1\section{Experimental design}2\label{sec:design}34\subsection{Baselines with a matched information set}5Every baseline sees exactly the completed bars available at the origin and is tuned on the training and validation6periods only. Non-neural: a random walk with zero drift and a Gaussian scale from the trailing root-mean-square7one-minute return (the reference throughout); a seasonal-volatility model that sums the past-20-session profile of8squared returns over the future slots, level-adjusted by the trailing 30-minute realised variance; an EWMA9($\lambda=0.97$ per minute, Student-$t$ with $\nu=5$); HAR-RV at the minute scale (log realised variance over the10next $H$ minutes on log trailing 30-minute, one-day and five-day realised variances and time of day, by OLS, with11$\nu$ from the kurtosis of standardised residuals); GARCH(1,1)-$t$ on 5-minute training returns per instrument12with the analytic variance term structure \citep{bollerslev1986generalized, hansen2005forecast}; ridge, elastic13net \citep{zou2005regularization} and LightGBM \citep{ke2017lightgbm} on nineteen origin features, predicting the14scaled cumulative return and the log scaled realised variance, assembled into a Student-$t$. Neural, on the15one-minute branch only: an MLP on the last sixty bars and a dilated temporal convolutional network16\citep{bai2018tcn}, both with the same Student-$t$ head and loss as the main model, and the one-minute-only17\MRPT{} itself, which is the equal-parameter patch-Transformer control \citep{nie2023patchtst}. Pretrained foundation18models \citep{ansari2024chronos, das2024timesfm} are not evaluated: their weights were not available offline on the19compute node, their tokenisers assume a single real-valued series without missingness masks, and their terms were20not reviewed within this project; iTransformer \citep{liu2024itransformer} is not implemented. EGARCH forecasts21beyond one step require simulation and were too slow for the number of evaluation origins. Table~\ref{tab:baselines}22lists the specifications.2324\subsection{Scores}25The primary scores are the sample-based $\CRPS$ of the cumulative return at each horizon (256 draws, energy-form26estimator), the weighted interval score \citep{bracher2021evaluating} over eleven central intervals, the mean27pinball loss at seven quantile levels, empirical coverage of the 50/80/95\,\% central intervals, PIT dispersion and28Kolmogorov--Smirnov statistics \citep{gneiting2007probabilistic}, and sharpness (90\,\% interval width). For29parametric forecasts the closed-form Student-$t$ $\CRPS$ \citep{jordan2019evaluating} and the log score are also30computed; the log score is reported only where comparable. Secondary: absolute and squared errors of the31cumulative return, QLIKE on the realised variance with positive forecasts \citep{patton2011volatility}, the Brier32score of the tail event, directional accuracy against the zero-drift reference, and compute cost. Path-level33scores (energy and variogram, $p=0.5$; \citealp{scheuerer2015variogram}) and $\CRPS$ of maximum drawdown and34realised volatility are computed for the Stage-B comparison. We report scaled $\CRPS$ ($\CRPS/(\sigma_t\sqrt{H})$)35to make instruments and horizons comparable; unscaled values are in the appendix.3637\subsection{Inference}38All intervals are trading-day cluster bootstraps (all instruments and origins of one session form one cluster,39500--2000 resamples). Pairwise comparisons use Diebold--Mariano statistics on the loss differential ordered40chronologically with a Bartlett-kernel HAC variance whose lag equals the overlap of consecutive evaluation windows41times the number of instruments, so that overlapping origins and cross-sectional dependence are both absorbed42\citep{diebold1995comparing, newey1987simple}; Holm and Benjamini--Hochberg adjustments are applied across horizons43and models. Subgroup results (asset class, dollar-volume and volatility tercile, sector, time of day, year,44stress days defined by the top decile of cross-sectional $\sigma_t$) use the same machinery. Economic evaluation45(Hypothesis~\ref{h5}) trades the sign of the predictive median only when its magnitude exceeds an assumed46round-trip cost, executes at the next bar with a one-minute delay, and reports gross and net returns per trade with47day-clustered intervals under several cost assumptions; it is a sensitivity analysis, not a strategy.4849\subsection{Ablations and falsification}50At the Small scale on the development test: resolutions (1m only, 1m+5m, 1m+5m+30m, equal parameters), fusion51(shared vs cross-attention), head (Gaussian vs Student-$t$), regime (none, statistics, learned), feature sets52(returns only, OHLCV without relative volume, time only), ticker embedding, three seeds, shuffled minute order53inside the one-minute window at training and evaluation (a falsification: if the model only uses marginal statistics,54shuffling should not hurt), the copula head against independent sampling, and model size (Small, Base). Zero-shot55evaluation on the sixty held-out instruments and the untouched 2025 period complete the protocol.56