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Research Questions, Scope, and Feasibility","\u002Fen\u002Facademic-writing\u002F01-research-questions-and-planning","en\u002Facademic-writing\u002F01-research-questions-and-planning",{"title":23,"path":24,"stem":25},"2. 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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Separate four uncertainties",[1810,1811,1812,1831],"table",{},[1813,1814,1815],"thead",{},[1816,1817,1818,1822,1825,1828],"tr",{},[1819,1820,1821],"th",{},"Source",[1819,1823,1824],{},"Meaning",[1819,1826,1827],{},"Example",[1819,1829,1830],{},"Typical treatment",[1832,1833,1834,1849,1863,1877],"tbody",{},[1816,1835,1836,1840,1843,1846],{},[1837,1838,1839],"td",{},"Process",[1837,1841,1842],{},"future claims vary even with known parameters",[1837,1844,1845],{},"next year's payments differ randomly",[1837,1847,1848],{},"stochastic model or simulation",[1816,1850,1851,1854,1857,1860],{},[1837,1852,1853],{},"Parameter",[1837,1855,1856],{},"factors and distribution parameters are estimated",[1837,1858,1859],{},"Dev 2→3 uses one origin year",[1837,1861,1862],{},"standard error, bootstrap, sensitivity",[1816,1864,1865,1868,1871,1874],{},[1837,1866,1867],{},"Model",[1837,1869,1870],{},"another plausible structure gives another answer",[1837,1872,1873],{},"calendar inflation breaks age-only development",[1837,1875,1876],{},"alternative models and scenarios",[1816,1878,1879,1882,1885,1888],{},[1837,1880,1881],{},"Operational\u002Fdata",[1837,1883,1884],{},"recorded information is incomplete or unstable",[1837,1886,1887],{},"reopened claims or system migration",[1837,1889,1890],{},"reconciliation, controls, data-quality allowance",[1793,1892,1893],{},"One confidence interval rarely captures all four.",[1805,1895,1897],{"id":1896},"_2-mack-chain-ladder-what-it-adds","2. Mack chain ladder: what it adds",[1793,1899,1900],{},"Mack's distribution-free framework keeps chain-ladder mean structure while estimating conditional variance under assumptions such as:",[1902,1903,1906],"span",{"className":1904},[1905],"katex-display",[1902,1907,1910,2006],{"className":1908},[1909],"katex",[1902,1911,1914],{"className":1912},[1913],"katex-mathml",[1915,1916,1919],"math",{"xmlns":1917,"display":1918},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML","block",[1920,1921,1922,2001],"semantics",{},[1923,1924,1925,1929,1934,1959,1962,1974,1977,1980,1987,1999],"mrow",{},[1926,1927,1928],"mi",{},"E",[1930,1931,1933],"mo",{"stretchy":1932},"false","[",[1935,1936,1937,1940],"msub",{},[1926,1938,1939],{},"C",[1923,1941,1942,1945,1949,1952,1955],{},[1926,1943,1944],{},"i",[1930,1946,1948],{"separator":1947},"true",",",[1926,1950,1951],{},"j",[1930,1953,1954],{},"+",[1956,1957,1958],"mn",{},"1",[1930,1960,1961],{},"∣",[1935,1963,1964,1966],{},[1926,1965,1939],{},[1923,1967,1968,1970,1972],{},[1926,1969,1944],{},[1930,1971,1948],{"separator":1947},[1926,1973,1951],{},[1930,1975,1976],{"stretchy":1932},"]",[1930,1978,1979],{},"=",[1935,1981,1982,1985],{},[1926,1983,1984],{},"f",[1926,1986,1951],{},[1935,1988,1989,1991],{},[1926,1990,1939],{},[1923,1992,1993,1995,1997],{},[1926,1994,1944],{},[1930,1996,1948],{"separator":1947},[1926,1998,1951],{},[1930,2000,1948],{"separator":1947},[2002,2003,2005],"annotation",{"encoding":2004},"application\u002Fx-tex","E[C_{i,j+1}\\mid C_{i,j}]=f_jC_{i,j},",[1902,2007,2010,2116,2184],{"className":2008,"ariaHidden":1947},[2009],"katex-html",[1902,2011,2014,2019,2025,2029,2104,2109,2113],{"className":2012},[2013],"base",[1902,2015],{"className":2016,"style":2018},[2017],"strut","height:1.0361em;vertical-align:-0.2861em;",[1902,2020,1928],{"className":2021,"style":2024},[2022,2023],"mord","mathnormal","margin-right:0.0576em;",[1902,2026,1933],{"className":2027},[2028],"mopen",[1902,2030,2032,2036],{"className":2031},[2022],[1902,2033,1939],{"className":2034,"style":2035},[2022,2023],"margin-right:0.0715em;",[1902,2037,2040],{"className":2038},[2039],"msupsub",[1902,2041,2045,2095],{"className":2042},[2043,2044],"vlist-t","vlist-t2",[1902,2046,2049,2090],{"className":2047},[2048],"vlist-r",[1902,2050,2054],{"className":2051,"style":2053},[2052],"vlist","height:0.3117em;",[1902,2055,2057,2062],{"style":2056},"top:-2.55em;margin-left:-0.0715em;margin-right:0.05em;",[1902,2058],{"className":2059,"style":2061},[2060],"pstrut","height:2.7em;",[1902,2063,2069],{"className":2064},[2065,2066,2067,2068],"sizing","reset-size6","size3","mtight",[1902,2070,2072,2075,2079,2083,2087],{"className":2071},[2022,2068],[1902,2073,1944],{"className":2074},[2022,2023,2068],[1902,2076,1948],{"className":2077},[2078,2068],"mpunct",[1902,2080,1951],{"className":2081,"style":2082},[2022,2023,2068],"margin-right:0.0572em;",[1902,2084,1954],{"className":2085},[2086,2068],"mbin",[1902,2088,1958],{"className":2089},[2022,2068],[1902,2091,2094],{"className":2092},[2093],"vlist-s","​",[1902,2096,2098],{"className":2097},[2048],[1902,2099,2102],{"className":2100,"style":2101},[2052],"height:0.2861em;",[1902,2103],{},[1902,2105],{"className":2106,"style":2108},[2107],"mspace","margin-right:0.2778em;",[1902,2110,1961],{"className":2111},[2112],"mrel",[1902,2114],{"className":2115,"style":2108},[2107],[1902,2117,2119,2122,2171,2175,2178,2181],{"className":2118},[2013],[1902,2120],{"className":2121,"style":2018},[2017],[1902,2123,2125,2128],{"className":2124},[2022],[1902,2126,1939],{"className":2127,"style":2035},[2022,2023],[1902,2129,2131],{"className":2130},[2039],[1902,2132,2134,2163],{"className":2133},[2043,2044],[1902,2135,2137,2160],{"className":2136},[2048],[1902,2138,2140],{"className":2139,"style":2053},[2052],[1902,2141,2142,2145],{"style":2056},[1902,2143],{"className":2144,"style":2061},[2060],[1902,2146,2148],{"className":2147},[2065,2066,2067,2068],[1902,2149,2151,2154,2157],{"className":2150},[2022,2068],[1902,2152,1944],{"className":2153},[2022,2023,2068],[1902,2155,1948],{"className":2156},[2078,2068],[1902,2158,1951],{"className":2159,"style":2082},[2022,2023,2068],[1902,2161,2094],{"className":2162},[2093],[1902,2164,2166],{"className":2165},[2048],[1902,2167,2169],{"className":2168,"style":2101},[2052],[1902,2170],{},[1902,2172,1976],{"className":2173},[2174],"mclose",[1902,2176],{"className":2177,"style":2108},[2107],[1902,2179,1979],{"className":2180},[2112],[1902,2182],{"className":2183,"style":2108},[2107],[1902,2185,2187,2191,2233,2282],{"className":2186},[2013],[1902,2188],{"className":2189,"style":2190},[2017],"height:0.9805em;vertical-align:-0.2861em;",[1902,2192,2194,2198],{"className":2193},[2022],[1902,2195,1984],{"className":2196,"style":2197},[2022,2023],"margin-right:0.1076em;",[1902,2199,2201],{"className":2200},[2039],[1902,2202,2204,2225],{"className":2203},[2043,2044],[1902,2205,2207,2222],{"className":2206},[2048],[1902,2208,2210],{"className":2209,"style":2053},[2052],[1902,2211,2213,2216],{"style":2212},"top:-2.55em;margin-left:-0.1076em;margin-right:0.05em;",[1902,2214],{"className":2215,"style":2061},[2060],[1902,2217,2219],{"className":2218},[2065,2066,2067,2068],[1902,2220,1951],{"className":2221,"style":2082},[2022,2023,2068],[1902,2223,2094],{"className":2224},[2093],[1902,2226,2228],{"className":2227},[2048],[1902,2229,2231],{"className":2230,"style":2101},[2052],[1902,2232],{},[1902,2234,2236,2239],{"className":2235},[2022],[1902,2237,1939],{"className":2238,"style":2035},[2022,2023],[1902,2240,2242],{"className":2241},[2039],[1902,2243,2245,2274],{"className":2244},[2043,2044],[1902,2246,2248,2271],{"className":2247},[2048],[1902,2249,2251],{"className":2250,"style":2053},[2052],[1902,2252,2253,2256],{"style":2056},[1902,2254],{"className":2255,"style":2061},[2060],[1902,2257,2259],{"className":2258},[2065,2066,2067,2068],[1902,2260,2262,2265,2268],{"className":2261},[2022,2068],[1902,2263,1944],{"className":2264},[2022,2023,2068],[1902,2266,1948],{"className":2267},[2078,2068],[1902,2269,1951],{"className":2270,"style":2082},[2022,2023,2068],[1902,2272,2094],{"className":2273},[2093],[1902,2275,2277],{"className":2276},[2048],[1902,2278,2280],{"className":2279,"style":2101},[2052],[1902,2281],{},[1902,2283,1948],{"className":2284},[2078],[1902,2286,2288],{"className":2287},[1905],[1902,2289,2291,2373],{"className":2290},[1909],[1902,2292,2294],{"className":2293},[1913],[1915,2295,2296],{"xmlns":1917,"display":1918},[1920,229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C_{i,j})=\\sigma_j^2C_{i,j},",[1902,2374,2376,2457,2524],{"className":2375,"ariaHidden":1947},[2009],[1902,2377,2379,2382,2390,2393,2448,2451,2454],{"className":2378},[2013],[1902,2380],{"className":2381,"style":2018},[2017],[1902,2383,2386],{"className":2384},[2385],"mop",[1902,2387,2303],{"className":2388},[2022,2389],"mathrm",[1902,2391,2309],{"className":2392},[2028],[1902,2394,2396,2399],{"className":2395},[2022],[1902,2397,1939],{"className":2398,"style":2035},[2022,2023],[1902,2400,2402],{"className":2401},[2039],[1902,2403,2405,2440],{"className":2404},[2043,2044],[1902,2406,2408,2437],{"className":2407},[2048],[1902,2409,2411],{"className":2410,"style":2053},[2052],[1902,2412,2413,2416],{"style":2056},[1902,2414],{"className":2415,"style":2061},[2060],[1902,2417,2419],{"className":2418},[2065,2066,2067,2068],[1902,2420,2422,2425,2428,2431,2434],{"className":2421},[2022,2068],[1902,2423,1944],{"className":2424},[2022,2023,2068],[1902,2426,1948],{"className":2427},[2078,2068],[1902,2429,1951],{"className":2430,"style":2082},[2022,2023,2068],[1902,2432,1954],{"className":2433},[2086,2068],[1902,2435,1958],{"className":2436},[2022,2068],[1902,2438,2094],{"className":2439},[2093],[1902,2441,2443],{"className":2442},[2048],[1902,2444,2446],{"className":2445,"style":2101},[2052],[1902,2447],{},[1902,2449],{"className":2450,"style":2108},[2107],[1902,2452,1961],{"className":2453},[2112],[1902,2455],{"className":2456,"style":2108},[2107],[1902,2458,2460,2463,2512,2515,2518,2521],{"className":2459},[2013],[1902,2461],{"className":2462,"style":2018},[2017],[1902,2464,2466,2469],{"className":2465},[2022],[1902,2467,1939],{"className":2468,"style":2035},[2022,2023],[1902,2470,2472],{"className":2471},[2039],[1902,2473,2475,2504],{"className":2474},[2043,2044],[1902,2476,2478,2501],{"className":2477},[2048],[1902,2479,2481],{"className":2480,"style":2053},[2052],[1902,2482,2483,2486],{"style":2056},[1902,2484],{"className":2485,"style":2061},[2060],[1902,2487,2489],{"className":2488},[2065,2066,2067,2068],[1902,2490,2492,2495,2498],{"className":2491},[2022,2068],[1902,2493,1944],{"className":2494},[2022,2023,2068],[1902,2496,1948],{"className":2497},[2078,2068],[1902,2499,1951],{"className":2500,"style":2082},[2022,2023,2068],[1902,2502,2094],{"className":2503},[2093],[1902,2505,2507],{"className":2506},[2048],[1902,2508,2510],{"className":2509,"style":2101},[2052],[1902,2511],{},[1902,2513,2342],{"className":2514},[2174],[1902,2516],{"className":2517,"style":2108},[2107],[1902,2519,1979],{"className":2520},[2112],[1902,2522],{"className":2523,"style":2108},[2107],[1902,2525,2527,2531,2587,2636],{"className":2526},[2013],[1902,2528],{"className":2529,"style":2530},[2017],"height:1.2472em;vertical-align:-0.3831em;",[1902,2532,2534,2538],{"className":2533},[2022],[1902,2535,2350],{"className":2536,"style":2537},[2022,2023],"margin-right:0.0359em;",[1902,2539,2541],{"className":2540},[2039],[1902,2542,2544,2578],{"className":2543},[2043,2044],[1902,2545,2547,2575],{"className":2546},[2048],[1902,2548,2551,2563],{"className":2549,"style":2550},[2052],"height:0.8641em;",[1902,2552,2554,2557],{"style":2553},"top:-2.453em;margin-left:-0.0359em;margin-right:0.05em;",[1902,2555],{"className":2556,"style":2061},[2060],[1902,2558,2560],{"className":2559},[2065,2066,2067,2068],[1902,2561,1951],{"className":2562,"style":2082},[2022,2023,2068],[1902,2564,2566,2569],{"style":2565},"top:-3.113em;margin-right:0.05em;",[1902,2567],{"className":2568,"style":2061},[2060],[1902,2570,2572],{"className":2571},[2065,2066,2067,2068],[1902,2573,2355],{"className":2574},[2022,2068],[1902,2576,2094],{"className":2577},[2093],[1902,2579,2581],{"className":2580},[2048],[1902,2582,2585],{"className":2583,"style":2584},[2052],"height:0.3831em;",[1902,2586],{},[1902,2588,2590,2593],{"className":2589},[2022],[1902,2591,1939],{"className":2592,"style":2035},[2022,2023],[1902,2594,2596],{"className":2595},[2039],[1902,2597,2599,2628],{"className":2598},[2043,2044],[1902,2600,2602,2625],{"className":2601},[2048],[1902,2603,2605],{"className":2604,"style":2053},[2052],[1902,2606,2607,2610],{"style":2056},[1902,2608],{"className":2609,"style":2061},[2060],[1902,2611,2613],{"className":2612},[2065,2066,2067,2068],[1902,2614,2616,2619,2622],{"className":2615},[2022,2068],[1902,2617,1944],{"className":2618},[2022,2023,2068],[1902,2620,1948],{"className":2621},[2078,2068],[1902,2623,1951],{"className":2624,"style":2082},[2022,2023,2068],[1902,2626,2094],{"className":2627},[2093],[1902,2629,2631],{"className":2630},[2048],[1902,2632,2634],{"className":2633,"style":2101},[2052],[1902,2635],{},[1902,2637,1948],{"className":2638},[2078],[1793,2640,2641],{},"with origin years independent. It yields standard errors for projected reserves without assuming a full claim distribution.",[2643,2644,2646],"warning",{"title":2645},"What a Mack standard error does not cover","It does not automatically cover changing inflation, a new claims process, dependence across origin years, an omitted tail, or uncertainty in manually selected factors. Those are model and operational questions.",[1805,2648,2650],{"id":2649},"_3-bootstrap-preserve-the-workflow","3. Bootstrap: preserve the workflow",[1793,2652,2653],{},"A reserving bootstrap typically:",[2655,2656,2657,2661,2664,2667,2670,2673],"ol",{},[2658,2659,2660],"li",{},"fits an incremental mean model;",[2658,2662,2663],{},"computes and scales residuals;",[2658,2665,2666],{},"resamples residuals to create pseudo-triangles;",[2658,2668,2669],{},"refits development parameters;",[2658,2671,2672],{},"simulates future process outcomes;",[2658,2674,2675],{},"stores total reserve and origin-year results.",[1793,2677,2678],{},"Refitting in each replicate captures parameter variation. Simulating future increments captures process variation. Merely sampling final point estimates captures neither correctly.",[1805,2680,2682],{"id":2681},"_4-backtest-by-valuation-date","4. Backtest by valuation date",[1793,2684,2685,2686,2716],{},"For each historical diagonal ",[1902,2687,2689,2703],{"className":2688},[1909],[1902,2690,2692],{"className":2691},[1913],[1915,2693,2694],{"xmlns":1917},[1920,2695,2696,2701],{},[1923,2697,2698],{},[1926,2699,2700],{},"t",[2002,2702,2700],{"encoding":2004},[1902,2704,2706],{"className":2705,"ariaHidden":1947},[2009],[1902,2707,2709,2713],{"className":2708},[2013],[1902,2710],{"className":2711,"style":2712},[2017],"height:0.6151em;",[1902,2714,2700],{"className":2715},[2022,2023],":",[2655,2718,2719,2751,2782,2785,2788],{},[2658,2720,2721,2722,2750],{},"hide all observations after ",[1902,2723,2725,2738],{"className":2724},[1909],[1902,2726,2728],{"className":2727},[1913],[1915,2729,2730],{"xmlns":1917},[1920,2731,2732,2736],{},[1923,2733,2734],{},[1926,2735,2700],{},[2002,2737,2700],{"encoding":2004},[1902,2739,2741],{"className":2740,"ariaHidden":1947},[2009],[1902,2742,2744,2747],{"className":2743},[2013],[1902,2745],{"className":2746,"style":2712},[2017],[1902,2748,2700],{"className":2749},[2022,2023],";",[2658,2752,2753,2754,2750],{},"fit the method using only information available at ",[1902,2755,2757,2770],{"className":2756},[1909],[1902,2758,2760],{"className":2759},[1913],[1915,2761,2762],{"xmlns":1917},[1920,2763,2764,2768],{},[1923,2765,2766],{},[1926,2767,2700],{},[2002,2769,2700],{"encoding":2004},[1902,2771,2773],{"className":2772,"ariaHidden":1947},[2009],[1902,2774,2776,2779],{"className":2775},[2013],[1902,2777],{"className":2778,"style":2712},[2017],[1902,2780,2700],{"className":2781},[2022,2023],[2658,2783,2784],{},"predict the next diagonal or later ultimate;",[2658,2786,2787],{},"compare with subsequently observed values;",[2658,2789,2790,2791,2819],{},"repeat over several ",[1902,2792,2794,2807],{"className":2793},[1909],[1902,2795,2797],{"className":2796},[1913],[1915,2798,2799],{"xmlns":1917},[1920,2800,2801,2805],{},[1923,2802,2803],{},[1926,2804,2700],{},[2002,2806,2700],{"encoding":2004},[1902,2808,2810],{"className":2809,"ariaHidden":1947},[2009],[1902,2811,2813,2816],{"className":2812},[2013],[1902,2814],{"className":2815,"style":2712},[2017],[1902,2817,2700],{"className":2818},[2022,2023],".",[1793,2821,2822,2823,2826],{},"Useful measures include signed error, absolute percentage error where denominators are stable, interval coverage, and error by development age. Reserve backtesting must avoid ",[1797,2824,2825],{},"look-ahead bias",": factor selections and exclusions should reflect what could have been known at the historical valuation date.",[2828,2829,2831],"h3",{"id":2830},"tiny-backtest-example","Tiny backtest example",[1793,2833,2834,2835,2924],{},"Using only AY 2020 and 2021 to estimate ",[1902,2836,2838,2863],{"className":2837},[1909],[1902,2839,2841],{"className":2840},[1913],[1915,2842,2843],{"xmlns":1917},[1920,2844,2845,2860],{},[1923,2846,2847],{},[1935,2848,2849,2851],{},[1926,2850,1984],{},[1923,2852,2853,2856,2858],{},[1956,2854,2855],{},"0",[1930,2857,2716],{},[1956,2859,1958],{},[2002,2861,2862],{"encoding":2004},"f_{0:1}",[1902,2864,2866],{"className":2865,"ariaHidden":1947},[2009],[1902,2867,2869,2873],{"className":2868},[2013],[1902,2870],{"className":2871,"style":2872},[2017],"height:0.8889em;vertical-align:-0.1944em;",[1902,2874,2876,2879],{"className":2875},[2022],[1902,2877,1984],{"className":2878,"style":2197},[2022,2023],[1902,2880,2882],{"className":2881},[2039],[1902,2883,2885,2915],{"className":2884},[2043,2044],[1902,2886,2888,2912],{"className":2887},[2048],[1902,2889,2892],{"className":2890,"style":2891},[2052],"height:0.3011em;",[1902,2893,2894,2897],{"style":2212},[1902,2895],{"className":2896,"style":2061},[2060],[1902,2898,2900],{"className":2899},[2065,2066,2067,2068],[1902,2901,2903,2906,2909],{"className":2902},[2022,2068],[1902,2904,2855],{"className":2905},[2022,2068],[1902,2907,2716],{"className":2908},[2112,2068],[1902,2910,1958],{"className":2911},[2022,2068],[1902,2913,2094],{"className":2914},[2093],[1902,2916,2918],{"className":2917},[2048],[1902,2919,2922],{"className":2920,"style":2921},[2052],"height:0.15em;",[1902,2923],{}," gives",[1902,2926,2928],{"className":2927},[1905],[1902,2929,2931,3003],{"className":2930},[1909],[1902,2932,2934],{"className":2933},[1913],[1915,2935,2936],{"xmlns":1917,"display":1918},[1920,2937,2938,3000],{},[1923,2939,2940,2970,2972,2995,2997],{},[2346,2941,2942,2950,2958],{},[2943,2944,2945,2947],"mover",{"accent":1947},[1926,2946,1984],{},[1930,2948,2949],{"stretchy":1947},"^",[1923,2951,2952,2954,2956],{},[1956,2953,2855],{},[1930,2955,2716],{},[1956,2957,1958],{},[1923,2959,2960,2962,2965,2968],{},[1930,2961,2309],{"stretchy":1932},[1930,2963,2964],{},"−",[1956,2966,2967],{},"2022",[1930,2969,2342],{"stretchy":1932},[1930,2971,1979],{},[2973,2974,2975,2985],"mfrac",{},[1923,2976,2977,2980,2982],{},[1956,2978,2979],{},"180",[1930,2981,1954],{},[1956,2983,2984],{},"220",[1923,2986,2987,2990,2992],{},[1956,2988,2989],{},"100",[1930,2991,1954],{},[1956,2993,2994],{},"120",[1930,2996,1979],{},[1956,2998,2999],{},"1.8182.",[2002,3001,3002],{"encoding":2004},"\\widehat f_{0:1}^{(-2022)}=\\frac{180+220}{100+120}=1.8182.",[1902,3004,3006,3154,3265],{"className":3005,"ariaHidden":1947},[2009],[1902,3007,3009,3013,3145,3148,3151],{"className":3008},[2013],[1902,3010],{"className":3011,"style":3012},[2017],"height:1.3111em;vertical-align:-0.2663em;",[1902,3014,3016,3075],{"className":3015},[2022],[1902,3017,3020],{"className":3018},[2022,3019],"accent",[1902,3021,3023,3066],{"className":3022},[2043,2044],[1902,3024,3026,3063],{"className":3025},[2048],[1902,3027,3030,3040],{"className":3028,"style":3029},[2052],"height:0.9344em;",[1902,3031,3033,3037],{"style":3032},"top:-3em;",[1902,3034],{"className":3035,"style":3036},[2060],"height:3em;",[1902,3038,1984],{"className":3039,"style":2197},[2022,2023],[1902,3041,3045,3048],{"className":3042,"style":3044},[3043],"svg-align","width:calc(100% - 0.3333em);margin-left:0.3333em;top:-3.6944em;",[1902,3046],{"className":3047,"style":3036},[2060],[1902,3049,3051],{"style":3050},"height:0.24em;",[3052,3053,3059],"svg",{"xmlns":3054,"width":3055,"height":3056,"viewBox":3057,"preserveAspectRatio":3058},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","100%","0.24em","0 0 1062 239","none",[3060,3061],"path",{"d":3062},"M529 0h5l519 115c5 1 9 5 9 10 0 1-1 2-1 3l-4 22\nc-1 5-5 9-11 9h-2L532 67 19 159h-2c-5 0-9-4-11-9l-5-22c-1-6 2-12 8-13z",[1902,3064,2094],{"className":3065},[2093],[1902,3067,3069],{"className":3068},[2048],[1902,3070,3073],{"className":3071,"style":3072},[2052],"height:0.1944em;",[1902,3074],{},[1902,3076,3078],{"className":3077},[2039],[1902,3079,3081,3136],{"className":3080},[2043,2044],[1902,3082,3084,3133],{"className":3083},[2048],[1902,3085,3088,3109],{"className":3086,"style":3087},[2052],"height:1.0448em;",[1902,3089,3091,3094],{"style":3090},"top:-2.4337em;margin-left:-0.1076em;margin-right:0.05em;",[1902,3092],{"className":3093,"style":2061},[2060],[1902,3095,3097],{"className":3096},[2065,2066,2067,2068],[1902,3098,3100,3103,3106],{"className":3099},[2022,2068],[1902,3101,2855],{"className":3102},[2022,2068],[1902,3104,2716],{"className":3105},[2112,2068],[1902,3107,1958],{"className":3108},[2022,2068],[1902,3110,3112,3115],{"style":3111},"top:-3.2198em;margin-right:0.05em;",[1902,3113],{"className":3114,"style":2061},[2060],[1902,3116,3118],{"className":3117},[2065,2066,2067,2068],[1902,3119,3121,3124,3127,3130],{"className":3120},[2022,2068],[1902,3122,2309],{"className":3123},[2028,2068],[1902,3125,2964],{"className":3126},[2022,2068],[1902,3128,2967],{"className":3129},[2022,2068],[1902,3131,2342],{"className":3132},[2174,2068],[1902,3134,2094],{"className":3135},[2093],[1902,3137,3139],{"className":3138},[2048],[1902,3140,3143],{"className":3141,"style":3142},[2052],"height:0.2663em;",[1902,3144],{},[1902,3146],{"className":3147,"style":2108},[2107],[1902,3149,1979],{"className":3150},[2112],[1902,3152],{"className":3153,"style":2108},[2107],[1902,3155,3157,3161,3256,3259,3262],{"className":3156},[2013],[1902,3158],{"className":3159,"style":3160},[2017],"height:2.0908em;vertical-align:-0.7693em;",[1902,3162,3164,3168,3253],{"className":3163},[2022],[1902,3165],{"className":3166},[2028,3167],"nulldelimiter",[1902,3169,3171],{"className":3170},[2973],[1902,3172,3174,3244],{"className":3173},[2043,2044],[1902,3175,3177,3241],{"className":3176},[2048],[1902,3178,3181,3206,3217],{"className":3179,"style":3180},[2052],"height:1.3214em;",[1902,3182,3184,3187],{"style":3183},"top:-2.314em;",[1902,3185],{"className":3186,"style":3036},[2060],[1902,3188,3190,3193,3197,3200,3203],{"className":3189},[2022],[1902,3191,2989],{"className":3192},[2022],[1902,3194],{"className":3195,"style":3196},[2107],"margin-right:0.2222em;",[1902,3198,1954],{"className":3199},[2086],[1902,3201],{"className":3202,"style":3196},[2107],[1902,3204,2994],{"className":3205},[2022],[1902,3207,3209,3212],{"style":3208},"top:-3.23em;",[1902,3210],{"className":3211,"style":3036},[2060],[1902,3213],{"className":3214,"style":3216},[3215],"frac-line","border-bottom-width:0.04em;",[1902,3218,3220,3223],{"style":3219},"top:-3.677em;",[1902,3221],{"className":3222,"style":3036},[2060],[1902,3224,3226,3229,3232,3235,3238],{"className":3225},[2022],[1902,3227,2979],{"className":3228},[2022],[1902,3230],{"className":3231,"style":3196},[2107],[1902,3233,1954],{"className":3234},[2086],[1902,3236],{"className":3237,"style":3196},[2107],[1902,3239,2984],{"className":3240},[2022],[1902,3242,2094],{"className":3243},[2093],[1902,3245,3247],{"className":3246},[2048],[1902,3248,3251],{"className":3249,"style":3250},[2052],"height:0.7693em;",[1902,3252],{},[1902,3254],{"className":3255},[2174,3167],[1902,3257],{"className":3258,"style":2108},[2107],[1902,3260,1979],{"className":3261},[2112],[1902,3263],{"className":3264,"style":2108},[2107],[1902,3266,3268,3272],{"className":3267},[2013],[1902,3269],{"className":3270,"style":3271},[2017],"height:0.6444em;",[1902,3273,2999],{"className":3274},[2022],[1793,3276,3277,3278,3356],{},"It predicts AY 2022 Dev 1 paid of ",[1902,3279,3281,3307],{"className":3280},[1909],[1902,3282,3284],{"className":3283},[1913],[1915,3285,3286],{"xmlns":1917},[1920,3287,3288,3304],{},[1923,3289,3290,3293,3296,3299,3301],{},[1956,3291,3292],{},"140",[1930,3294,3295],{},"×",[1956,3297,3298],{},"1.8182",[1930,3300,1979],{},[1956,3302,3303],{},"254.5",[2002,3305,3306],{"encoding":2004},"140\\times1.8182=254.5",[1902,3308,3310,3329,3347],{"className":3309,"ariaHidden":1947},[2009],[1902,3311,3313,3317,3320,3323,3326],{"className":3312},[2013],[1902,3314],{"className":3315,"style":3316},[2017],"height:0.7278em;vertical-align:-0.0833em;",[1902,3318,3292],{"className":3319},[2022],[1902,3321],{"className":3322,"style":3196},[2107],[1902,3324,3295],{"className":3325},[2086],[1902,3327],{"className":3328,"style":3196},[2107],[1902,3330,3332,3335,3338,3341,3344],{"className":3331},[2013],[1902,3333],{"className":3334,"style":3271},[2017],[1902,3336,3298],{"className":3337},[2022],[1902,3339],{"className":3340,"style":2108},[2107],[1902,3342,1979],{"className":3343},[2112],[1902,3345],{"className":3346,"style":2108},[2107],[1902,3348,3350,3353],{"className":3349},[2013],[1902,3351],{"className":3352,"style":3271},[2017],[1902,3354,3303],{"className":3355},[2022],", versus £260m observed. The next-diagonal error is £5.5m, or 2.1% of observed. One good prediction is not validation; the example shows the information boundary.",[1805,3358,3360],{"id":3359},"_5-residual-patterns-diagnose-structure","5. Residual patterns diagnose structure",[1810,3362,3363,3373],{},[1813,3364,3365],{},[1816,3366,3367,3370],{},[1819,3368,3369],{},"Pattern",[1819,3371,3372],{},"Interpretation to investigate",[1832,3374,3375,3383,3391,3399,3407],{},[1816,3376,3377,3380],{},[1837,3378,3379],{},"residuals trend across origin years",[1837,3381,3382],{},"portfolio mix, exposure, or underwriting change",[1816,3384,3385,3388],{},[1837,3386,3387],{},"residuals align on calendar diagonals",[1837,3389,3390],{},"inflation, legislation, catastrophe, or operations",[1816,3392,3393,3396],{},[1837,3394,3395],{},"variance rises faster than fitted mean",[1837,3397,3398],{},"heteroscedasticity or large-loss mixture",[1816,3400,3401,3404],{},[1837,3402,3403],{},"paid and incurred residuals diverge",[1837,3405,3406],{},"settlement and case-reserve processes changed",[1816,3408,3409,3412],{},[1837,3410,3411],{},"youngest years fail repeatedly",[1837,3413,3414],{},"prior or development pattern is stale",[1793,3416,3417],{},"Residuals are prompts for investigation, not mechanical deletion rules.",[1805,3419,3421],{"id":3420},"_6-scenario-table-for-the-reserve-committee","6. Scenario table for the reserve committee",[1810,3423,3424,3437],{},[1813,3425,3426],{},[1816,3427,3428,3431,3434],{},[1819,3429,3430],{},"Scenario",[1819,3432,3433],{},"Change from baseline",[1819,3435,3436],{},"Question answered",[1832,3438,3439,3450,3461,3472,3483,3494],{},[1816,3440,3441,3444,3447],{},[1837,3442,3443],{},"factor selection",[1837,3445,3446],{},"use trimmed or credibility-weighted link ratios",[1837,3448,3449],{},"sensitivity to influential cells",[1816,3451,3452,3455,3458],{},[1837,3453,3454],{},"tail",[1837,3456,3457],{},"add plausible tail factors",[1837,3459,3460],{},"cost beyond observed development",[1816,3462,3463,3466,3469],{},[1837,3464,3465],{},"inflation",[1837,3467,3468],{},"increase future severity\u002Fcalendar effect",[1837,3470,3471],{},"sensitivity to claims inflation",[1816,3473,3474,3477,3480],{},[1837,3475,3476],{},"large loss",[1837,3478,3479],{},"model separately or cap for factor selection",[1837,3481,3482],{},"concentration risk",[1816,3484,3485,3488,3491],{},[1837,3486,3487],{},"prior",[1837,3489,3490],{},"vary ELR in BF",[1837,3492,3493],{},"dependence on external expectation",[1816,3495,3496,3499,3502],{},[1837,3497,3498],{},"settlement speed",[1837,3500,3501],{},"shift payment timing without changing ultimate",[1837,3503,3504],{},"paid-pattern instability",[1793,3506,3507],{},"Present the rationale and probability status: a deterministic stress is not a percentile unless linked to a probabilistic model.",[1805,3509,3511],{"id":3510},"_7-current-research-richer-time-and-claim-information","7. Current research: richer time and claim information",[1793,3513,3514,3515,3518,3519,3522],{},"Recent work develops two complementary directions. State-space models make aggregate reserving dynamics and sampling distributions explicit. Individual-claim approaches use transaction histories, claim status, covariates, and survival methods. Examples include Selukar's state-space workflow (2025), the CAS ",[1797,3516,3517],{},"Claim Life Cycle Model"," (2024), the ",[1797,3520,3521],{},"ReSurv"," claim-count framework (2025), and a 2026 preprint connecting chain ladder with individual-claim prediction.",[1793,3524,3525],{},"The teaching conclusion is measured:",[3527,3528,3529,3532,3535,3538],"ul",{},[2658,3530,3531],{},"individual data can explain reporting, closure, reopening, and payment timing;",[2658,3533,3534],{},"richer data do not remove selection bias, censoring, or operational drift;",[2658,3536,3537],{},"aggregate triangles remain valuable for reconciliation and benchmarking;",[2658,3539,3540],{},"recent preprints are research-frontier evidence, not settled professional standards.",[1805,3542,3544],{"id":3543},"_8-minimum-reserve-report","8. Minimum reserve report",[1793,3546,3547],{},"A reviewer should be able to reproduce:",[2655,3549,3550,3553,3556,3559,3562,3565,3568,3571],{},[2658,3551,3552],{},"data scope and valuation date;",[2658,3554,3555],{},"triangle transformations and exclusions;",[2658,3557,3558],{},"factor\u002Fprior\u002Ftail selections;",[2658,3560,3561],{},"central estimate by origin year;",[2658,3563,3564],{},"process and parameter uncertainty where modelled;",[2658,3566,3567],{},"alternative methods and scenarios;",[2658,3569,3570],{},"backtest results and known failure modes;",[2658,3572,3573],{},"judgement, ownership, and limitations.",[1805,3575,3577],{"id":3576},"practice","Practice",[2655,3579,3580,3583,3586],{},[2658,3581,3582],{},"Classify “future claim amounts vary around a correct expected value.”",[2658,3584,3585],{},"Classify “a repair-cost shock affects all cells on the latest diagonal.”",[2658,3587,3588],{},"Why is fitting on the full triangle and then pretending to backtest an earlier diagonal invalid?",[3590,3591,3593],"legacy-details",{"title":3592},"Answers",[2655,3594,3595,3598,3601],{},[2658,3596,3597],{},"Process uncertainty.",[2658,3599,3600],{},"Primarily model\u002Fcalendar uncertainty; parameter and process effects may accompany it.",[2658,3602,3603],{},"The selected factors have already seen the held-out observations, so the error is optimistically biased by information leakage.",[1805,3605,3607],{"id":3606},"sources-and-further-reading","Sources and further reading",[3527,3609,3610,3618,3625,3634,3641,3648],{},[2658,3611,3612,3613,3617],{},"Mack, T. (1993), “Distribution-Free Calculation of the Standard Error of Chain Ladder Reserve Estimates,” ",[3614,3615,3616],"em",{},"ASTIN Bulletin",", 23(2), 213–225.",[2658,3619,3620,3621,3624],{},"England, P. D. and Verrall, R. J. (2002), “Stochastic Claims Reserving in General Insurance,” ",[3614,3622,3623],{},"British Actuarial Journal",", 8(3), 443–518.",[2658,3626,3627],{},[3628,3629,3633],"a",{"href":3630,"rel":3631},"https:\u002F\u002Fforum.casact.org\u002Farticle\u002F122947-the-development-and-use-of-claim-life-cycle-model",[3632],"nofollow","CAS — The Development and Use of a Claim Life Cycle Model (2024)",[2658,3635,3636],{},[3628,3637,3640],{"href":3638,"rel":3639},"https:\u002F\u002Fforum.casact.org\u002Farticle\u002F131925-claim-counts-prediction-using-individual-data-with-resurv",[3632],"CAS — Claim Counts Prediction Using Individual Data with ReSurv (2025)",[2658,3642,3643],{},[3628,3644,3647],{"href":3645,"rel":3646},"https:\u002F\u002Farxiv.org\u002Fabs\u002F2504.09292",[3632],"Selukar — Stochastic Claims Reserving Using State Space Modeling (2025 preprint)",[2658,3649,3650],{},[3628,3651,3654],{"href":3652,"rel":3653},"https:\u002F\u002Farxiv.org\u002Fabs\u002F2602.15385",[3632],"Richman and Wüthrich — From Chain-Ladder to Individual Claims Reserving (2026 preprint)",{"title":10,"searchDepth":3656,"depth":3656,"links":3657},2,[3658,3659,3660,3661,3665,3666,3667,3668,3669,3670],{"id":1807,"depth":3656,"text":1808},{"id":1896,"depth":3656,"text":1897},{"id":2649,"depth":3656,"text":2650},{"id":2681,"depth":3656,"text":2682,"children":3662},[3663],{"id":2830,"depth":3664,"text":2831},3,{"id":3359,"depth":3656,"text":3360},{"id":3420,"depth":3656,"text":3421},{"id":3510,"depth":3656,"text":3511},{"id":3543,"depth":3656,"text":3544},{"id":3576,"depth":3656,"text":3577},{"id":3606,"depth":3656,"text":3607},"Distinguish process, parameter, and model uncertainty; backtest reserving assumptions.","md",{"sidebar":3674},{"order":3675},4,true,{"title":854,"description":3671},"9ZCiY7c5WRt8Cda0NTB6p8ZnK96ewNaVJrlTrH9MUuw",[3680,3682],{"title":850,"path":851,"stem":852,"description":3681,"children":-1},"Blend an expected-loss prior with observed maturity without letting early random payments dominate.",{"title":858,"path":859,"stem":860,"description":3683,"children":-1},"Select loss models from the insurance question, observation process, and tail—not from a distribution list.",1785754734368]