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1\section{Introduction}2\label{sec:introduction}34Every minute of a U.S. trading day leaves behind one bar---open, high, low, close, volume---for each of several5thousand instruments. Foundation models for time series promise to learn ``universal'' representations from such6streams and to forecast any series zero-shot \citep{ansari2024chronos, das2024timesfm}, and a growing literature7applies deep sequence models to intraday prices \citep{sirignano2019universal, zhang2019deeplob, kolm2023deep}.8Whether a compact model that reads several resolutions of minute-level history improves \emph{calibrated}9forecasts of the next hour, relative to the simplest volatility models an econometrician would write down, is10however an empirical question that is rarely posed with matched information sets, proper scoring rules and11dependence-aware inference. This paper poses it narrowly and answers it on data.1213We build CHRONOS-X, a research package around a Multi-Resolution Patch Transformer (\MRPT{}). At a decision time14inside the regular session the model reads the last 390 completed one-minute bars, the last five days of completed155-minute aggregates and the last twenty days of 30-minute aggregates, each tokenised in patches with gated feature16projections, resolution and temporal-gap embeddings; a shared pre-norm Transformer encoder and a direct decoder17with sixty future-calendar queries emit a Student-$t$ marginal for each of the next sixty minute returns, and a18second-stage low-rank Gaussian copula turns the marginals into coherent sample paths. All inputs are strictly19causal, scale-free (divided by a trailing volatility computed at the origin) and masked where the source has no20bar; the model carries no ticker identity. Five hypotheses were written before any tuning: multi-resolution history21helps at equal parameters (H1), pooled training transfers to unseen instruments (H2), history-only regime22conditioning improves calibration under stress (H3), coherent paths beat independent marginals on path scores23(H4), and---exploratory---the forecasts carry economic content after costs (H5).2425The data are 300 U.S. stocks and ETFs selected point-in-time at the end of 2017, stratified by asset class, dollar26volume, volatility and sector, with sixty instruments held out entirely; \num{234} million one-minute bars from a27private FirstRate Data lakehouse (FinData~OS) over 2018--2025, audited for timestamp conventions, session28boundaries, early closes, daylight-saving time, missing minutes, splits and dividends. Training uses 2018--2022,29validation 2023, the development test 2024 and an untouched final period 2025; evaluation uses \num{986468}30origins in 2024 alone. Baselines share the information set exactly: random walk, seasonal volatility, EWMA,31HAR-RV at the minute scale, GARCH(1,1)-$t$, ridge, elastic net, LightGBM, an MLP and a TCN with the same Student-$t$32head, and the one-minute-only \MRPT{} as the equal-parameter patch-Transformer control. Scores are the CRPS, the33weighted interval score, quantile losses, coverage, PIT diagnostics, QLIKE, tail Brier scores and, for paths,34energy and variogram scores; inference clusters by trading day and uses overlap-aware HAC Diebold--Mariano35statistics with multiple-testing control, because a million overlapping windows are not a million observations.3637The answer is precise and mostly negative for the architecture, and informative about the data. Every model beats38the random walk by 3.5--4.9\,\% in CRPS at every horizon: the minute stream carries real information about the39dispersion of the next hour, and none about its direction (directional accuracy 0.50, median magnitudes below one40basis point, no economic content after costs; H5 rejected). The sequence models are the best at five minutes;41from fifteen minutes on, a heterogeneous autoregression of realised variance with a kurtosis-matched Student-$t$42is both sharper and better calibrated than any neural model, by 0.3--0.7\,\%. The multi-resolution context that43defines \MRPT{} improves on the one-minute-only twin by at most a tenth of a percent---statistically detectable on a44million origins, economically nil (H1 rejected in substance); a 20.7-million-parameter model does no better than a453.5-million one. The remaining hypotheses are examined in the same spirit in Sections~\ref{sec:results}46and~\ref{sec:ablations}: zero-shot transfer to the sixty held-out instruments, regime conditioning on stress days,47the copula paths against independent sampling, and the untouched 2025 period.4849The contribution is therefore a replicable measurement rather than a new state of the art: a documented data50pipeline and evaluation protocol for minute-level probabilistic forecasting under a private-use license, a compact51model that is competitive without being superior, and a set of null results that a reader can reproduce from the52released code and synthetic fixtures. Section~\ref{sec:hypotheses} states the hypotheses, Section~\ref{sec:literature}53places them in the literature, Sections~\ref{sec:data}--\ref{sec:design} describe data, model and design,54Sections~\ref{sec:results}--\ref{sec:ablations} report the results, and Sections~\ref{sec:limitations}--\ref{sec:conclusion}55discuss limitations, reproducibility and what the evidence does and does not say.56
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