJ0KGhfbmV4dCkKVmFSXzk5IDwtIC1yZXR1cm5fcXVhbnRpbGUKRVNfOTkgPC0gc3FydChoX25leHQpICogZG5vcm0ocW5vcm0ocCkpIC8gcAoKel9oYXQgPC0gciAvIHNxcnQoaF9oYXQpCnJlc3VsdCA8LSByYmluZCh0cnVlID0gdHJ1ZSwgZXN0aW1hdGVkID0gcm91bmQoZXN0aW1hdGUsIDQpKQoKbGlzdCgKICBwYXJhbWV0ZXJzID0gcmVzdWx0LAogIHBlcnNpc3RlbmNlID0gcm91bmQoc3VtKGVzdGltYXRlW2MoImFscGhhIiwgImJldGEiKV0pLCA0KSwKICBuZXh0X3ZhcmlhbmNlID0gcm91bmQoaF9uZXh0LCA0KSwKICByaXNrX2luX3JldHVybl91bml0cyA9IHJvdW5kKGMoVmFSXzk5ID0gVmFSXzk5LCBFU185OSA9IEVTXzk5KSwgNCksCiAgc3F1YXJlZF9yZXNpZHVhbF9hY2YxID0gcm91bmQoY29yKHpfaGF0Wy0xXV4yLCB6X2hhdFstVG5dXjIpLCAzKSwKICBvcHRpbWlzYXRpb25fY29udmVyZ2VuY2UgPSBmaXQkY29udmVyZ2VuY2UKKQ==","vertical","Simulate and estimate a GARCH(1,1) with base R",[1798,6210,6211],{},"The constraints are built into the parameter transformation. This is safer than accepting negative variances after optimisation. The simulated returns are in percentage-like units, so the reported VaR and ES use the same units.",[1793,6213,6215],{"id":6214},"heavy-tails-and-leverage","Heavy tails and leverage",[1798,6217,6218],{},"Two extensions answer different diagnostics:",[3775,6220,6221,6257],{},[3778,6222,6223,6256],{},[5542,6224,6225,6226,6255],{},"Student-",[1802,6227,6229,6242],{"className":6228},[1809],[1802,6230,6232],{"className":6231},[1813],[1815,6233,6234],{"xmlns":1817},[1820,6235,6236,6240],{},[1823,6237,6238],{},[1829,6239,1834],{},[1975,6241,1834],{"encoding":1977},[1802,6243,6245],{"className":6244,"ariaHidden":1858},[1982],[1802,6246,6248,6252],{"className":6247},[1986],[1802,6249],{"className":6250,"style":6251},[1990],"height:0.6151em;",[1802,6253,1834],{"className":6254},[1995,1999]," innovations:"," large standardised shocks occur more often than under a Normal distribution.",[3778,6258,6259,6262],{},[5542,6260,6261],{},"Asymmetric variance dynamics:"," negative and positive shocks of equal magnitude can affect future volatility differently.",[1798,6264,6265],{},"For example, a GJR-style recursion is",[1802,6267,6269],{"className":6268},[1805],[1802,6270,6272,6372],{"className":6271},[1809],[1802,6273,6275],{"className":6274},[1813],[1815,6276,6277],{"xmlns":1817,"display":1818},[1820,6278,6279,6369],{},[1823,6280,6281,6287,6289,6291,6293,6295,6309,6311,6314,6317,6319,6331,6333,6335,6337,6351,6353,6355,6367],{},[1826,6282,6283,6285],{},[1829,6284,1879],{},[1829,6286,1834],{},[1836,6288,1838],{},[1829,6290,3112],{},[1836,6292,1848],{},[1829,6294,3117],{},[1944,6296,6297,6299,6307],{},[1829,6298,1853],{},[1823,6300,6301,6303,6305],{},[1829,6302,1834],{},[1836,6304,1921],{},[1923,6306,1925],{},[1923,6308,1952],{},[1836,6310,1848],{},[1829,6312,6313],{},"γ",[1829,6315,6316],{},"I",[1836,6318,1899],{"stretchy":1898},[1826,6320,6321,6323],{},[1829,6322,1853],{},[1823,6324,6325,6327,6329],{},[1829,6326,1834],{},[1836,6328,1921],{},[1923,6330,1925],{},[1836,6332,3492],{},[1923,6334,1933],{},[1836,6336,1928],{"stretchy":1898},[1944,6338,6339,6341,6349],{},[1829,6340,1853],{},[1823,6342,6343,6345,6347],{},[1829,6344,1834],{},[1836,6346,1921],{},[1923,6348,1925],{},[1923,6350,1952],{},[1836,6352,1848],{},[1829,6354,3136],{},[1826,6356,6357,6359],{},[1829,6358,1879],{},[1823,6360,6361,6363,6365],{},[1829,6362,1834],{},[1836,6364,1921],{},[1923,6366,1925],{},[1829,6368,3066],{"mathvariant":3595},[1975,6370,6371],{"encoding":1977},"h_t=\\omega+\\alpha\\varepsilon_{t-1}^2+\n\\gamma I(\\varepsilon_{t-1}\u003C0)\\varepsilon_{t-1}^2+\\beta h_{t-1}.",[1802,6373,6375,6430,6448,6526,6601,6682],{"className":6374,"ariaHidden":1858},[1982],[1802,6376,6378,6381,6421,6424,6427],{"className":6377},[1986],[1802,6379],{"className":6380,"style":2791},[1990],[1802,6382,6384,6387],{"className":6383},[1995],[1802,6385,1879],{"className":6386},[1995,1999],[1802,6388,6390],{"className":6389},[2004],[1802,6391,6393,6413],{"className":6392},[2008,2009],[1802,6394,6396,6410],{"className":6395},[2013],[1802,6397,6399],{"className":6398,"style":2018},[2017],[1802,6400,6401,6404],{"style":2089},[1802,6402],{"className":6403,"style":2026},[2025],[1802,6405,6407],{"className":6406},[2030,2031,2032,2033],[1802,6408,1834],{"className":6409},[1995,1999,2033],[1802,6411,2041],{"className":6412},[2040],[1802,6414,6416],{"className":6415},[2013],[1802,6417,6419],{"className":6418,"style":2048},[2017],[1802,6420],{},[1802,6422],{"className":6423,"style":2054},[1861],[1802,6425,1838],{"className":6426},[2058],[1802,6428],{"className":6429,"style":2054},[1861],[1802,6431,6433,6436,6439,6442,6445],{"className":6432},[1986],[1802,6434],{"className":6435,"style":3243},[1990],[1802,6437,3112],{"className":6438,"style":3247},[1995,1999],[1802,6440],{"className":6441,"style":2113},[1861],[1802,6443,1848],{"className":6444},[2117],[1802,6446],{"className":6447,"style":2113},[1861],[1802,6449,6451,6454,6457,6517,6520,6523],{"className":6450},[1986],[1802,6452],{"className":6453,"style":3263},[1990],[1802,6455,3117],{"className":6456,"style":3267},[1995,1999],[1802,6458,6460,6463],{"className":6459},[1995],[1802,6461,1853],{"className":6462},[1995,1999],[1802,6464,6466],{"className":6465},[2004],[1802,6467,6469,6509],{"className":6468},[2008,2009],[1802,6470,6472,6506],{"className":6471},[2013],[1802,6473,6475,6495],{"className":6474,"style":2564},[2017],[1802,6476,6477,6480],{"style":3288},[1802,6478],{"className":6479,"style":2026},[2025],[1802,6481,6483],{"className":6482},[2030,2031,2032,2033],[1802,6484,6486,6489,6492],{"className":6485},[1995,2033],[1802,6487,1834],{"className":6488},[1995,1999,2033],[1802,6490,1921],{"className":6491},[2117,2033],[1802,6493,1925],{"className":6494},[1995,2033],[1802,6496,6497,6500],{"style":2579},[1802,6498],{"className":6499,"style":2026},[2025],[1802,6501,6503],{"className":6502},[2030,2031,2032,2033],[1802,6504,1952],{"className":6505},[1995,2033],[1802,6507,2041],{"className":6508},[2040],[1802,6510,6512],{"className":6511},[2013],[1802,6513,6515],{"className":6514,"style":3327},[2017],[1802,6516],{},[1802,6518],{"className":6519,"style":2113},[1861],[1802,6521,1848],{"className":6522},[2117],[1802,6524],{"className":6525,"style":2113},[1861],[1802,6527,6529,6532,6536,6540,6543,6592,6595,6598],{"className":6528},[1986],[1802,6530],{"className":6531,"style":2452},[1990],[1802,6533,6313],{"className":6534,"style":6535},[1995,1999],"margin-right:0.0556em;",[1802,6537,6316],{"className":6538,"style":6539},[1995,1999],"margin-right:0.0785em;",[1802,6541,1899],{"className":6542},[2396],[1802,6544,6546,6549],{"className":6545},[1995],[1802,6547,1853],{"className":6548},[1995,1999],[1802,6550,6552],{"className":6551},[2004],[1802,6553,6555,6584],{"className":6554},[2008,2009],[1802,6556,6558,6581],{"className":6557},[2013],[1802,6559,6561],{"className":6560,"style":2473},[2017],[1802,6562,6563,6566],{"style":2089},[1802,6564],{"className":6565,"style":2026},[2025],[1802,6567,6569],{"className":6568},[2030,2031,2032,2033],[1802,6570,6572,6575,6578],{"className":6571},[1995,2033],[1802,6573,1834],{"className":6574},[1995,1999,2033],[1802,6576,1921],{"className":6577},[2117,2033],[1802,6579,1925],{"className":6580},[1995,2033],[1802,6582,2041],{"className":6583},[2040],[1802,6585,6587],{"className":6586},[2013],[1802,6588,6590],{"className":6589,"style":2504},[2017],[1802,6591],{},[1802,6593],{"className":6594,"style":2054},[1861],[1802,6596,3492],{"className":6597},[2058],[1802,6599],{"className":6600,"style":2054},[1861],[1802,6602,6604,6607,6610,6613,6673,6676,6679],{"className":6603},[1986],[1802,6605],{"className":6606,"style":3263},[1990],[1802,6608,1933],{"className":6609},[1995],[1802,6611,1928],{"className":6612},[2510],[1802,6614,6616,6619],{"className":6615},[1995],[1802,6617,1853],{"className":6618},[1995,1999],[1802,6620,6622],{"className":6621},[2004],[1802,6623,6625,6665],{"className":6624},[2008,2009],[1802,6626,6628,6662],{"className":6627},[2013],[1802,6629,6631,6651],{"className":6630,"style":2564},[2017],[1802,6632,6633,6636],{"style":3288},[1802,6634],{"className":6635,"style":2026},[2025],[1802,6637,6639],{"className":6638},[2030,2031,2032,2033],[1802,6640,6642,6645,6648],{"className":6641},[1995,2033],[1802,6643,1834],{"className":6644},[1995,1999,2033],[1802,6646,1921],{"className":6647},[2117,2033],[1802,6649,1925],{"className":6650},[1995,2033],[1802,6652,6653,6656],{"style":2579},[1802,6654],{"className":6655,"style":2026},[2025],[1802,6657,6659],{"className":6658},[2030,2031,2032,2033],[1802,6660,1952],{"className":6661},[1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represents a larger variance response after negative news. Do not use asymmetry and heavy tails as interchangeable explanations.",[1793,6799,6801],{"id":6800},"from-volatility-to-a-risk-decision","From volatility to a risk decision",[1798,6803,6804,6805,6833,6834,6923],{},"For lower-tail probability ",[1802,6806,6808,6821],{"className":6807},[1809],[1802,6809,6811],{"className":6810},[1813],[1815,6812,6813],{"xmlns":1817},[1820,6814,6815,6819],{},[1823,6816,6817],{},[1829,6818,1798],{},[1975,6820,1798],{"encoding":1977},[1802,6822,6824],{"className":6823,"ariaHidden":1858},[1982],[1802,6825,6827,6830],{"className":6826},[1986],[1802,6828],{"className":6829,"style":2127},[1990],[1802,6831,1798],{"className":6832},[1995,1999],", define the return quantile ",[1802,6835,6837,6862],{"className":6836},[1809],[1802,6838,6840],{"className":6839},[1813],[1815,6841,6842],{"xmlns":1817},[1820,6843,6844,6859],{},[1823,6845,6846],{},[1826,6847,6848,6851],{},[1829,6849,6850],{},"q",[1823,6852,6853,6855,6857],{},[1829,6854,1798],{},[1836,6856,1859],{"separator":1858},[1829,6858,1834],{},[1975,6860,6861],{"encoding":1977},"q_{p,t}",[1802,6863,6865],{"className":6864,"ariaHidden":1858},[1982],[1802,6866,6868,6872],{"className":6867},[1986],[1802,6869],{"className":6870,"style":6871},[1990],"height:0.7167em;vertical-align:-0.2861em;",[1802,6873,6875,6878],{"className":6874},[1995],[1802,6876,6850],{"className":6877,"style":3247},[1995,1999],[1802,6879,6881],{"className":6880},[2004],[1802,6882,6884,6914],{"className":6883},[2008,2009],[1802,6885,6887,6911],{"className":6886},[2013],[1802,6888,6890],{"className":6889,"style":2018},[2017],[1802,6891,6893,6896],{"style":6892},"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;",[1802,6894],{"className":6895,"style":2026},[2025],[1802,6897,6899],{"className":6898},[2030,2031,2032,2033],[1802,6900,6902,6905,6908],{"className":6901},[1995,2033],[1802,6903,1798],{"className":6904},[1995,1999,2033],[1802,6906,1859],{"className":6907},[2171,2033],[1802,6909,1834],{"className":6910},[1995,1999,2033],[1802,6912,2041],{"className":6913},[2040],[1802,6915,6917],{"className":6916},[2013],[1802,6918,6921],{"className":6919,"style":6920},[2017],"height:0.2861em;",[1802,6922],{}," by",[1802,6925,6927],{"className":6926},[1805],[1802,6928,6930,6992],{"className":6929},[1809],[1802,6931,6933],{"className":6932},[1813],[1815,6934,6935],{"xmlns":1817,"display":1818},[1820,6936,6937,6989],{},[1823,6938,6939,6942,6944,6946,6952,6955,6967,6969,6981,6983,6985,6987],{},[1829,6940,6941],{},"Pr",[1836,6943,4034],{},[1836,6945,1899],{"stretchy":1898},[1826,6947,6948,6950],{},[1829,6949,1831],{},[1829,6951,1834],{},[1836,6953,6954],{},"≤",[1826,6956,6957,6959],{},[1829,6958,6850],{},[1823,6960,6961,6963,6965],{},[1829,6962,1798],{},[1836,6964,1859],{"separator":1858},[1829,6966,1834],{},[1836,6968,1908],{},[1826,6970,6971,6973],{},[1829,6972,1914],{"mathvariant":1913},[1823,6974,6975,6977,6979],{},[1829,6976,1834],{},[1836,6978,1921],{},[1923,6980,1925],{},[1836,6982,1928],{"stretchy":1898},[1836,6984,1838],{},[1829,6986,1798],{},[1829,6988,3066],{"mathvariant":3595},[1975,6990,6991],{"encoding":1977},"\\Pr(r_t\\le q_{p,t}\\mid\\mathcal F_{t-1})=p.",[1802,6993,6995,7056,7121,7188],{"className":6994,"ariaHidden":1858},[1982],[1802,6996,6998,7001,7004,7007,7047,7050,7053],{"className":6997},[1986],[1802,6999],{"className":7000,"style":2452},[1990],[1802,7002,6941],{"className":7003},[4175],[1802,7005,1899],{"className":7006},[2396],[1802,7008,7010,7013],{"className":7009},[1995],[1802,7011,1831],{"className":7012,"style":2000},[1995,1999],[1802,7014,7016],{"className":7015},[2004],[1802,7017,7019,7039],{"className":7018},[2008,2009],[1802,7020,7022,7036],{"className":7021},[2013],[1802,7023,7025],{"className":7024,"style":2018},[2017],[1802,7026,7027,7030],{"style":2021},[1802,7028],{"className":7029,"style":2026},[2025],[1802,7031,7033],{"className":7032},[2030,2031,2032,2033],[1802,7034,1834],{"className":7035},[1995,1999,2033],[1802,7037,2041],{"className":7038},[2040],[1802,7040,7042],{"className":7041},[2013],[1802,7043,7045],{"className":7044,"style":2048},[2017],[1802,7046],{},[1802,7048],{"className":7049,"style":2054},[1861],[1802,7051,6954],{"className":7052},[2058],[1802,7054],{"className":7055,"style":2054},[1861],[1802,7057,7059,7063,7112,7115,7118],{"className":7058},[1986],[1802,7060],{"className":7061,"style":7062},[1990],"height:1.0361em;vertical-align:-0.2861em;",[1802,7064,7066,7069],{"className":7065},[1995],[1802,7067,6850],{"className":7068,"style":3247},[1995,1999],[1802,7070,7072],{"className":7071},[2004],[1802,7073,7075,7104],{"className":7074},[2008,2009],[1802,7076,7078,7101],{"className":7077},[2013],[1802,7079,7081],{"className":7080,"style":2018},[2017],[1802,7082,7083,7086],{"style":6892},[1802,7084],{"className":7085,"style":2026},[2025],[1802,7087,7089],{"className":7088},[2030,2031,2032,2033],[1802,7090,7092,7095,7098],{"className":7091},[1995,2033],[1802,7093,1798],{"className":7094},[1995,1999,2033],[1802,7096,1859],{"className":7097},[2171,2033],[1802,7099,1834],{"className":7100},[1995,1999,2033],[1802,7102,2041],{"className":7103},[2040],[1802,7105,7107],{"className":7106},[2013],[1802,7108,7110],{"className":7109,"style":6920},[2017],[1802,7111],{},[1802,7113],{"className":7114,"style":2054},[1861],[1802,7116,1908],{"className":7117},[2058],[1802,7119],{"className":7120,"style":2054},[1861],[1802,7122,7124,7127,7176,7179,7182,7185],{"className":7123},[1986],[1802,7125],{"className":7126,"style":2452},[1990],[1802,7128,7130,7133],{"className":7129},[1995],[1802,7131,1914],{"className":7132,"style":2460},[1995,2459],[1802,7134,7136],{"className":7135},[2004],[1802,7137,7139,7168],{"className":7138},[2008,2009],[1802,7140,7142,7165],{"className":7141},[2013],[1802,7143,7145],{"className":7144,"style":2473},[2017],[1802,7146,7147,7150],{"style":2476},[1802,7148],{"className":7149,"style":2026},[2025],[1802,7151,7153],{"className":7152},[2030,2031,2032,2033],[1802,7154,7156,7159,7162],{"className":7155},[1995,2033],[1802,7157,1834],{"className":7158},[1995,1999,2033],[1802,7160,1921],{"className":7161},[2117,2033],[1802,7163,1925],{"className":7164},[1995,2033],[1802,7166,2041],{"className":7167},[2040],[1802,7169,7171],{"className":7170},[2013],[1802,7172,7174],{"className":7173,"style":2504},[2017],[1802,7175],{},[1802,7177,1928],{"className":7178},[2510],[1802,7180],{"className":7181,"style":2054},[1861],[1802,7183,1838],{"className":7184},[2058],[1802,7186],{"className":7187,"style":2054},[1861],[1802,7189,7191,7194,7197],{"className":7190},[1986],[1802,7192],{"className":7193,"style":2127},[1990],[1802,7195,1798],{"className":7196},[1995,1999],[1802,7198,3066],{"className":7199},[1995],[1798,7201,7202,7203,7343,7344,7533],{},"If losses are ",[1802,7204,7206,7235],{"className":7205},[1809],[1802,7207,7209],{"className":7208},[1813],[1815,7210,7211],{"xmlns":1817},[1820,7212,7213,7232],{},[1823,7214,7215,7222,7224,7226],{},[1826,7216,7217,7220],{},[1829,7218,7219],{},"L",[1829,7221,1834],{},[1836,7223,1838],{},[1836,7225,1921],{},[1826,7227,7228,7230],{},[1829,7229,1831],{},[1829,7231,1834],{},[1975,7233,7234],{"encoding":1977},"L_t=-r_t",[1802,7236,7238,7293],{"className":7237,"ariaHidden":1858},[1982],[1802,7239,7241,7244,7284,7287,7290],{"className":7240},[1986],[1802,7242],{"className":7243,"style":4350},[1990],[1802,7245,7247,7250],{"className":7246},[1995],[1802,7248,7219],{"className":7249},[1995,1999],[1802,7251,7253],{"className":7252},[2004],[1802,7254,7256,7276],{"className":7255},[2008,2009],[1802,7257,7259,7273],{"className":7258},[2013],[1802,7260,7262],{"className":7261,"style":2018},[2017],[1802,7263,7264,7267],{"style":2089},[1802,7265],{"className":7266,"style":2026},[2025],[1802,7268,7270],{"className":7269},[2030,2031,2032,2033],[1802,7271,1834],{"className":7272},[1995,1999,2033],[1802,7274,2041],{"className":7275},[2040],[1802,7277,7279],{"className":7278},[2013],[1802,7280,7282],{"className":7281,"style":2048},[2017],[1802,7283],{},[1802,7285],{"className":7286,"style":2054},[1861],[1802,7288,1838],{"className":7289},[2058],[1802,7291],{"className":7292,"style":2054},[1861],[1802,7294,7296,7300,7303],{"className":7295},[1986],[1802,7297],{"className":7298,"style":7299},[1990],"height:0.7333em;vertical-align:-0.15em;",[1802,7301,1921],{"className":7302},[1995],[1802,7304,7306,7309],{"className":7305},[1995],[1802,7307,1831],{"className":7308,"style":2000},[1995,1999],[1802,7310,7312],{"className":7311},[2004],[1802,7313,7315,7335],{"className":7314},[2008,2009],[1802,7316,7318,7332],{"className":7317},[2013],[1802,7319,7321],{"className":7320,"style":2018},[2017],[1802,7322,7323,7326],{"style":2021},[1802,7324],{"className":7325,"style":2026},[2025],[1802,7327,7329],{"className":7328},[2030,2031,2032,2033],[1802,7330,1834],{"className":7331},[1995,1999,2033],[1802,7333,2041],{"className":7334},[2040],[1802,7336,7338],{"className":7337},[2013],[1802,7339,7341],{"className":7340,"style":2048},[2017],[1802,7342],{},", then ",[1802,7345,7347,7396],{"className":7346},[1809],[1802,7348,7350],{"className":7349},[1813],[1815,7351,7352],{"xmlns":1817},[1820,7353,7354,7393],{},[1823,7355,7356,7377,7379,7381],{},[1826,7357,7358,7365],{},[1823,7359,7360,7363],{},[1829,7361,7362],{"mathvariant":3595},"VaR",[1836,7364,4034],{},[1823,7366,7367,7369,7371,7373,7375],{},[1923,7368,1925],{},[1836,7370,1921],{},[1829,7372,1798],{},[1836,7374,1859],{"separator":1858},[1829,7376,1834],{},[1836,7378,1838],{},[1836,7380,1921],{},[1826,7382,7383,7385],{},[1829,7384,6850],{},[1823,7386,7387,7389,7391],{},[1829,7388,1798],{},[1836,7390,1859],{"separator":1858},[1829,7392,1834],{},[1975,7394,7395],{"encoding":1977},"\\operatorname{VaR}_{1-p,t}=-q_{p,t}",[1802,7397,7399,7474],{"className":7398,"ariaHidden":1858},[1982],[1802,7400,7402,7406,7465,7468,7471],{"className":7401},[1986],[1802,7403],{"className":7404,"style":7405},[1990],"height:0.9694em;vertical-align:-0.2861em;",[1802,7407,7409,7415],{"className":7408},[4175],[1802,7410,7412],{"className":7411},[4175],[1802,7413,7362],{"className":7414},[1995,4179],[1802,7416,7418],{"className":7417},[2004],[1802,7419,7421,7457],{"className":7420},[2008,2009],[1802,7422,7424,7454],{"className":7423},[2013],[1802,7425,7427],{"className":7426,"style":2473},[2017],[1802,7428,7430,7433],{"style":7429},"top:-2.55em;margin-right:0.05em;",[1802,7431],{"className":7432,"style":2026},[2025],[1802,7434,7436],{"className":7435},[2030,2031,2032,2033],[1802,7437,7439,7442,7445,7448,7451],{"className":7438},[1995,2033],[1802,7440,1925],{"className":7441},[1995,2033],[1802,7443,1921],{"className":7444},[2117,2033],[1802,7446,1798],{"className":7447},[1995,1999,2033],[1802,7449,1859],{"className":7450},[2171,2033],[1802,7452,1834],{"className":7453},[1995,1999,2033],[1802,7455,2041],{"className":7456},[2040],[1802,7458,7460],{"className":7459},[2013],[1802,7461,7463],{"className":7462,"style":6920},[2017],[1802,7464],{},[1802,7466],{"className":7467,"style":2054},[1861],[1802,7469,1838],{"className":7470},[2058],[1802,7472],{"className":7473,"style":2054},[1861],[1802,7475,7477,7481,7484],{"className":7476},[1986],[1802,7478],{"className":7479,"style":7480},[1990],"height:0.8694em;vertical-align:-0.2861em;",[1802,7482,1921],{"className":7483},[1995],[1802,7485,7487,7490],{"className":7486},[1995],[1802,7488,6850],{"className":7489,"style":3247},[1995,1999],[1802,7491,7493],{"className":7492},[2004],[1802,7494,7496,7525],{"className":7495},[2008,2009],[1802,7497,7499,7522],{"className":7498},[2013],[1802,7500,7502],{"className":7501,"style":2018},[2017],[1802,7503,7504,7507],{"style":6892},[1802,7505],{"className":7506,"style":2026},[2025],[1802,7508,7510],{"className":7509},[2030,2031,2032,2033],[1802,7511,7513,7516,7519],{"className":7512},[1995,2033],[1802,7514,1798],{"className":7515},[1995,1999,2033],[1802,7517,1859],{"className":7518},[2171,2033],[1802,7520,1834],{"className":7521},[1995,1999,2033],[1802,7523,2041],{"className":7524},[2040],[1802,7526,7528],{"className":7527},[2013],[1802,7529,7531],{"className":7530,"style":6920},[2017],[1802,7532],{},". Expected shortfall is the expected loss beyond VaR. State the sign convention; otherwise a “negative VaR” can mean either a gain or a loss.",[1798,7535,7536],{},"A volatility model is not validated merely because its likelihood is high:",[7538,7539,7540,7553],"table",{},[7541,7542,7543],"thead",{},[7544,7545,7546,7550],"tr",{},[7547,7548,7549],"th",{},"Layer",[7547,7551,7552],{},"Diagnostic",[7554,7555,7556,7679,7687,7695],"tbody",{},[7544,7557,7558,7562],{},[7559,7560,7561],"td",{},"variance dynamics",[7559,7563,7564,7565],{},"dependence remaining in ",[1802,7566,7568,7591],{"className":7567},[1809],[1802,7569,7571],{"className":7570},[1813],[1815,7572,7573],{"xmlns":1817},[1820,7574,7575,7589],{},[1823,7576,7577],{},[1944,7578,7579,7585,7587],{},[5638,7580,7581,7583],{"accent":1858},[1829,7582,1886],{},[1836,7584,5644],{},[1829,7586,1834],{},[1923,7588,1952],{},[1975,7590,6005],{"encoding":1977},[1802,7592,7594],{"className":7593,"ariaHidden":1858},[1982],[1802,7595,7597,7600],{"className":7596},[1986],[1802,7598],{"className":7599,"style":6015},[1990],[1802,7601,7603,7634],{"className":7602},[1995],[1802,7604,7606],{"className":7605},[1995,5694],[1802,7607,7609],{"className":7608},[2008],[1802,7610,7612],{"className":7611},[2013],[1802,7613,7615,7623],{"className":7614,"style":5704},[2017],[1802,7616,7617,7620],{"style":5707},[1802,7618],{"className":7619,"style":3699},[2025],[1802,7621,1886],{"className":7622,"style":2344},[1995,1999],[1802,7624,7625,7628],{"style":5707},[1802,7626],{"className":7627,"style":3699},[2025],[1802,7629,7631],{"className":7630,"style":5723},[5722],[1802,7632,5644],{"className":7633},[1995],[1802,7635,7637],{"className":7636},[2004],[1802,7638,7640,7671],{"className":7639},[2008,2009],[1802,7641,7643,7668],{"className":7642},[2013],[1802,7644,7646,7657],{"className":7645,"style":5476},[2017],[1802,7647,7648,7651],{"style":2567},[1802,7649],{"className":7650,"style":2026},[2025],[1802,7652,7654],{"className":7653},[2030,2031,2032,2033],[1802,7655,1834],{"className":7656},[1995,1999,2033],[1802,7658,7659,7662],{"style":5490},[1802,7660],{"className":7661,"style":2026},[2025],[1802,7663,7665],{"className":7664},[2030,2031,2032,2033],[1802,7666,1952],{"className":7667},[1995,2033],[1802,7669,2041],{"className":7670},[2040],[1802,7672,7674],{"className":7673},[2013],[1802,7675,7677],{"className":7676,"style":2598},[2017],[1802,7678],{},[7544,7680,7681,7684],{},[7559,7682,7683],{},"distribution",[7559,7685,7686],{},"quantile and tail calibration",[7544,7688,7689,7692],{},[7559,7690,7691],{},"decision",[7559,7693,7694],{},"VaR exceptions, expected-shortfall loss, capital or utility impact",[7544,7696,7697,7700],{},[7559,7698,7699],{},"stability",[7559,7701,7702],{},"rolling performance through calm and stressed periods",[7704,7705,7707],"warning",{"title":7706},"Scope","Normal GARCH in the example teaches recursion and likelihood. It is not automatically suitable for regulatory capital, intraday microstructure, options, or a portfolio with changing weights.",[1793,7709,7711],{"id":7710},"finance-versus-economics","Finance versus economics",[1798,7713,7714],{},"GARCH is central in finance because the conditional scale of returns is itself a decision input. In macroeconomics it is useful only when time-varying uncertainty is part of the question—for example inflation uncertainty or exchange-rate volatility. For GDP nowcasting, publication timing and latent-state estimation are usually more central than a daily GARCH recursion.",[1793,7716,7718],{"id":7717},"practice","Practice",[7720,7721,7722,7799,7802],"ol",{},[3778,7723,3471,7724,7798],{},[1802,7725,7727,7750],{"className":7726},[1809],[1802,7728,7730],{"className":7729},[1813],[1815,7731,7732],{"xmlns":1817},[1820,7733,7734,7747],{},[1823,7735,7736,7738,7740,7742,7744],{},[1829,7737,3117],{},[1836,7739,1848],{},[1829,7741,3136],{},[1836,7743,1838],{},[1923,7745,7746],{},"0.98",[1975,7748,7749],{"encoding":1977},"\\alpha+\\beta=0.98",[1802,7751,7753,7771,7789],{"className":7752,"ariaHidden":1858},[1982],[1802,7754,7756,7759,7762,7765,7768],{"className":7755},[1986],[1802,7757],{"className":7758,"style":3243},[1990],[1802,7760,3117],{"className":7761,"style":3267},[1995,1999],[1802,7763],{"className":7764,"style":2113},[1861],[1802,7766,1848],{"className":7767},[2117],[1802,7769],{"className":7770,"style":2113},[1861],[1802,7772,7774,7777,7780,7783,7786],{"className":7773},[1986],[1802,7775],{"className":7776,"style":3426},[1990],[1802,7778,3136],{"className":7779,"style":3349},[1995,1999],[1802,7781],{"className":7782,"style":2054},[1861],[1802,7784,1838],{"className":7785},[2058],[1802,7787],{"className":7788,"style":2054},[1861],[1802,7790,7792,7795],{"className":7791},[1986],[1802,7793],{"className":7794,"style":2683},[1990],[1802,7796,7746],{"className":7797},[1995],", what fraction of a variance deviation remains after ten forecast steps?",[3778,7800,7801],{},"Why can uncorrelated returns still be dependent?",[3778,7803,7804],{},"A model has correct average VaR coverage but all exceptions occur in one crisis month. Is it calibrated?",[7806,7807,7809],"legacy-details",{"title":7808},"Answers",[7720,7810,7811,7908,7911],{},[3778,7812,7813,7814,7907],{},"Approximately ",[1802,7815,7817,7843],{"className":7816},[1809],[1802,7818,7820],{"className":7819},[1813],[1815,7821,7822],{"xmlns":1817},[1820,7823,7824,7840],{},[1823,7825,7826,7834,7837],{},[7827,7828,7829,7831],"msup",{},[1923,7830,7746],{},[1923,7832,7833],{},"10",[1836,7835,7836],{},"≈",[1923,7838,7839],{},"0.817",[1975,7841,7842],{"encoding":1977},"0.98^{10}\\approx0.817",[1802,7844,7846,7898],{"className":7845,"ariaHidden":1858},[1982],[1802,7847,7849,7852,7856,7889,7892,7895],{"className":7848},[1986],[1802,7850],{"className":7851,"style":5476},[1990],[1802,7853,7855],{"className":7854},[1995],"0.9",[1802,7857,7859,7863],{"className":7858},[1995],[1802,7860,7862],{"className":7861},[1995],"8",[1802,7864,7866],{"className":7865},[2004],[1802,7867,7869],{"className":7868},[2008],[1802,7870,7872],{"className":7871},[2013],[1802,7873,7875],{"className":7874,"style":5476},[2017],[1802,7876,7877,7880],{"style":5490},[1802,7878],{"className":7879,"style":2026},[2025],[1802,7881,7883],{"className":7882},[2030,2031,2032,2033],[1802,7884,7886],{"className":7885},[1995,2033],[1802,7887,7833],{"className":7888},[1995,2033],[1802,7890],{"className":7891,"style":2054},[1861],[1802,7893,7836],{"className":7894},[2058],[1802,7896],{"className":7897,"style":2054},[1861],[1802,7899,7901,7904],{"className":7900},[1986],[1802,7902],{"className":7903,"style":2683},[1990],[1802,7905,7839],{"className":7906},[1995],"; mean reversion is slow.",[3778,7909,7910],{},"Their conditional variances can be dependent, so squared returns cluster.",[3778,7912,7913],{},"Not dynamically: unconditional coverage can hide clustered exceptions.",[1798,7915,7916,7917,3066],{},"Next: ",[3074,7918,442],{"href":7919},"..\u002F05-unit-roots-cointegration\u002F",{"title":10,"searchDepth":7921,"depth":7921,"links":7922},2,[7923,7924,7925,7926,7927,7928,7929,7930,7931],{"id":1795,"depth":7921,"text":1796},{"id":3069,"depth":7921,"text":3070},{"id":3985,"depth":7921,"text":3986},{"id":4991,"depth":7921,"text":4992},{"id":6201,"depth":7921,"text":6202},{"id":6214,"depth":7921,"text":6215},{"id":6800,"depth":7921,"text":6801},{"id":7710,"depth":7921,"text":7711},{"id":7717,"depth":7921,"text":7718},"Conditional variance, GARCH quasi-likelihood, leverage, heavy tails, and translation into VaR and expected shortfall.","md",{"sidebar":7935},{"order":7936},4,true,{"title":436,"description":7932},"zNRU063vVU8zuA5pdP9oLn8AagViWucvQvULBAwSTbg",[7941,7943],{"title":430,"path":431,"stem":432,"description":7942,"children":-1},"Matrix derivations for forecasting regressions, overlapping horizons, persistent predictors, and Newey–West inference.",{"title":442,"path":443,"stem":444,"description":7944,"children":-1},"Diagnose spurious levels, derive reduced-rank error correction, and distinguish financial spreads from economic equilibria.",1785754724014]