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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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They do not begin with a large empirical dataset or automated model selection. Each starts from a mathematical object whose answer is known well enough to check.",[1799,1803,1804],{},"Every code cell is:",[1806,1807,1808,1812,1820,1823],"ul",{},[1809,1810,1811],"li",{},"self-contained and runnable in the browser with webR;",[1809,1813,1814,1815,1819],{},"written with base R and the recommended ",[1816,1817,1818],"code",{},"stats"," package;",[1809,1821,1822],{},"explicit about dimensions and parameter conventions;",[1809,1824,1825],{},"followed by a numerical identity or error check.",[1794,1827,1829],{"id":1828},"lab-map","Lab map",[1831,1832,1833,1852],"table",{},[1834,1835,1836],"thead",{},[1837,1838,1839,1843,1846,1849],"tr",{},[1840,1841,1842],"th",{},"Lab",[1840,1844,1845],{},"Central equation",[1840,1847,1848],{},"Main R tools",[1840,1850,1851],{},"Output",[1853,1854,1855,2077,2337,2527],"tbody",{},[1837,1856,1857,1865,2062,2074],{},[1858,1859,1860],"td",{},[1861,1862,1864],"a",{"href":1863},".\u002F01-covariance-matrices","1. Covariance geometry",[1858,1866,1867],{},[1868,1869,1872,1931],"span",{"className":1870},[1871],"katex",[1868,1873,1876],{"className":1874},[1875],"katex-mathml",[1877,1878,1880],"math",{"xmlns":1879},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[1881,1882,1883,1926],"semantics",{},[1884,1885,1886,1897,1901,1905,1908,1911,1914,1917,1920,1923],"mrow",{},[1887,1888,1889,1894],"msub",{},[1890,1891,1893],"mi",{"mathvariant":1892},"normal","Γ",[1890,1895,1896],{},"n",[1898,1899,1900],"mo",{},"=",[1898,1902,1904],{"stretchy":1903},"false","[",[1890,1906,1907],{},"γ",[1898,1909,1910],{"stretchy":1903},"(",[1890,1912,1913],{},"i",[1898,1915,1916],{},"−",[1890,1918,1919],{},"j",[1898,1921,1922],{"stretchy":1903},")",[1898,1924,1925],{"stretchy":1903},"]",[1927,1928,1930],"annotation",{"encoding":1929},"application\u002Fx-tex","\\Gamma_n=[\\gamma(i-j)]",[1868,1932,1936,2015,2047],{"className":1933,"ariaHidden":1935},[1934],"katex-html","true",[1868,1937,1940,1945,2003,2008,2012],{"className":1938},[1939],"base",[1868,1941],{"className":1942,"style":1944},[1943],"strut","height:0.8333em;vertical-align:-0.15em;",[1868,1946,1949,1952],{"className":1947},[1948],"mord",[1868,1950,1893],{"className":1951},[1948],[1868,1953,1956],{"className":1954},[1955],"msupsub",[1868,1957,1961,1994],{"className":1958},[1959,1960],"vlist-t","vlist-t2",[1868,1962,1965,1989],{"className":1963},[1964],"vlist-r",[1868,1966,1970],{"className":1967,"style":1969},[1968],"vlist","height:0.1514em;",[1868,1971,1973,1978],{"style":1972},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[1868,1974],{"className":1975,"style":1977},[1976],"pstrut","height:2.7em;",[1868,1979,1985],{"className":1980},[1981,1982,1983,1984],"sizing","reset-size6","size3","mtight",[1868,1986,1896],{"className":1987},[1948,1988,1984],"mathnormal",[1868,1990,1993],{"className":1991},[1992],"vlist-s","​",[1868,1995,1997],{"className":1996},[1964],[1868,1998,2001],{"className":1999,"style":2000},[1968],"height:0.15em;",[1868,2002],{},[1868,2004],{"className":2005,"style":2007},[2006],"mspace","margin-right:0.2778em;",[1868,2009,1900],{"className":2010},[2011],"mrel",[1868,2013],{"className":2014,"style":2007},[2006],[1868,2016,2018,2022,2026,2030,2033,2036,2040,2044],{"className":2017},[1939],[1868,2019],{"className":2020,"style":2021},[1943],"height:1em;vertical-align:-0.25em;",[1868,2023,1904],{"className":2024},[2025],"mopen",[1868,2027,1907],{"className":2028,"style":2029},[1948,1988],"margin-right:0.0556em;",[1868,2031,1910],{"className":2032},[2025],[1868,2034,1913],{"className":2035},[1948,1988],[1868,2037],{"className":2038,"style":2039},[2006],"margin-right:0.2222em;",[1868,2041,1916],{"className":2042},[2043],"mbin",[1868,2045],{"className":2046,"style":2039},[2006],[1868,2048,2050,2053,2057],{"className":2049},[1939],[1868,2051],{"className":2052,"style":2021},[1943],[1868,2054,1919],{"className":2055,"style":2056},[1948,1988],"margin-right:0.0572em;",[1868,2058,2061],{"className":2059},[2060],"mclose",")]",[1858,2063,2064,2067,2068,2067,2071],{},[1816,2065,2066],{},"toeplitz",", ",[1816,2069,2070],{},"eigen",[1816,2072,2073],{},"chol",[1858,2075,2076],{},"valid finite covariance block",[1837,2078,2079,2085,2324,2334],{},[1858,2080,2081],{},[1861,2082,2084],{"href":2083},".\u002F02-ar-recursions","2. AR recursions",[1858,2086,2087],{},[1868,2088,2090,2143],{"className":2089},[1871],[1868,2091,2093],{"className":2092},[1875],[1877,2094,2095],{"xmlns":1879},[1881,2096,2097,2140],{},[1884,2098,2099,2108,2110,2113,2127,2130,2133],{},[1887,2100,2101,2105],{},[1890,2102,2104],{"mathvariant":2103},"bold","s",[1890,2106,2107],{},"t",[1898,2109,1900],{},[1890,2111,2112],{},"F",[1887,2114,2115,2117],{},[1890,2116,2104],{"mathvariant":2103},[1884,2118,2119,2121,2123],{},[1890,2120,2107],{},[1898,2122,1916],{},[2124,2125,2126],"mn",{},"1",[1898,2128,2129],{},"+",[1890,2131,2132],{},"G",[1887,2134,2135,2138],{},[1890,2136,2137],{},"ε",[1890,2139,2107],{},[1927,2141,2142],{"encoding":1929},"\\mathbf s_t=F\\mathbf s_{t-1}+G\\varepsilon_t",[1868,2144,2146,2204,2275],{"className":2145,"ariaHidden":1935},[1934],[1868,2147,2149,2153,2195,2198,2201],{"className":2148},[1939],[1868,2150],{"className":2151,"style":2152},[1943],"height:0.5944em;vertical-align:-0.15em;",[1868,2154,2156,2160],{"className":2155},[1948],[1868,2157,2104],{"className":2158},[1948,2159],"mathbf",[1868,2161,2163],{"className":2162},[1955],[1868,2164,2166,2187],{"className":2165},[1959,1960],[1868,2167,2169,2184],{"className":2168},[1964],[1868,2170,2173],{"className":2171,"style":2172},[1968],"height:0.2806em;",[1868,2174,2175,2178],{"style":1972},[1868,2176],{"className":2177,"style":1977},[1976],[1868,2179,2181],{"className":2180},[1981,1982,1983,1984],[1868,2182,2107],{"className":2183},[1948,1988,1984],[1868,2185,1993],{"className":2186},[1992],[1868,2188,2190],{"className":2189},[1964],[1868,2191,2193],{"className":2192,"style":2000},[1968],[1868,2194],{},[1868,2196],{"className":2197,"style":2007},[2006],[1868,2199,1900],{"className":2200},[2011],[1868,2202],{"className":2203,"style":2007},[2006],[1868,2205,2207,2211,2215,2266,2269,2272],{"className":2206},[1939],[1868,2208],{"className":2209,"style":2210},[1943],"height:0.8917em;vertical-align:-0.2083em;",[1868,2212,2112],{"className":2213,"style":2214},[1948,1988],"margin-right:0.1389em;",[1868,2216,2218,2221],{"className":2217},[1948],[1868,2219,2104],{"className":2220},[1948,2159],[1868,2222,2224],{"className":2223},[1955],[1868,2225,2227,2257],{"className":2226},[1959,1960],[1868,2228,2230,2254],{"className":2229},[1964],[1868,2231,2234],{"className":2232,"style":2233},[1968],"height:0.3011em;",[1868,2235,2236,2239],{"style":1972},[1868,2237],{"className":2238,"style":1977},[1976],[1868,2240,2242],{"className":2241},[1981,1982,1983,1984],[1868,2243,2245,2248,2251],{"className":2244},[1948,1984],[1868,2246,2107],{"className":2247},[1948,1988,1984],[1868,2249,1916],{"className":2250},[2043,1984],[1868,2252,2126],{"className":2253},[1948,1984],[1868,2255,1993],{"className":2256},[1992],[1868,2258,2260],{"className":2259},[1964],[1868,2261,2264],{"className":2262,"style":2263},[1968],"height:0.2083em;",[1868,2265],{},[1868,2267],{"className":2268,"style":2039},[2006],[1868,2270,2129],{"className":2271},[2043],[1868,2273],{"className":2274,"style":2039},[2006],[1868,2276,2278,2281,2284],{"className":2277},[1939],[1868,2279],{"className":2280,"style":1944},[1943],[1868,2282,2132],{"className":2283},[1948,1988],[1868,2285,2287,2290],{"className":2286},[1948],[1868,2288,2137],{"className":2289},[1948,1988],[1868,2291,2293],{"className":2292},[1955],[1868,2294,2296,2316],{"className":2295},[1959,1960],[1868,2297,2299,2313],{"className":2298},[1964],[1868,2300,2302],{"className":2301,"style":2172},[1968],[1868,2303,2304,2307],{"style":1972},[1868,2305],{"className":2306,"style":1977},[1976],[1868,2308,2310],{"className":2309},[1981,1982,1983,1984],[1868,2311,2107],{"className":2312},[1948,1988,1984],[1868,2314,1993],{"className":2315},[1992],[1868,2317,2319],{"className":2318},[1964],[1868,2320,2322],{"className":2321,"style":2000},[1968],[1868,2323],{},[1858,2325,2326,2067,2329,2067,2331],{},[1816,2327,2328],{},"polyroot",[1816,2330,2070],{},[1816,2332,2333],{},"ARMAacf",[1858,2335,2336],{},"roots, impulse responses, Yule–Walker solution",[1837,2338,2339,2345,2514,2524],{},[1858,2340,2341],{},[1861,2342,2344],{"href":2343},".\u002F03-prediction-likelihood","3. Prediction and likelihood",[1858,2346,2347,2407,2408],{},[1868,2348,2350,2371],{"className":2349},[1871],[1868,2351,2353],{"className":2352},[1875],[1877,2354,2355],{"xmlns":1879},[1881,2356,2357,2368],{},[1884,2358,2359,2361,2363,2365],{},[1890,2360,1893],{"mathvariant":1892},[1890,2362,1861],{"mathvariant":2103},[1898,2364,1900],{},[1890,2366,2367],{"mathvariant":2103},"g",[1927,2369,2370],{"encoding":1929},"\\Gamma\\mathbf a=\\mathbf g",[1868,2372,2374,2396],{"className":2373,"ariaHidden":1935},[1934],[1868,2375,2377,2381,2384,2387,2390,2393],{"className":2376},[1939],[1868,2378],{"className":2379,"style":2380},[1943],"height:0.6833em;",[1868,2382,1893],{"className":2383},[1948],[1868,2385,1861],{"className":2386},[1948,2159],[1868,2388],{"className":2389,"style":2007},[2006],[1868,2391,1900],{"className":2392},[2011],[1868,2394],{"className":2395,"style":2007},[2006],[1868,2397,2399,2403],{"className":2398},[1939],[1868,2400],{"className":2401,"style":2402},[1943],"height:0.6389em;vertical-align:-0.1944em;",[1868,2404,2367],{"className":2405,"style":2406},[1948,2159],"margin-right:0.016em;"," and ",[1868,2409,2411,2443],{"className":2410},[1871],[1868,2412,2414],{"className":2413},[1875],[1877,2415,2416],{"xmlns":1879},[1881,2417,2418,2440],{},[1884,2419,2420,2423,2425,2428,2431,2438],{},[1890,2421,2422],{"mathvariant":1892},"ℓ",[1898,2424,1910],{"stretchy":1903},[1890,2426,2427],{},"θ",[1898,2429,2430],{"separator":1935},";",[1887,2432,2433,2436],{},[1890,2434,2435],{"mathvariant":1892},"Σ",[1890,2437,2427],{},[1898,2439,1922],{"stretchy":1903},[1927,2441,2442],{"encoding":1929},"\\ell(\\theta;\\Sigma_\\theta)",[1868,2444,2446],{"className":2445,"ariaHidden":1935},[1934],[1868,2447,2449,2452,2455,2458,2462,2466,2470,2511],{"className":2448},[1939],[1868,2450],{"className":2451,"style":2021},[1943],[1868,2453,2422],{"className":2454},[1948],[1868,2456,1910],{"className":2457},[2025],[1868,2459,2427],{"className":2460,"style":2461},[1948,1988],"margin-right:0.0278em;",[1868,2463,2430],{"className":2464},[2465],"mpunct",[1868,2467],{"className":2468,"style":2469},[2006],"margin-right:0.1667em;",[1868,2471,2473,2476],{"className":2472},[1948],[1868,2474,2435],{"className":2475},[1948],[1868,2477,2479],{"className":2478},[1955],[1868,2480,2482,2503],{"className":2481},[1959,1960],[1868,2483,2485,2500],{"className":2484},[1964],[1868,2486,2489],{"className":2487,"style":2488},[1968],"height:0.3361em;",[1868,2490,2491,2494],{"style":1972},[1868,2492],{"className":2493,"style":1977},[1976],[1868,2495,2497],{"className":2496},[1981,1982,1983,1984],[1868,2498,2427],{"className":2499,"style":2461},[1948,1988,1984],[1868,2501,1993],{"className":2502},[1992],[1868,2504,2506],{"className":2505},[1964],[1868,2507,2509],{"className":2508,"style":2000},[1968],[1868,2510],{},[1868,2512,1922],{"className":2513},[2060],[1858,2515,2516,2067,2519,2067,2521],{},[1816,2517,2518],{},"solve",[1816,2520,2073],{},[1816,2522,2523],{},"optim",[1858,2525,2526],{},"predictor plus exact Gaussian estimate",[1837,2528,2529,2535,2538,2547],{},[1858,2530,2531],{},[1861,2532,2534],{"href":2533},".\u002F04-state-space","4. State space",[1858,2536,2537],{},"Kalman prediction and correction",[1858,2539,2540,2067,2543,2546],{},[1816,2541,2542],{},"%*%",[1816,2544,2545],{},"kronecker",", loops",[1858,2548,2549],{},"filtered states and forecast covariance",[1794,2551,2553],{"id":2552},"working-conventions","Working conventions",[2555,2556,2557,2563,2690,3131,3177],"ol",{},[1809,2558,2559,2560,2562],{},"Vectors in the notes are columns. R vectors acquire column meaning when used with ",[1816,2561,2542],{},".",[1809,2564,2565,2568,2569,2599,2600,2562],{},[1816,2566,2567],{},"chol(Sigma)"," returns an upper-triangular ",[1868,2570,2572,2586],{"className":2571},[1871],[1868,2573,2575],{"className":2574},[1875],[1877,2576,2577],{"xmlns":1879},[1881,2578,2579,2584],{},[1884,2580,2581],{},[1890,2582,2583],{},"U",[1927,2585,2583],{"encoding":1929},[1868,2587,2589],{"className":2588,"ariaHidden":1935},[1934],[1868,2590,2592,2595],{"className":2591},[1939],[1868,2593],{"className":2594,"style":2380},[1943],[1868,2596,2583],{"className":2597,"style":2598},[1948,1988],"margin-right:0.109em;"," satisfying 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U=\\Sigma",[1868,2630,2632,2681],{"className":2631,"ariaHidden":1935},[1934],[1868,2633,2635,2639,2669,2672,2675,2678],{"className":2634},[1939],[1868,2636],{"className":2637,"style":2638},[1943],"height:0.8491em;",[1868,2640,2642,2645],{"className":2641},[1948],[1868,2643,2583],{"className":2644,"style":2598},[1948,1988],[1868,2646,2648],{"className":2647},[1955],[1868,2649,2651],{"className":2650},[1959],[1868,2652,2654],{"className":2653},[1964],[1868,2655,2657],{"className":2656,"style":2638},[1968],[1868,2658,2660,2663],{"style":2659},"top:-3.063em;margin-right:0.05em;",[1868,2661],{"className":2662,"style":1977},[1976],[1868,2664,2666],{"className":2665},[1981,1982,1983,1984],[1868,2667,2619],{"className":2668},[1948,1984],[1868,2670,2583],{"className":2671,"style":2598},[1948,1988],[1868,2673],{"className":2674,"style":2007},[2006],[1868,2676,1900],{"className":2677},[2011],[1868,2679],{"className":2680,"style":2007},[2006],[1868,2682,2684,2687],{"className":2683},[1939],[1868,2685],{"className":2686,"style":2380},[1943],[1868,2688,2435],{"className":2689},[1948],[1809,2691,2692,2694,2695,2562],{},[1816,2693,2333],{}," follows R's model convention\n",[1868,2696,2698,2775],{"className":2697},[1871],[1868,2699,2701],{"className":2700},[1875],[1877,2702,2703],{"xmlns":1879},[1881,2704,2705,2772],{},[1884,2706,2707,2714,2716,2723,2735,2737,2740,2742,2748,2750,2756,2768,2770],{},[1887,2708,2709,2712],{},[1890,2710,2711],{},"X",[1890,2713,2107],{},[1898,2715,1900],{},[1887,2717,2718,2721],{},[1890,2719,2720],{},"ϕ",[2124,2722,2126],{},[1887,2724,2725,2727],{},[1890,2726,2711],{},[1884,2728,2729,2731,2733],{},[1890,2730,2107],{},[1898,2732,1916],{},[2124,2734,2126],{},[1898,2736,2129],{},[1898,2738,2739],{},"⋯",[1898,2741,2129],{},[1887,2743,2744,2746],{},[1890,2745,2137],{},[1890,2747,2107],{},[1898,2749,2129],{},[1887,2751,2752,2754],{},[1890,2753,2427],{},[2124,2755,2126],{},[1887,2757,2758,2760],{},[1890,2759,2137],{},[1884,2761,2762,2764,2766],{},[1890,2763,2107],{},[1898,2765,1916],{},[2124,2767,2126],{},[1898,2769,2129],{},[1898,2771,2739],{},[1927,2773,2774],{"encoding":1929},"X_t=\\phi_1X_{t-1}+\\cdots+\\varepsilon_t+\\theta_1\\varepsilon_{t-1}+\\cdots",[1868,2776,2778,2835,2940,2960,3016,3121],{"className":2777,"ariaHidden":1935},[1934],[1868,2779,2781,2784,2826,2829,2832],{"className":2780},[1939],[1868,2782],{"className":2783,"style":1944},[1943],[1868,2785,2787,2791],{"className":2786},[1948],[1868,2788,2711],{"className":2789,"style":2790},[1948,1988],"margin-right:0.0785em;",[1868,2792,2794],{"className":2793},[1955],[1868,2795,2797,2818],{"className":2796},[1959,1960],[1868,2798,2800,2815],{"className":2799},[1964],[1868,2801,2803],{"className":2802,"style":2172},[1968],[1868,2804,2806,2809],{"style":2805},"top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;",[1868,2807],{"className":2808,"style":1977},[1976],[1868,2810,2812],{"className":2811},[1981,1982,1983,1984],[1868,2813,2107],{"className":2814},[1948,1988,1984],[1868,2816,1993],{"className":2817},[1992],[1868,2819,2821],{"className":2820},[1964],[1868,2822,2824],{"className":2823,"style":2000},[1968],[1868,2825],{},[1868,2827],{"className":2828,"style":2007},[2006],[1868,2830,1900],{"className":2831},[2011],[1868,2833],{"className":2834,"style":2007},[2006],[1868,2836,2838,2842,2882,2931,2934,2937],{"className":2837},[1939],[1868,2839],{"className":2840,"style":2841},[1943],"height:0.9028em;vertical-align:-0.2083em;",[1868,2843,2845,2848],{"className":2844},[1948],[1868,2846,2720],{"className":2847},[1948,1988],[1868,2849,2851],{"className":2850},[1955],[1868,2852,2854,2874],{"className":2853},[1959,1960],[1868,2855,2857,2871],{"className":2856},[1964],[1868,2858,2860],{"className":2859,"style":2233},[1968],[1868,2861,2862,2865],{"style":1972},[1868,2863],{"className":2864,"style":1977},[1976],[1868,2866,2868],{"className":2867},[1981,1982,1983,1984],[1868,2869,2126],{"className":2870},[1948,1984],[1868,2872,1993],{"className":2873},[1992],[1868,2875,2877],{"className":2876},[1964],[1868,2878,2880],{"className":2879,"style":2000},[1968],[1868,2881],{},[1868,2883,2885,2888],{"className":2884},[1948],[1868,2886,2711],{"className":2887,"style":2790},[1948,1988],[1868,2889,2891],{"className":2890},[1955],[1868,2892,2894,2923],{"className":2893},[1959,1960],[1868,2895,2897,2920],{"className":2896},[1964],[1868,2898,2900],{"className":2899,"style":2233},[1968],[1868,2901,2902,2905],{"style":2805},[1868,2903],{"className":2904,"style":1977},[1976],[1868,2906,2908],{"className":2907},[1981,1982,1983,1984],[1868,2909,2911,2914,2917],{"className":2910},[1948,1984],[1868,2912,2107],{"className":2913},[1948,1988,1984],[1868,2915,1916],{"className":2916},[2043,1984],[1868,2918,2126],{"className":2919},[1948,1984],[1868,2921,1993],{"className":2922},[1992],[1868,2924,2926],{"className":2925},[1964],[1868,2927,2929],{"className":2928,"style":2263},[1968],[1868,2930],{},[1868,2932],{"className":2933,"style":2039},[2006],[1868,2935,2129],{"className":2936},[2043],[1868,2938],{"className":2939,"style":2039},[2006],[1868,2941,2943,2947,2951,2954,2957],{"className":2942},[1939],[1868,2944],{"className":2945,"style":2946},[1943],"height:0.6667em;vertical-align:-0.0833em;",[1868,2948,2739],{"className":2949},[2950],"minner",[1868,2952],{"className":2953,"style":2039},[2006],[1868,2955,2129],{"className":2956},[2043],[1868,2958],{"className":2959,"style":2039},[2006],[1868,2961,2963,2967,3007,3010,3013],{"className":2962},[1939],[1868,2964],{"className":2965,"style":2966},[1943],"height:0.7333em;vertical-align:-0.15em;",[1868,2968,2970,2973],{"className":2969},[1948],[1868,2971,2137],{"className":2972},[1948,1988],[1868,2974,2976],{"className":2975},[1955],[1868,2977,2979,2999],{"className":2978},[1959,1960],[1868,2980,2982,2996],{"className":2981},[1964],[1868,2983,2985],{"className":2984,"style":2172},[1968],[1868,2986,2987,2990],{"style":1972},[1868,2988],{"className":2989,"style":1977},[1976],[1868,2991,2993],{"className":2992},[1981,1982,1983,1984],[1868,2994,2107],{"className":2995},[1948,1988,1984],[1868,2997,1993],{"className":2998},[1992],[1868,3000,3002],{"className":3001},[1964],[1868,3003,3005],{"className":3004,"style":2000},[1968],[1868,3006],{},[1868,3008],{"className":3009,"style":2039},[2006],[1868,3011,2129],{"className":3012},[2043],[1868,3014],{"className":3015,"style":2039},[2006],[1868,3017,3019,3022,3063,3112,3115,3118],{"className":3018},[1939],[1868,3020],{"className":3021,"style":2841},[1943],[1868,3023,3025,3028],{"className":3024},[1948],[1868,3026,2427],{"className":3027,"style":2461},[1948,1988],[1868,3029,3031],{"className":3030},[1955],[1868,3032,3034,3055],{"className":3033},[1959,1960],[1868,3035,3037,3052],{"className":3036},[1964],[1868,3038,3040],{"className":3039,"style":2233},[1968],[1868,3041,3043,3046],{"style":3042},"top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;",[1868,3044],{"className":3045,"style":1977},[1976],[1868,3047,3049],{"className":3048},[1981,1982,1983,1984],[1868,3050,2126],{"className":3051},[1948,1984],[1868,3053,1993],{"className":3054},[1992],[1868,3056,3058],{"className":3057},[1964],[1868,3059,3061],{"className":3060,"style":2000},[1968],[1868,3062],{},[1868,3064,3066,3069],{"className":3065},[1948],[1868,3067,2137],{"className":3068},[1948,1988],[1868,3070,3072],{"className":3071},[1955],[1868,3073,3075,3104],{"className":3074},[1959,1960],[1868,3076,3078,3101],{"className":3077},[1964],[1868,3079,3081],{"className":3080,"style":2233},[1968],[1868,3082,3083,3086],{"style":1972},[1868,3084],{"className":3085,"style":1977},[1976],[1868,3087,3089],{"className":3088},[1981,1982,1983,1984],[1868,3090,3092,3095,3098],{"className":3091},[1948,1984],[1868,3093,2107],{"className":3094},[1948,1988,1984],[1868,3096,1916],{"className":3097},[2043,1984],[1868,3099,2126],{"className":3100},[1948,1984],[1868,3102,1993],{"className":3103},[1992],[1868,3105,3107],{"className":3106},[1964],[1868,3108,3110],{"className":3109,"style":2263},[1968],[1868,3111],{},[1868,3113],{"className":3114,"style":2039},[2006],[1868,3116,2129],{"className":3117},[2043],[1868,3119],{"className":3120,"style":2039},[2006],[1868,3122,3124,3128],{"className":3123},[1939],[1868,3125],{"className":3126,"style":3127},[1943],"height:0.313em;",[1868,3129,2739],{"className":3130},[2950],[1809,3132,3133,3136,3137,3176],{},[1816,3134,3135],{},"matrix(v, nrow=k)"," fills by columns, matching the usual ",[1868,3138,3140,3158],{"className":3139},[1871],[1868,3141,3143],{"className":3142},[1875],[1877,3144,3145],{"xmlns":1879},[1881,3146,3147,3155],{},[1884,3148,3149,3152],{},[1890,3150,3151],{"mathvariant":1892},"vec",[1898,3153,3154],{},"⁡",[1927,3156,3157],{"encoding":1929},"\\operatorname{vec}",[1868,3159,3161],{"className":3160,"ariaHidden":1935},[1934],[1868,3162,3164,3168],{"className":3163},[1939],[1868,3165],{"className":3166,"style":3167},[1943],"height:0.4306em;",[1868,3169,3172],{"className":3170},[3171],"mop",[1868,3173,3151],{"className":3174},[1948,3175],"mathrm"," operator.",[1809,3178,3179,3180,3183,3184,3244,3245,3248],{},"Use ",[1816,3181,3182],{},"solve(A, b)"," for ",[1868,3185,3187,3210],{"className":3186},[1871],[1868,3188,3190],{"className":3189},[1875],[1877,3191,3192],{"xmlns":1879},[1881,3193,3194,3207],{},[1884,3195,3196,3199,3202,3204],{},[1890,3197,3198],{},"A",[1890,3200,3201],{"mathvariant":2103},"x",[1898,3203,1900],{},[1890,3205,3206],{"mathvariant":2103},"b",[1927,3208,3209],{"encoding":1929},"A\\mathbf x=\\mathbf b",[1868,3211,3213,3234],{"className":3212,"ariaHidden":1935},[1934],[1868,3214,3216,3219,3222,3225,3228,3231],{"className":3215},[1939],[1868,3217],{"className":3218,"style":2380},[1943],[1868,3220,3198],{"className":3221},[1948,1988],[1868,3223,3201],{"className":3224},[1948,2159],[1868,3226],{"className":3227,"style":2007},[2006],[1868,3229,1900],{"className":3230},[2011],[1868,3232],{"className":3233,"style":2007},[2006],[1868,3235,3237,3241],{"className":3236},[1939],[1868,3238],{"className":3239,"style":3240},[1943],"height:0.6944em;",[1868,3242,3206],{"className":3243},[1948,2159],"; reserve ",[1816,3246,3247],{},"solve(A)"," for occasions when the full inverse is genuinely needed.",[1794,3250,3252],{"id":3251},"how-to-submit-a-lab","How to submit a lab",[1799,3254,3255],{},"For each cell, report four items:",[3257,3258,3263],"pre",{"className":3259,"code":3261,"language":3262,"meta":10},[3260],"language-text","Equation:\nDimensions:\nNumerical check:\nOne-parameter perturbation and predicted effect:\n","text",[1816,3264,3261],{"__ignoreMap":10},[1799,3266,3267],{},"“The output looks right” is not a check. Examples of checks are",[1868,3269,3272],{"className":3270},[3271],"katex-display",[1868,3273,3275,3387],{"className":3274},[1871],[1868,3276,3278],{"className":3277},[1875],[1877,3279,3281],{"xmlns":1879,"display":3280},"block",[1881,3282,3283,3384],{},[1884,3284,3285,3288,3290,3292,3298,3305,3308,3320,3323,3326,3329,3331,3338,3340,3342,3344,3347,3350,3352,3354,3356,3358,3360,3362,3364,3370,3372,3382],{},[1890,3286,3287],{"mathvariant":1892},"∥",[1890,3289,1893],{"mathvariant":1892},[1898,3291,1916],{},[2613,3293,3294,3296],{},[1890,3295,1893],{"mathvariant":1892},[1890,3297,2619],{"mathvariant":1892},[1887,3299,3300,3302],{},[1890,3301,3287],{"mathvariant":1892},[1890,3303,3304],{"mathvariant":1892},"∞",[1898,3306,3307],{},"\u003C",[2613,3309,3310,3313],{},[2124,3311,3312],{},"10",[1884,3314,3315,3317],{},[1898,3316,1916],{},[2124,3318,3319],{},"12",[1898,3321,3322],{"separator":1935},",",[2006,3324],{"width":3325},"2em",[1890,3327,3328],{},"min",[1898,3330,3154],{},[1887,3332,3333,3336],{},[1890,3334,3335],{},"λ",[1890,3337,1913],{},[1898,3339,1910],{"stretchy":1903},[1890,3341,1893],{"mathvariant":1892},[1898,3343,1922],{"stretchy":1903},[1898,3345,3346],{},">",[2124,3348,3349],{},"0",[1898,3351,3322],{"separator":1935},[2006,3353],{"width":3325},[1890,3355,3287],{"mathvariant":1892},[1890,3357,1893],{"mathvariant":1892},[1890,3359,1861],{"mathvariant":2103},[1898,3361,1916],{},[1890,3363,2367],{"mathvariant":2103},[1887,3365,3366,3368],{},[1890,3367,3287],{"mathvariant":1892},[1890,3369,3304],{"mathvariant":1892},[1898,3371,3307],{},[2613,3373,3374,3376],{},[2124,3375,3312],{},[1884,3377,3378,3380],{},[1898,3379,1916],{},[2124,3381,3312],{},[1890,3383,2562],{"mathvariant":1892},[1927,3385,3386],{"encoding":1929},"\\|\\Gamma-\\Gamma^\\top\\|_\\infty\u003C10^{-12},\n\\qquad\n\\min\\lambda_i(\\Gamma)>0,\n\\qquad\n\\|\\Gamma\\mathbf a-\\mathbf g\\|_\\infty\u003C10^{-10}.",[1868,3388,3390,3409,3496,3617,3650,3708],{"className":3389,"ariaHidden":1935},[1934],[1868,3391,3393,3396,3400,3403,3406],{"className":3392},[1939],[1868,3394],{"className":3395,"style":2021},[1943],[1868,3397,3399],{"className":3398},[1948],"∥Γ",[1868,3401],{"className":3402,"style":2039},[2006],[1868,3404,1916],{"className":3405},[2043],[1868,3407],{"className":3408,"style":2039},[2006],[1868,3410,3412,3416,3447,3487,3490,3493],{"className":3411},[1939],[1868,3413],{"className":3414,"style":3415},[1943],"height:1.1491em;vertical-align:-0.25em;",[1868,3417,3419,3422],{"className":3418},[1948],[1868,3420,1893],{"className":3421},[1948],[1868,3423,3425],{"className":3424},[1955],[1868,3426,3428],{"className":3427},[1959],[1868,3429,3431],{"className":3430},[1964],[1868,3432,3435],{"className":3433,"style":3434},[1968],"height:0.8991em;",[1868,3436,3438,3441],{"style":3437},"top:-3.113em;margin-right:0.05em;",[1868,3439],{"className":3440,"style":1977},[1976],[1868,3442,3444],{"className":3443},[1981,1982,1983,1984],[1868,3445,2619],{"className":3446},[1948,1984],[1868,3448,3450,3453],{"className":3449},[1948],[1868,3451,3287],{"className":3452},[1948],[1868,3454,3456],{"className":3455},[1955],[1868,3457,3459,3479],{"className":3458},[1959,1960],[1868,3460,3462,3476],{"className":3461},[1964],[1868,3463,3465],{"className":3464,"style":1969},[1968],[1868,3466,3467,3470],{"style":1972},[1868,3468],{"className":3469,"style":1977},[1976],[1868,3471,3473],{"className":3472},[1981,1982,1983,1984],[1868,3474,3304],{"className":3475},[1948,1984],[1868,3477,1993],{"className":3478},[1992],[1868,3480,3482],{"className":3481},[1964],[1868,3483,3485],{"className":3484,"style":2000},[1968],[1868,3486],{},[1868,3488],{"className":3489,"style":2007},[2006],[1868,3491,3307],{"className":3492},[2011],[1868,3494],{"className":3495,"style":2007},[2006],[1868,3497,3499,3503,3506,3542,3545,3549,3552,3555,3558,3599,3602,3605,3608,3611,3614],{"className":3498},[1939],[1868,3500],{"className":3501,"style":3502},[1943],"height:1.1141em;vertical-align:-0.25em;",[1868,3504,2126],{"className":3505},[1948],[1868,3507,3509,3512],{"className":3508},[1948],[1868,3510,3349],{"className":3511},[1948],[1868,3513,3515],{"className":3514},[1955],[1868,3516,3518],{"className":3517},[1959],[1868,3519,3521],{"className":3520},[1964],[1868,3522,3525],{"className":3523,"style":3524},[1968],"height:0.8641em;",[1868,3526,3527,3530],{"style":3437},[1868,3528],{"className":3529,"style":1977},[1976],[1868,3531,3533],{"className":3532},[1981,1982,1983,1984],[1868,3534,3536,3539],{"className":3535},[1948,1984],[1868,3537,1916],{"className":3538},[1948,1984],[1868,3540,3319],{"className":3541},[1948,1984],[1868,3543,3322],{"className":3544},[2465],[1868,3546],{"className":3547,"style":3548},[2006],"margin-right:2em;",[1868,3550],{"className":3551,"style":2469},[2006],[1868,3553,3328],{"className":3554},[3171],[1868,3556],{"className":3557,"style":2469},[2006],[1868,3559,3561,3564],{"className":3560},[1948],[1868,3562,3335],{"className":3563},[1948,1988],[1868,3565,3567],{"className":3566},[1955],[1868,3568,3570,3591],{"className":3569},[1959,1960],[1868,3571,3573,3588],{"className":3572},[1964],[1868,3574,3577],{"className":3575,"style":3576},[1968],"height:0.3117em;",[1868,3578,3579,3582],{"style":1972},[1868,3580],{"className":3581,"style":1977},[1976],[1868,3583,3585],{"className":3584},[1981,1982,1983,1984],[1868,3586,1913],{"className":3587},[1948,1988,1984],[1868,3589,1993],{"className":3590},[1992],[1868,3592,3594],{"className":3593},[1964],[1868,3595,3597],{"className":3596,"style":2000},[1968],[1868,3598],{},[1868,3600,1910],{"className":3601},[2025],[1868,3603,1893],{"className":3604},[1948],[1868,3606,1922],{"className":3607},[2060],[1868,3609],{"className":3610,"style":2007},[2006],[1868,3612,3346],{"className":3613},[2011],[1868,3615],{"className":3616,"style":2007},[2006],[1868,3618,3620,3623,3626,3629,3632,3635,3638,3641,3644,3647],{"className":3619},[1939],[1868,3621],{"className":3622,"style":2021},[1943],[1868,3624,3349],{"className":3625},[1948],[1868,3627,3322],{"className":3628},[2465],[1868,3630],{"className":3631,"style":3548},[2006],[1868,3633],{"className":3634,"style":2469},[2006],[1868,3636,3399],{"className":3637},[1948],[1868,3639,1861],{"className":3640},[1948,2159],[1868,3642],{"className":3643,"style":2039},[2006],[1868,3645,1916],{"className":3646},[2043],[1868,3648],{"className":3649,"style":2039},[2006],[1868,3651,3653,3656,3659,3699,3702,3705],{"className":3652},[1939],[1868,3654],{"className":3655,"style":2021},[1943],[1868,3657,2367],{"className":3658,"style":2406},[1948,2159],[1868,3660,3662,3665],{"className":3661},[1948],[1868,3663,3287],{"className":3664},[1948],[1868,3666,3668],{"className":3667},[1955],[1868,3669,3671,3691],{"className":3670},[1959,1960],[1868,3672,3674,3688],{"className":3673},[1964],[1868,3675,3677],{"className":3676,"style":1969},[1968],[1868,3678,3679,3682],{"style":1972},[1868,3680],{"className":3681,"style":1977},[1976],[1868,3683,3685],{"className":3684},[1981,1982,1983,1984],[1868,3686,3304],{"className":3687},[1948,1984],[1868,3689,1993],{"className":3690},[1992],[1868,3692,3694],{"className":3693},[1964],[1868,3695,3697],{"className":3696,"style":2000},[1968],[1868,3698],{},[1868,3700],{"className":3701,"style":2007},[2006],[1868,3703,3307],{"className":3704},[2011],[1868,3706],{"className":3707,"style":2007},[2006],[1868,3709,3711,3714,3717,3752],{"className":3710},[1939],[1868,3712],{"className":3713,"style":3524},[1943],[1868,3715,2126],{"className":3716},[1948],[1868,3718,3720,3723],{"className":3719},[1948],[1868,3721,3349],{"className":3722},[1948],[1868,3724,3726],{"className":3725},[1955],[1868,3727,3729],{"className":3728},[1959],[1868,3730,3732],{"className":3731},[1964],[1868,3733,3735],{"className":3734,"style":3524},[1968],[1868,3736,3737,3740],{"style":3437},[1868,3738],{"className":3739,"style":1977},[1976],[1868,3741,3743],{"className":3742},[1981,1982,1983,1984],[1868,3744,3746,3749],{"className":3745},[1948,1984],[1868,3747,1916],{"className":3748},[1948,1984],[1868,3750,3312],{"className":3751},[1948,1984],[1868,3753,2562],{"className":3754},[1948],[1794,3756,3758],{"id":3757},"workload","Workload",[1799,3760,3761],{},"Each lab is designed for 45–60 minutes:",[1806,3763,3764,3767,3770,3773],{},[1809,3765,3766],{},"10 minutes: reproduce one derivation by hand;",[1809,3768,3769],{},"15 minutes: run and annotate the original cells;",[1809,3771,3772],{},"15 minutes: make one controlled parameter change;",[1809,3774,3775],{},"10–20 minutes: answer the exercises and write the mathematical conclusion.",[1794,3777,3779],{"id":3778},"start","Start",[1799,3781,3782,3783,3786,3787,3817,3818,2562],{},"Open ",[1861,3784,3785],{"href":1863},"Lab 1",". Before running code, predict what happens to the smallest eigenvalue and condition number when an AR(1) coefficient moves from ",[1868,3788,3790,3804],{"className":3789},[1871],[1868,3791,3793],{"className":3792},[1875],[1877,3794,3795],{"xmlns":1879},[1881,3796,3797,3802],{},[1884,3798,3799],{},[2124,3800,3801],{},"0.6",[1927,3803,3801],{"encoding":1929},[1868,3805,3807],{"className":3806,"ariaHidden":1935},[1934],[1868,3808,3810,3814],{"className":3809},[1939],[1868,3811],{"className":3812,"style":3813},[1943],"height:0.6444em;",[1868,3815,3801],{"className":3816},[1948]," to ",[1868,3819,3821,3835],{"className":3820},[1871],[1868,3822,3824],{"className":3823},[1875],[1877,3825,3826],{"xmlns":1879},[1881,3827,3828,3833],{},[1884,3829,3830],{},[2124,3831,3832],{},"0.95",[1927,3834,3832],{"encoding":1929},[1868,3836,3838],{"className":3837,"ariaHidden":1935},[1934],[1868,3839,3841,3844],{"className":3840},[1939],[1868,3842],{"className":3843,"style":3813},[1943],[1868,3845,3832],{"className":3846},[1948],{"title":10,"searchDepth":3848,"depth":3848,"links":3849},2,[3850,3851,3852,3853,3854,3855],{"id":1796,"depth":3848,"text":1797},{"id":1828,"depth":3848,"text":1829},{"id":2552,"depth":3848,"text":2553},{"id":3251,"depth":3848,"text":3252},{"id":3757,"depth":3848,"text":3758},{"id":3778,"depth":3848,"text":3779},"Four browser-based base R laboratories for covariance matrices, AR recursions, linear prediction, likelihood, and state space.","md",{"sidebar":3859},{"order":3860},7,true,{"title":995,"description":3856},"eJZ93EsIjo6YNPrVngSqR_t8T7oWASFS_YCyfReywGs",[3865,3867],{"title":989,"path":990,"stem":991,"description":3866,"children":-1},"Translate autocovariance into frequency, estimate spectra, diagnose cycles, and avoid aliasing and filtering leakage.",{"title":1001,"path":1002,"stem":1003,"description":3868,"children":-1},"Construct stationary Toeplitz covariance matrices, test positive definiteness, factor them, and simulate Gaussian finite blocks.",1785754739066]