1\section{Data, market coverage and realized variance measurement}\label{sec:data}23\paragraph{Source and licence.} All prices come from FinData OS, the author's private lakehouse of FirstRate Data4one-minute and daily bars, accessed through its documented REST interface (OpenAPI 3.1, \texttt{findata.spboucher.ai/api/v1}).5The audit script of the replication package records, for every instrument, the dataset identifiers, the dataset6version numbers (snapshots are immutable and versioned on the server), the SHA-256 of every exported file, the row counts and7the licence text; the vendor licence permits private research use and the publication of derived statistics but not the8redistribution of bars, so the package ships code, manifests, checksums, aggregate forecasts and losses, and a synthetic9fixture rather than the raw data (Appendix~\ref{app:provenance}).1011\paragraph{Universe.} The pre-registered universe (frozen before any test-period loss was computed) holds12\NInstruments{} instruments in five classes: fifteen liquid ETFs (SPY, QQQ, IWM, DIA, EEM, EFA, XLF, XLE, TLT, IEF, HYG, LQD,13GLD, SLV, USO), ten large-capitalization stocks (AAPL, MSFT, AMZN, NVDA, JPM, XOM, JNJ, PG, KO, WMT), nine continuous14futures (ES, NQ, CL, NG, GC, SI, HG, ZN, ZC), six spot exchange rates (EURUSD, USDJPY, GBPUSD, AUDUSD, USDCAD, USDCHF)15and two cryptocurrencies (BTC, ETH). Daily histories start in 2000 (ETFs and stocks, except later listings),162008 (futures), 2010 (FX), 2013 (BTC) and 2016 (ETH) and end on 2026-10-30 (Figure~\ref{fig:coverage}). All instruments are17alive at the end of the sample: the universe therefore describes liquid, surviving benchmarks, a selection we disclose rather18than correct, since the question is about model comparison on exactly such series rather than about the cross-section.1920\paragraph{Sessions and calendars.} Vendor timestamps are bar-open times in UTC. We define, per asset class, the session21window over which both the daily return and the realized measures are computed: for ETFs and stocks the XNYS trading day2209:30--16:00 ET including the closing print, with official early closes (13:00 ET) taken from the exchange calendar and the23overnight segment from the previous close to the open; for futures the CME trading day from 18:00 ET of the previous24calendar day to 17:00 ET, with the 17:00--18:00 maintenance break treated as the ``overnight'' segment; for FX the2517:00--17:00 ET New York day, and for crypto the UTC calendar day. This matters because the vendor's own session date for26futures and FX is an ET calendar day, which would split the overnight part of a trading day across two dates; the audit shows271{,}380 (ES), 1{,}440 (EURUSD) and 1{,}440 (BTC) one-minute bars on a full session and 391 for SPY in regular hours.28Zero-volume minutes are absent from the source and are never filled.2930\paragraph{Returns.} Daily returns are $r_t=100\log(C_t/C_{t-1})$ in percent. For ETFs and stocks, $C_t$ is the vendor's31split- and dividend-adjusted daily close (a price-return series with dividends reinvested at the ex-date, verified on the32AAPL 4:1 split of 2020-08-31 and the SPY ex-dividend date of 2024-03-15), and the overnight return $r^{on}_t=100\log(O_t/C_{t-1})$33uses the same series. For futures the continuous series is the vendor's ratio-back-adjusted splice, whose log returns are34free of roll jumps by construction (the ratio between adjusted and unadjusted closes is piecewise constant across the35March~2024 ES roll in the audit); the roll dates themselves are fixed by the vendor and not documented per contract, so36realized measures on roll days span two contracts, a limitation we note. FX and crypto returns are built from the last37one-minute bar of each session; FX bars are mid quotes aggregated from four money-center banks, and crypto bars are an38exchange aggregate.3940\paragraph{Realized measures.} Within each session we compute, from one-minute closes, the one-minute realized variance,41the five-minute calendar-time realized variance (previous-tick sampling on a grid anchored at the window start), its42subsampled version averaged over the five one-minute grid offsets \citep{zhang2005tale}, bipower variation43\citep{barndorff2004power}, realized semivariances \citep{barndorff2010measuring} and the median realized variance, all in44percent$^2$. A session is \emph{valid} for realized measures when it contains at least 60\% of the instrument's modal45number of one-minute bars (391 or 211 for equities by calendar; the modal count for the other classes, which ranges from46780 for corn futures to 1{,}440 for FX and crypto). The overnight component is kept separate and added back when the model47target is the close-to-close variance: the primary proxy is48$y_t=\RV^{5m,ss}_t+(r^{on}_t)^2$, so that intraday realized variance is never presented as a measure of the full-day49variance \citep{hansen2005realized}. Over valid sessions, the ratio of the mean primary proxy to the mean squared daily50return lies between 0.93 and 1.17 for every ETF, stock, futures and FX instrument---the signature of an approximately51unbiased full-day proxy. Cryptocurrencies are the exception: the vendor's one-minute aggregate exhibits severe cross-venue52bounce before 2022 (the one-minute realized variance of BTC exceeds the squared daily return by one to two orders of53magnitude in 2013--2019 and by a factor of 1.3--3 in 2020--2021), so crypto realized measures are declared invalid before542022-01-01 and crypto forecasts are scored on 2022--2026 only; this decision was taken on the audit, before the protocol55freeze. Secondary proxies for sensitivity analysis are the five-minute, one-minute, bipower and median variants with the56overnight term, the squared daily return, and the whole-day scaling of \citet{hansen2005realized} with a scaling constant57estimated on the estimation window at each origin.5859\paragraph{Regime variables.} Regimes are defined without look-ahead: terciles of the 22-day trailing realized variance of60each instrument at the forecast origin, with thresholds fixed on the validation period; the sign of the previous day's61return; and three calendar episodes fixed in the protocol (COVID, 2020-02-20 to 2020-06-30; the 2022 rate shock; the April--May622025 tariff shock). The VIX is retained for descriptive purposes only.6364\begin{figure}[tp]\centering65\includegraphics[width=\textwidth]{figures/fig_coverage.pdf}66\caption{Sample coverage of the 42 instruments (daily panels). The number at the right of each bar is the share of sessions67with valid realized measures (percent). Dashed lines mark the start of the validation (2012) and test (2016) periods.}\label{fig:coverage}68\end{figure}69\begin{figure}[tp]\centering70\includegraphics[width=\textwidth]{figures/fig_volseries.pdf}71\caption{Twenty-two-day moving averages of annualized full-day realized volatility for one instrument per class72(SPY, CL, EURUSD, BTC). Shaded bands are the pre-registered calendar episodes.}\label{fig:volseries}73\end{figure}74