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--- current
+++ proposed
@@ -1,58 +1,69 @@
-
 \label{sec:introduction}
 
-Every minute of a U.S. trading day leaves behind one bar---open, high, low, close, volume---for each of several
-thousand instruments. Foundation models for time series promise to learn ``universal'' representations from such
-streams and to forecast any series zero-shot \citep{ansari2024chronos, das2024timesfm}, and a growing literature
-applies deep sequence models to intraday prices \citep{sirignano2019universal, zhang2019deeplob, kolm2023deep}.
-Whether a compact model that reads several resolutions of minute-level history improves \emph{calibrated}
-forecasts of the next hour, relative to the simplest volatility models an econometrician would write down, is
-however an empirical question that is rarely posed with matched information sets, proper scoring rules and
-dependence-aware inference. This paper poses it narrowly and answers it on data.
+Every minute of a U.S. trading day leaves behind one bar (open, high, low, close, volume) for each of several thousand instruments. Two literatures offer different accounts of what such a stream contains. Foundation models for time series promise to learn ``universal'' representations from it and to forecast any series zero-shot \citep{ansari2024chronos, das2024timesfm}, and a growing body of work applies deep sequence models to intraday prices \citep{sirignano2019universal, zhang2019deeplob, kolm2023deep}. Financial econometrics instead describes intraday returns as a deterministic periodic component combined with persistent conditional heteroskedasticity \citep{andersen1997intraday}. In that tradition, simple heterogeneous autoregressions forecast volatility well \citep{corsi2009simple}, and little beats a GARCH(1,1) once the comparison is fair \citep{hansen2005forecast}. The two accounts make different predictions about what a model that reads minute-level history can learn.
 
-We build CHRONOS-X, a research package around a Multi-Resolution Patch Transformer (\MRPT{}). At a decision time
-inside the regular session the model reads the last 390 completed one-minute bars, the last five days of completed
-5-minute aggregates and the last twenty days of 30-minute aggregates, each tokenised in patches with gated feature
-projections, resolution and temporal-gap embeddings; a shared pre-norm Transformer encoder and a direct decoder
-with sixty future-calendar queries emit a Student-$t$ marginal for each of the next sixty minute returns, and a
-second-stage low-rank Gaussian copula turns the marginals into coherent sample paths. All inputs are strictly
-causal, scale-free (divided by a trailing volatility computed at the origin) and masked where the source has no
-bar; the model carries no ticker identity. Five hypotheses were written before any tuning: multi-resolution history
-helps at equal parameters (H1), pooled training transfers to unseen instruments (H2), history-only regime
-conditioning improves calibration under stress (H3), coherent paths beat independent marginals on path scores
-(H4), and---exploratory---the forecasts carry economic content after costs (H5).
+We ask whether a compact model that reads several resolutions of that history produces better \emph{calibrated} forecasts of the next hour than the simplest volatility models an econometrician would write down. The question is empirical. It is rarely posed with matched information sets, proper scoring rules and dependence-aware inference. This paper poses it narrowly and answers it on data.
 
-The data are 300 U.S. stocks and ETFs selected point-in-time at the end of 2017, stratified by asset class, dollar
-volume, volatility and sector, with sixty instruments held out entirely; \num{234} million one-minute bars from a
-private FirstRate Data lakehouse (FinData~OS) over 2018--2025, audited for timestamp conventions, session
-boundaries, early closes, daylight-saving time, missing minutes, splits and dividends. Training uses 2018--2022,
-validation 2023, the development test 2024 and an untouched final period 2025; evaluation uses \num{986468}
-origins in 2024 alone. Baselines share the information set exactly: random walk, seasonal volatility, EWMA,
-HAR-RV at the minute scale, GARCH(1,1)-$t$, ridge, elastic net, LightGBM, an MLP and a TCN with the same Student-$t$
-head, and the one-minute-only \MRPT{} as the equal-parameter patch-Transformer control. Scores are the CRPS, the
-weighted interval score, quantile losses, coverage, PIT diagnostics, QLIKE, tail Brier scores and, for paths,
-energy and variogram scores; inference clusters by trading day and uses overlap-aware HAC Diebold--Mariano
-statistics with multiple-testing control, because a million overlapping windows are not a million observations.
+The yardstick matters as much as the model. On a one-minute grid the random walk is a formidable point forecaster, and a model can look impressive on price-level errors while learning nothing \citep{cont2001empirical}. We therefore train and score on returns rather than prices. Full predictive distributions of the next 5, 15, 30 and 60 minutes are judged by strictly proper scoring rules \citep{matheson1976scoring, gneiting2007strictly}.
 
-The answer is precise and mostly negative for the architecture, and informative about the data. Every model beats
-the random walk by 3.5--4.9\,\% in CRPS at every horizon: the minute stream carries real information about the
-dispersion of the next hour, and none about its direction (directional accuracy 0.50, median magnitudes below one
-basis point, no economic content after costs; H5 rejected). The sequence models are the best at five minutes;
-from fifteen minutes on, a heterogeneous autoregression of realised variance with a kurtosis-matched Student-$t$
-is both sharper and better calibrated than any neural model, by 0.3--0.7\,\%. The multi-resolution context that
-defines \MRPT{} improves on the one-minute-only twin by at most a tenth of a percent---statistically detectable on a
-million origins, economically nil (H1 rejected in substance); a 20.7-million-parameter model does no better than a
-3.5-million one. The remaining hypotheses are examined in the same spirit in Sections~\ref{sec:results}
-and~\ref{sec:ablations}: zero-shot transfer to the sixty held-out instruments, regime conditioning on stress days,
-the copula paths against independent sampling, and the untouched 2025 period.
+\paragraph{What the design can and cannot identify.}
+The comparisons are designed to isolate one factor at a time. All baselines receive exactly the information set of the main model, so score differences reflect how each method uses the same inputs, not access to different data. An equal-parameter one-minute-only twin isolates the contribution of the coarser context. Sixty instruments that are never seen in training isolate cross-sectional transfer. An untouched final year guards against selection on the development test. Because a million overlapping windows are not a million observations, inference clusters by trading day and uses overlap-aware HAC Diebold--Mariano statistics \citep{diebold1995comparing, harvey1997testing, newey1987simple}, with Holm and Benjamini--Hochberg adjustments \citep{holm1979simple, benjamini1995controlling}.
 
-The contribution is therefore a replicable measurement rather than a new state of the art: a documented data
-pipeline and evaluation protocol for minute-level probabilistic forecasting under a private-use license, a compact
-model that is competitive without being superior, and a set of null results that a reader can reproduce from the
-released code and synthetic fixtures. Section~\ref{sec:hypotheses} states the hypotheses, Section~\ref{sec:literature}
-places them in the literature, Sections~\ref{sec:data}--\ref{sec:design} describe data, model and design,
-Sections~\ref{sec:results}--\ref{sec:ablations} report the results, and Sections~\ref{sec:limitations}--\ref{sec:conclusion}
-discuss limitations, reproducibility and what the evidence does and does not say.
+These are statements about the relative predictive accuracy of estimated forecasting methods in this sample. They are not causal statements about price formation. They are conditional on four features of the setting:
+\begin{itemize}
+\item a universe of liquid U.S. instruments with at least 80\,\% regular-hours coverage, close to a survivor sample;
+\item bars as the only input, with no quote or order-book data;
+\item the 2018--2025 period;
+\item for the economic test, assumed rather than observed trading costs.
+\end{itemize}
+With roughly a million origins per year, statistical detectability and economic relevance diverge. We report both and base our conclusions on the latter.
 
+\paragraph{Model.}
+We build CHRONOS-X, a research package around a Multi-Resolution Patch Transformer (\MRPT{}). At a decision time inside the regular session, the model reads three streams: the last 390 completed one-minute bars, the last five days of completed 5-minute aggregates and the last twenty days of 30-minute aggregates. Each stream is tokenised in patches with gated feature projections and with resolution and temporal-gap embeddings. A shared pre-norm Transformer encoder feeds a direct decoder with sixty future-calendar queries, which emits a Student-$t$ marginal for each of the next sixty minute returns. A second-stage low-rank Gaussian copula turns the marginals into coherent sample paths. All inputs are strictly causal, scale-free (divided by a trailing volatility computed at the origin) and masked where the source has no bar. The model carries no ticker identity.
 
+\paragraph{Hypotheses.}
+Before any tuning we wrote down five hypotheses, each with a pre-specified test (Section~\ref{sec:hypotheses}):
+\begin{itemize}
+\item[(H1)] multi-resolution history helps at equal parameters;
+\item[(H2)] pooled training transfers to unseen instruments;
+\item[(H3)] history-only regime conditioning improves calibration under stress;
+\item[(H4)] coherent paths beat independent marginals on path scores;
+\item[(H5)] the forecasts carry economic content after costs. This hypothesis is exploratory.
+\end{itemize}
 
+\paragraph{Data and comparisons.}
+The data are 300 U.S. stocks and ETFs selected point-in-time at the end of 2017. Selection is stratified by asset class, dollar volume, volatility and sector, and sixty instruments are held out entirely. The sample comprises \num{234} million one-minute bars over 2018--2025 from a private FirstRate Data lakehouse (FinData~OS). The bars are audited for timestamp conventions, session boundaries, early closes, daylight-saving time, missing minutes, splits and dividends. We train on 2018--2022 and validate on 2023. The development test is 2024, which alone supplies \num{986468} evaluation origins. The final period, 2025, is left untouched.
+
+The baselines fall into four groups:
+\begin{itemize}
+\item econometric volatility models: random walk, seasonal volatility, EWMA, HAR-RV at the minute scale and GARCH(1,1)-$t$;
+\item regularised and tree-based regressions: ridge, elastic net and LightGBM;
+\item neural benchmarks: an MLP and a TCN with the same Student-$t$ head;
+\item the one-minute-only \MRPT{}, which serves as the equal-parameter control.
+\end{itemize}
+Forecasts are scored by the CRPS, the weighted interval score, quantile losses, coverage, PIT diagnostics, QLIKE and tail Brier scores. Paths are additionally scored by energy and variogram scores.
+
+\paragraph{Findings.}
+The answer is mostly negative for the architecture and informative about the data.
+\begin{enumerate}
+\item \textbf{Dispersion, not direction.} Every model beats the trailing-scale random walk by 3.5--4.9\,\% in CRPS at every horizon. The improvement is a volatility improvement. Directional accuracy is 0.50 and median magnitudes are below one basis point. We find no economic content after the assumed costs, so H5 is rejected, with the caveat that costs are assumptions.
+\item \textbf{The horizon determines the winner.} The sequence models are best at five minutes. From fifteen minutes on, a heterogeneous autoregression of realised variance with a kurtosis-matched Student-$t$ is both sharper and better calibrated than any neural model, by 0.3--0.7\,\%.
+\item \textbf{Neither coarser context nor size matters economically.} The multi-resolution context improves on the one-minute-only twin by at most a tenth of a percent in the development test and by nothing in the untouched period. The in-sample gain is statistically detectable on \num{986468} origins over 252 days, but it is economically nil, so H1 is rejected in substance. A 20.7-million-parameter model does no better than a 3.5-million-parameter one.
+\item \textbf{Regime conditioning and joint paths add nothing.} Regime conditioning does not improve on the unconditioned model (H3). Copula paths do not improve on independent sampling of the same marginals (H4). This is consistent with the model finding no exploitable dependence among the next sixty minute returns once the recent history is conditioned on.
+\item \textbf{Transfer holds, but what transfers is small.} Pooled training transfers to the sixty unseen instruments without penalty relative to pooled instruments. Yet a model that reads only the trailing volatility and the clock recovers nine tenths of the full model's skill.
+\end{enumerate}
+
+Within the scope set out above, these results locate the information in minute bars. For liquid U.S. instruments with bars as the only input, the predictable part of the next hour is largely a scale, a clock and a heavy tail. What remains is a small residual that sequence models and variance regressions extract in different proportions at different horizons.
+
+\paragraph{Contribution.}
+The paper does not claim a new state of the art. Its contribution is a replicable measurement in three parts:
+\begin{itemize}
+\item a documented data pipeline and evaluation protocol for minute-level probabilistic forecasting under a private-use license, with matched information sets, point-in-time selection, held-out instruments, an untouched year and dependence-aware inference;
+\item a compact model that is competitive without being superior;
+\item a set of null results that a reader can reproduce from the released code and synthetic fixtures.
+\end{itemize}
+
+The results speak to three strands of work. First, \citet{sirignano2019universal} show that a single neural model trained on pooled order-book data transfers across stocks. With bars alone we also find transfer, but what transfers is mostly volatility. Second, the results carry to the intraday distributional setting the evidence that simple linear and variance-regression baselines are hard to beat \citep{zeng2023transformers, hansen2005forecast}. Third, they bear on the promise of zero-shot foundation models \citep{ansari2024chronos, das2024timesfm}, although these models are not evaluated here, for reasons given in Section~\ref{sec:design}.
+
+\paragraph{Outline.}
+Section~\ref{sec:hypotheses} states the hypotheses and their tests, and Section~\ref{sec:literature} places them in the literature. Sections~\ref{sec:data}--\ref{sec:design} describe the data, the model and the experimental design. Sections~\ref{sec:results}--\ref{sec:ablations} report the results and the ablations. Sections~\ref{sec:limitations}--\ref{sec:conclusion} discuss limitations and reproducibility, and set out what the evidence does and does not say.