spb/wp46_uqo

1\section{Introduction}\label{sec:intro}23Forty-four years after \citet{engle1982autoregressive} and thirty-eight after \citet{bollerslev1986generalized}, the4GARCH(1,1) model remains the default description of daily return volatility in textbooks, risk systems and applied5research, while the literature that followed produced dozens of alternatives designed to repair one or another of its6shortcomings---asymmetry, long memory, regime shifts, fat and skewed tails, the information in intraday data. The question7of whether these alternatives forecast better was asked most directly by \citet{hansen2005forecast}, who compared 3308specifications on two series and found nothing that beat GARCH(1,1) on exchange-rate data, while asymmetric models won on9a single stock. Two decades later the answer is still assembled from studies that differ in assets, horizons, proxies,10losses, estimation windows and software, and that rarely report what happens when a model fails to converge or how much it11costs to run. This paper revisits the question with a single, pre-registered design.1213We benchmark \NModels{} conditional volatility architectures---every canonical member of the GARCH family that has a vetted14implementation in version-locked software, the realized-measure models that use intraday information, a score-driven15comparator and six multivariate covariance models---on \NInstruments{} instruments spanning equity ETFs, large-capitalization16stocks, Treasury, energy, metal and agricultural futures, major exchange rates and two cryptocurrencies, with one-minute data17from 2000 to 2026. Forecasts of the variance of the next 1, 5 and 22 trading days are produced at every origin from18rolling re-estimations and scored with the QLIKE loss against a full-day realized variance proxy; inference uses19Diebold--Mariano tests with HAC variances, the model confidence set, the superior predictive ability test and a block20bootstrap that resamples dates jointly across instruments. The design separates three information tiers so that models21are never compared on different information sets without saying so, pre-defines market regimes without look-ahead, and22treats estimation failures, inadmissible estimates and computing time as outcomes rather than nuisances. The protocol, with23six falsifiable hypotheses, was frozen in the repository before any test-period loss was computed; the test period runs24from 2016 to October~2026 and includes the COVID crash, the 2022 rate shock and the 2025 tariff episode.2526The contributions are fourfold. First, a definition-faithful taxonomy: each architecture is implemented from its original27equations, with its admissibility domain enforced by the optimizer, its own multi-step recursion, and a model card that28records the cross-package verification---because ``TGARCH'' means different things in different packages and the29differences matter. Second, the benchmark itself, whose breadth across assets, horizons and tiers is, to our knowledge,30without precedent for the GARCH family. Third, a complexity--accuracy--robustness frontier that prices accuracy gains in31failure rates and compute, and reports results both on the common-success sample and on each model's operational sample.32Fourth, an open replication package with configurations, manifests, checksums, tests, aggregate forecasts and losses, and a33synthetic fixture, since the raw data cannot be redistributed.3435\paragraph{Findings.}36\input{sections/intro_findings}3738The rest of the paper is organized as follows. Section~\ref{sec:literature} reviews the literature; Section~\ref{sec:taxonomy}39sets out the taxonomy; Section~\ref{sec:data} describes the data and the realized measures; Section~\ref{sec:design} the40design; Sections~\ref{sec:daily}--\ref{sec:frontier} report the daily-information, realized-measure, tail-risk and41multivariate, heterogeneity and frontier results; Section~\ref{sec:conclusion} concludes. The appendices give the complete42formulas, provenance, verification and additional tables.43