\section{Experimental design}
\label{sec:design}

\subsection{Baselines with a matched information set}
Every baseline sees exactly the completed bars available at the origin and is tuned on the training and validation
periods only. Non-neural: a random walk with zero drift and a Gaussian scale from the trailing root-mean-square
one-minute return (the reference throughout); a seasonal-volatility model that sums the past-20-session profile of
squared returns over the future slots, level-adjusted by the trailing 30-minute realised variance; an EWMA
($\lambda=0.97$ per minute, Student-$t$ with $\nu=5$); HAR-RV at the minute scale (log realised variance over the
next $H$ minutes on log trailing 30-minute, one-day and five-day realised variances and time of day, by OLS, with
$\nu$ from the kurtosis of standardised residuals); GARCH(1,1)-$t$ on 5-minute training returns per instrument
with the analytic variance term structure \citep{bollerslev1986generalized, hansen2005forecast}; ridge, elastic
net \citep{zou2005regularization} and LightGBM \citep{ke2017lightgbm} on nineteen origin features, predicting the
scaled cumulative return and the log scaled realised variance, assembled into a Student-$t$. Neural, on the
one-minute branch only: an MLP on the last sixty bars and a dilated temporal convolutional network
\citep{bai2018tcn}, both with the same Student-$t$ head and loss as the main model, and the one-minute-only
\MRPT{} itself, which is the equal-parameter patch-Transformer control \citep{nie2023patchtst}. Pretrained foundation
models \citep{ansari2024chronos, das2024timesfm} are not evaluated: their weights were not available offline on the
compute node, their tokenisers assume a single real-valued series without missingness masks, and their terms were
not reviewed within this project; iTransformer \citep{liu2024itransformer} is not implemented. EGARCH forecasts
beyond one step require simulation and were too slow for the number of evaluation origins. Table~\ref{tab:baselines}
lists the specifications.

\subsection{Scores}
The primary scores are the sample-based $\CRPS$ of the cumulative return at each horizon (256 draws, energy-form
estimator), the weighted interval score \citep{bracher2021evaluating} over eleven central intervals, the mean
pinball loss at seven quantile levels, empirical coverage of the 50/80/95\,\% central intervals, PIT dispersion and
Kolmogorov--Smirnov statistics \citep{gneiting2007probabilistic}, and sharpness (90\,\% interval width). For
parametric forecasts the closed-form Student-$t$ $\CRPS$ \citep{jordan2019evaluating} and the log score are also
computed; the log score is reported only where comparable. Secondary: absolute and squared errors of the
cumulative return, QLIKE on the realised variance with positive forecasts \citep{patton2011volatility}, the Brier
score of the tail event, directional accuracy against the zero-drift reference, and compute cost. Path-level
scores (energy and variogram, $p=0.5$; \citealp{scheuerer2015variogram}) and $\CRPS$ of maximum drawdown and
realised volatility are computed for the Stage-B comparison. We report scaled $\CRPS$ ($\CRPS/(\sigma_t\sqrt{H})$)
to make instruments and horizons comparable; unscaled values are in the appendix.

\subsection{Inference}
All intervals are trading-day cluster bootstraps (all instruments and origins of one session form one cluster,
500--2000 resamples). Pairwise comparisons use Diebold--Mariano statistics on the loss differential ordered
chronologically with a Bartlett-kernel HAC variance whose lag equals the overlap of consecutive evaluation windows
times the number of instruments, so that overlapping origins and cross-sectional dependence are both absorbed
\citep{diebold1995comparing, newey1987simple}; Holm and Benjamini--Hochberg adjustments are applied across horizons
and models. Subgroup results (asset class, dollar-volume and volatility tercile, sector, time of day, year,
stress days defined by the top decile of cross-sectional $\sigma_t$) use the same machinery. Economic evaluation
(Hypothesis~\ref{h5}) trades the sign of the predictive median only when its magnitude exceeds an assumed
round-trip cost, executes at the next bar with a one-minute delay, and reports gross and net returns per trade with
day-clustered intervals under several cost assumptions; it is a sensitivity analysis, not a strategy.

\subsection{Ablations and falsification}
At the Small scale on the development test: resolutions (1m only, 1m+5m, 1m+5m+30m, equal parameters), fusion
(shared vs cross-attention), head (Gaussian vs Student-$t$), regime (none, statistics, learned), feature sets
(returns only, OHLCV without relative volume, time only), ticker embedding, three seeds, shuffled minute order
inside the one-minute window at training and evaluation (a falsification: if the model only uses marginal statistics,
shuffling should not hurt), the copula head against independent sampling, and model size (Small, Base). Zero-shot
evaluation on the sixty held-out instruments and the untouched 2025 period complete the protocol.