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1# Owner's brief (verbatim, received 2026-11-09) — authoritative text for WP4623CLAUDE.md — UQO Research WP46: The Great GARCH Benchmark45Mission and non-negotiable objective67You are the lead quantitative research engineering agent for WP46 in the Université du Québec en Outaouais (UQO) research program. Build a publication-grade, fully reproducible empirical and methodological assessment of conditional volatility models, from ARCH through modern GARCH-family, realized-measure, regime-switching, multivariate, and adjacent conditional-volatility alternatives.89Working title: Four Decades of Conditional Volatility Modeling: A Comprehensive Empirical Benchmark Across Assets, Frequencies, and Market Regimes.1011Core question: Across asset classes, forecast horizons, market regimes and information sets, when—if ever—do more complex conditional volatility models reliably outperform parsimonious GARCH(1,1), and is any gain worth the numerical and computational cost?1213Author/project: Simon-Pierre Boucher, UQO research, WP46. Write the manuscript, code comments, exhibits and technical documentation in polished academic English. Do not claim results before running analyses. The desired target is a strong econometrics/empirical finance journal submission, not an unverified survey.1415Treat this file as operating instructions. Never fabricate data, estimates, references, API fields, p-values, confidence intervals, performance figures, sample periods, or evidence of novelty. Clearly distinguish planned work from completed work.1617First actions: reconnaissance before implementation1819Inspect the actual UQO research repository, its CLAUDE.md, coding conventions, existing WP folders, data governance, bibliographies and CI. Do not overwrite unrelated work. Find the exact WP naming pattern and create WP46 consistently; if no convention exists use wp46_garch_benchmark/.2021Discover how to access Findata at https://findata.spboucher.ai (user may refer to it as indata.spboucher.ai). Confirm the correct hostname and official API contract. Do not guess endpoints or authenticate against speculative hosts. Inspect public docs and the repo's existing configured integration; request a credential or API documentation only if unavailable. Never log tokens or place keys in source files.2223Audit the true data inventory: tickers/instrument types, exchanges, timezone, timestamp precision, adjusted prices, bid/ask/trades/OHLCV, minute and five-minute history, daily history, corporate actions, futures rolls, licensing, missingness, API limits, coverage start/end and export permissions. Write docs/findata_audit.md with evidence and unresolved questions. A reference to an instrument below is a proposal, not proof of coverage.2425Search and audit current methodological literature through an explicit cutoff date. Build a verified bibliography with DOIs and source links. Identify closely related large-scale benchmarks, including Hansen and Lunde (2005), and explain incremental contribution honestly.2627Prepare docs/preregistered_protocol.md before inspecting out-of-sample performance. Freeze the primary universe, date ranges, metrics, model selection policy and multiplicity corrections. Keep exploratory work labeled exploratory.2829Produce docs/feasibility_report.md and a small execution pilot. Then proceed in independently validated phases. Never fake successful runs.3031Scientific contributions to pursue3233C1 — Taxonomy and mathematical reference3435Create a traceable ontology of conditional volatility models: defining equations, conditional mean, innovation law, parameter constraints, positivity, stationarity and moment conditions, leverage/asymmetry, estimation objective, forecast recursion, nested relationships, identifiable failure modes and original references. Preserve differences between similarly named variants across papers and packages; never silently equate TGARCH definitions, for example.3637C2 — Multi-asset out-of-sample benchmark3839Use identical pre-registered information sets, rolling origins, forecast targets and loss definitions within a comparison tier. Comparisons across tiers must explain the additional data available to realized-measure models. Evaluate statistical significance and uncertainty—not just rank tables.4041C3 — Complexity–accuracy–robustness frontier4243Estimate whether incremental gains survive transaction-relevant/risk-specific evaluation, computation, convergence screening and market-regime changes. Report Pareto frontiers rather than a single arbitrary aggregate ranking.4445C4 — Open benchmark and replication package4647Publish reproducible configurations, instrument/data manifests, code, tests, tables and provenance, subject to data licensing. If raw data cannot legally be redistributed, publish scripts, schemas, checksums, synthetic fixtures and access instructions instead.4849Formal boundaries and taxonomy5051Inventory all materially distinct canonical GARCH architectures feasible from the literature; do not claim to implement literally every variant ever published. Maintain a model_registry.yaml with references, precise mathematical definition, software implementation, implementation status, estimation method, admissibility rules, feature requirements and validation evidence. Different parameter orders and innovation distributions are specifications, not separate architectures.5253Candidate model families (verify nomenclature and primary citations before inclusion):5455Classical: ARCH(q), GARCH(p,q), IGARCH, GARCH-M, GARCH-X; useful baseline constant variance/EWMA and historical volatility.5657Asymmetric and power: EGARCH, GJR-GARCH, threshold/TGARCH with unambiguous definition, APARCH, AVGARCH, NGARCH/NAGARCH, QGARCH, selected flexible formulations.5859Fractional persistence: FIGARCH, FIEGARCH, FIAPARCH, HYGARCH, with careful numerical approximations and stationarity distinctions.6061Components and regime shifts: component GARCH, Markov-switching GARCH, smooth-transition GARCH and GARCH-MIDAS (only if the explanatory frequency and feature availability justify it).6263Realized-measure and high-frequency: Realized GARCH, Realized EGARCH, HEAVY, realized-input GARCH-X; verify exact joint measurement equations and observation timing.6465Multivariate: CCC, DCC, asymmetric DCC, BEKK, GO-GARCH and selected scalable alternatives. Evaluate covariance/correlation forecasts separately, not as if they were univariate variance competitors.6667Adjacent comparators, explicitly labeled non-GARCH where applicable: GAS/score-driven volatility, HAR-RV/HAR-X, realized volatility benchmark, stochastic-volatility variants if feasible; reserve modern ML models for a clearly designated extension, not for redefining the GARCH family.6869For feasible architectures, test Gaussian, standardized Student-t, skewed Student-t and GED/generalized-error innovations only where formally valid and correctly parameterized. Prefer a preregistered small grid of orders (e.g., 1,1 and selected 2,1/1,2) over combinatorial overfitting. Record unsupported model–distribution combinations as unsupported, not failed performance.7071Create one detailed model_cards/<slug>.md per architecture: seminal citation, formula in LaTeX, assumptions, interpretation, optimizer, standard errors, forecast formula, implementation links, unit tests, known limitations, computational footprint and literature expectations.7273Data and measurement specification7475Plan cross-asset coverage including liquid equity ETFs (SPY/QQQ/IWM), large-cap single stocks, Treasury instruments, energy, precious metals, foreign exchange and BTC/ETH if and only if Findata can supply them at adequate quality. Substitute verified liquid proxies, and disclose changes. Minimum viable pilot: at least one equity ETF, one individual equity, and one commodity or FX instrument if covered. Preferred final sample: approximately 20–40 well-documented assets, not a blind target count.7677Implement:7879Exchange calendars, trading sessions, market holidays, half-days, daylight saving transitions, quote/trade consolidation and timestamp alignment. Distinguish 24/7 crypto calendars.8081Split/dividend-adjusted total-return or price-return conventions; survivorship and selection bias documentation.8283Contract-continuous futures with explicit roll convention, back-adjustment implications and no spurious roll returns. Do not mix spot and futures series without labeling.8485Point-in-time data availability and strict as-of joins; prevent look-ahead for fundamentals, implied measures, macro regressors and realized measures.8687Daily log returns with explicit percentage versus decimal scaling. Intraday log returns at 1- and 5-minute frequency where valid.8889Realized variance RV_t = sum_j r_{t,j}^2, realized semivariances, bipower variation and robust/noise-aware realized measures when data suffice. Treat overnight variance separately; avoid claiming intraday RV equals full 24-hour integrated variance.9091Missing ticks, sparse assets, zero prices, bid–ask bounce, stale quotes, outliers and corporate action anomalies; predefine exclusions and sensitivity checks.9293Immutable raw snapshots where permitted, checksums, provenance records, rate-limit-aware retrieval, retries with backoff and resumable ingestion.9495All timestamps, returns and variance forecasts must have explicit units and horizon conventions. Match one-day-ahead daily conditional variance to a same-horizon variance proxy, not to volatility in standard-deviation units.9697Experimental protocol9899Information tiers100101Tier A (daily only): common daily return information set, standard GARCH and daily alternatives.102103Tier B (intraday measures): models using lagged realized measures; compare against strong daily baselines but disclose unequal information set. Optionally provide a matched-information comparison where daily baselines gain appropriate realized covariates.104105Tier C (multivariate): covariance and correlation forecasts on fixed asset baskets with separate scoring rules.106107Backtesting108109Separate chronologically ordered training, tuning/validation and untouched test periods, with dates selected after data audit but before model ranking.110111Rolling and expanding estimation windows; rolling forecasts at horizons 1, 5 and 22 trading days as viable. Explain overlapping target dependence and use HAC/block bootstrap where needed.112113Re-estimation cadence, optimizer budgets, stopping tolerances and available compute fixed within comparable groups. No future data in volatility filters or recursive forecasts.114115For multi-step forecasts, follow exact model-specific conditional expectation or clearly justified simulation; do not extrapolate one-step predictions naively.116117Parameter selection only in training/validation, never via final test losses. Publish tuning grids and seeds.118119Forecast persistence baselines, GARCH(1,1), asymmetric GARCH and HAR-RV when realized information is available.120121Primary and secondary accuracy122123Primary: QLIKE for strictly positive variance forecasts and a documented positive variance proxy: QLIKE(y,h) = y/h - log(y/h) - 1 for y>0,h>0; for proxy zeros use the equivalent loss log(h)+y/h, whose omitted y-only terms do not affect forecast rankings. Record exact implementation and numerical handling.124125Secondary: MSE of variance forecasts, MAE, volatility-scale losses as sensitivity analyses, log predictive score where a full conditional density is supplied, and calibration/Mincer–Zarnowitz checks.126127Evaluate imperfect volatility-proxy sensitivity (different intraday sampling intervals, semivariances, robust RV, squared daily returns as noisy diagnostic). Cite Patton (2011), acknowledging proxy assumptions.128129Tail risk: 1% and 5% conditional VaR and relevant expected shortfall evaluations using statistically appropriate unconditional/conditional coverage and joint VaR–ES scoring/backtests. Respect innovation distribution assumptions.130131Risk covariance: use multivariate loss/portfolio risk diagnostics only for valid positive-definite covariance forecasts.132133Inferential rigor134135Apply Diebold–Mariano-style comparisons with horizon/serial-correlation-appropriate variance estimators, Hansen's SPA/White-style multiple-comparison controls where relevant, and Model Confidence Set (Hansen–Lunde–Nason) with justified stationary/block bootstrap settings. Report confidence intervals, adjusted p-values, effect sizes, MCS memberships and sample sizes. Distinguish statistical significance from economic materiality. Cluster or bootstrap across assets/time where cross-sectional dependence matters. No global leaderboard without discussing dependence and multiplicity.136137Regime analysis138139Predefine market stress classification independently of future outcomes and avoid endogenous arbitrary crisis windows. Report tranquil/stressed markets, COVID-type episodes if covered, equity drawdowns, volatility quantiles, positive/negative return shocks and asset classes; sensitivity to regime definitions is mandatory.140141Computation, failures and fairness142143Measure median runtime, total CPU time, peak resident memory, iteration counts, optimization failures, non-positive variance, nonstationary or nonadmissible estimates and forecast coverage. Define a common fallback policy: bounded retry sequence, alternative starting values, optimizer diagnostics; never replace a failed complex forecast with a baseline's output without explicit flagging. Report both accuracy on common-success sample and failure-adjusted operational performance to avoid survivorship bias. Distinguish analytic, quasi-MLE, simulation and Bayesian compute budgets.144145Mathematics and software verification146147Implement numerical gradients/Hessians with stable constrained transforms, e.g. log/softplus for positive parameters as appropriate, and exact stationarity domains; do not assume alpha+beta<1 universally applies to EGARCH, IGARCH or fractional models. Parameter inference must respect innovation moments, identification and nonregular boundaries. Reconcile probability density conventions for skewed distributions.148149Before accepting an implementation:150151Unit tests of recursion, likelihood, admissibility, multi-step forecasts and seeded simulation recovery.152153Numerical gradient checks where practical; log-likelihood comparison against at least one authoritative library or original paper replication on a shared synthetic data fixture.154155Edge cases: constant returns, extreme shocks, nearly integrated persistence, tiny positive variance, short samples and missingness.156157Monte Carlo calibration tests across distributions and parameter regimes.158159Diagnostic plots and residual tests; no silent overflow, underflow or discarded warnings.160161Independent check of publication references and model equations.162163Use established vetted libraries (e.g. Python arch, R rugarch, rmgarch, and appropriate realized/regime-specialist packages) where they faithfully implement the cited model; version-lock and cross-check them. Custom implementations must justify necessity and pass stronger simulation and replication tests. Pin environments and document any cross-language interfaces.164165Research repository structure166167Adapt to the actual repository conventions rather than forcibly recreating existing structure:168169wp46_garch_benchmark/170 CLAUDE.md171 README.md172 pyproject.toml / renv.lock (as appropriate)173 configs/174 study.yaml175 instruments.yaml176 model_registry.yaml177 forecast_protocol.yaml178 docs/179 findata_audit.md180 literature_matrix.md181 preregistered_protocol.md182 feasibility_report.md183 methodology_decisions.md184 data_dictionary.md185 replication_guide.md186 data/187 README.md188 manifests/189 raw/ # ignored; licensed/private190 interim/ # ignored191 processed/ # ignored unless permitted192 synthetic/193 src/wp46/194 findata_client/195 calendars/196 preprocessing/197 realized_measures/198 models/199 estimation/200 forecasts/201 scoring/202 inference/203 diagnostics/204 reporting/205 tests/206 unit/207 integration/208 simulation/209 replication/210 model_cards/211 experiments/212 results/213 manifests/214 metrics/215 figures/216 tables/217 logs/218 paper/219 main.tex220 sections/221 appendices/222 figures/223 tables/224 references.bib225 scripts/226 audit_findata.py227 run_pilot.py228 run_benchmark.py229 build_paper.py230231Use stable forecast keys (dataset_version, instrument_id, model_id, specification_id, origin_timestamp, horizon, estimation_window, information_tier, code_revision) and record training/test cutoffs. Save machine-readable run manifests with git SHA, package versions, hardware, random seeds and data hashes. Large data and secrets stay out of git.232233Publication-quality exhibits234235Create compelling, precise, journal-ready vector graphics and LaTeX tables; use accessible color palettes, consistent typography and no misleading truncated axes:236237Historical timeline and ontology of ARCH–GARCH architectures.238239Model equations/taxonomy table and parameter/estimation comparison.240241Coverage map and sample descriptive statistics.242243Volatility time series with documented crises and realized proxies.244245Cross-asset × model-family heatmaps of out-of-sample QLIKE improvement versus GARCH(1,1).246247Model Confidence Set membership matrices and uncertainty annotations.248249Horizon-dependent forecast performance and calibration.250251VaR/ES calibration and exceedance diagnostics.252253Complexity versus incremental accuracy Pareto charts, with failure rate and compute cost.254255Regime-specific rankings and sensitivity analyses.256257Forecast failure/convergence diagnostics and robust versus fragile models.258259Reproducibility flow and audited dataset lineage.260261Avoid displaying a large undifferentiated ranking across incomparable information tiers or metrics. Put detailed full-model tables in appendices and public machine-readable supplements.262263Paper structure264265Introduction: motivation, hypotheses, contributions, and relation to past broad benchmarks.266267Related literature: ARCH/GARCH taxonomy, realized volatility, model selection and empirical forecasting comparisons.268269Unified model taxonomy and mathematical framework.270271Data, market coverage and realized variance measurement.272273Experimental design, estimators, forecasting and inference.274275Main daily-information comparison.276277High-frequency/realized-measure comparison.278279Tail risk and multivariate extensions.280281Cross-market, regime and horizon heterogeneity.282283Complexity–accuracy–robustness frontier and practical implications.284285Limitations, reproducibility and conclusion.286287Appendices: complete formulas/regularity conditions, model cards, instrument provenance, simulation verification, extra losses, sensitivity tables, multiple testing, and implementation details.288289Draft the paper in LaTeX with latexmk, biblatex/BibTeX consistent with repository convention, all tables and figures generated by source code, references checked against primary sources. The paper must compile cleanly and cite every nontrivial methodological claim. Do not optimize for length at the expense of substantive rigor; keep the main paper readable and publish detailed technical appendices.290291Required phases and acceptance gates292293Phase 0 — Inventory and literature. Repository inspection, Findata access audit, literature matrix, novelty assessment. Gate: evidence-backed viable data/instrument list; no invented endpoints.294295Phase 1 — Preregistered protocol. Freeze primary design, model taxonomy, metrics, date splits and robustness analysis. Gate: protocol document and model registry reviewed before test-set evaluation.296297Phase 2 — Trusted data and pilot. Ingest reproducibly; inspect samples; implement GARCH(1,1), EGARCH, GJR-GARCH, APARCH and HAR-RV if data permit. Gate: leakage tests, exact units, simulated recovery and full 1-day OOS pilot.298299Phase 3 — Broad univariate benchmark. Complete feasible canonical classes and innovation distributions. Gate: model cards, convergence accounting, tests and replicable summaries for every accepted implementation.300301Phase 4 — Realized and multivariate tiers. Implement specialist models with separate fair comparisons. Gate: verified forecast-target alignment and positive-definite covariance checks.302303Phase 5 — Statistical inference. Multiplicity, MCS, block bootstrap, tail risk, regime and sensitivity studies. Gate: no interpretation without uncertainty and common-sample validation.304305Phase 6 — Manuscript and artifacts. Fully compiled paper, technical appendices, repository README, replication scripts, tables, figures and limitations. Gate: a fresh-environment smoke reproduction and an independent audit checklist.306307At each gate, maintain progress.md with completed commands, timestamps, test outcomes, blocked dependencies, scientifically important decisions and next actions. If blocked, produce an actionable issue list rather than pretending the phase is complete.308309Mandatory integrity rules310311No use of the final test set for selecting the model grid, optimizer, best regime definitions or loss function.312313No comparison of different forecast horizons, proxies, return scaling or information sets without explicit reconciliation.314315No cherry-picking assets, regimes, failures or plots to make a favored model win.316317No reliance on AIC/BIC or in-sample likelihood alone to claim forecast superiority.318319No claiming high-frequency RV is an unbiased latent variance proxy without documenting assumptions and sensitivity.320321No reference included without bibliographic verification; no fabricated URLs or DOIs.322323No unsupported blanket conclusion like "GARCH is obsolete" or "neural models always win."324325No private keys, raw licensed data or sensitive logs in commits or manuscript artifacts.326327No automatic external publication, repository push, submission or expensive cloud spend without explicit authorization.328329Keep a clearly marked distinction between substantive scientific findings and exploratory observations.330331Seminal literature to verify and expand332333Engle (1982), autoregressive conditional heteroskedasticity.334Bollerslev (1986), generalized ARCH.335Nelson (1991), EGARCH.336Glosten, Jagannathan and Runkle (1993), asymmetric volatility relation.337Ding, Granger and Engle (1993), long-memory volatility/APARCH family.338Baillie, Bollerslev and Mikkelsen (1996), FIGARCH.339Engle (2002), dynamic conditional correlation.340Hansen and Lunde (2005), A Forecast Comparison of Volatility Models: Does Anything Beat a GARCH(1,1)?, Journal of Applied Econometrics, DOI 10.1002/jae.800.341Shephard and Sheppard (2010), Realising the Future: Forecasting with High-Frequency-Based Volatility (HEAVY) Models, Journal of Applied Econometrics, DOI 10.1002/jae.1158.342Patton (2011), Volatility Forecast Comparison Using Imperfect Volatility Proxies, Journal of Econometrics.343Hansen, Lunde and Nason (2011), The Model Confidence Set, Econometrica, DOI 10.3982/ECTA5771.344Hansen, Huang and Shek (2012), Realized GARCH: A Joint Model of Returns and Realized Measures of Volatility, Journal of Applied Econometrics.345346Verify bibliographic details and actively extend through the current literature cutoff; this list is a starting point, not an exhaustive or final review.347348Start now349350Begin with repository reconnaissance, a documented Findata audit and a rigorous literature/novelty map. Then write the preregistered protocol and implement a validated pilot before scaling. Show the user a concise Phase 0–2 progress report with concrete evidence, open risks and the exact commands necessary to reproduce. Proceed autonomously within permitted local research operations but stop and ask for missing credentials, material dataset-selection decisions, unexpected paid compute, or external publication permissions.351