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1\section{Related work}2\label{sec:literature}34\paragraph{Intraday volatility and probabilistic evaluation.}5The classical description of intraday returns combines a deterministic periodic component with persistent6conditional heteroskedasticity \citep{andersen1997intraday, bollerslev1986generalized, nelson1991conditional,7engle2001garch}. Realised measures built from intraday returns turned volatility into an (almost) observable8quantity and showed that simple heterogeneous autoregressions forecast it well \citep{andersen2003modeling,9barndorff2002econometric, corsi2009simple, bollerslev2016exploiting}; \citet{hansen2005forecast} found that little10beats a GARCH(1,1) once the comparison is fair, and \citet{patton2011volatility} showed that only a few loss11functions (QLIKE, MSE) rank variance forecasts consistently under noisy proxies. These results frame our baselines:12seasonal profiles, EWMA, HAR-RV, GARCH-$t$. For distributional forecasts we rely on the theory of proper scoring rules13\citep{matheson1976scoring, gneiting2007strictly}, the calibration--sharpness paradigm and PIT diagnostics14\citep{gneiting2007probabilistic}, the weighted interval score \citep{bracher2021evaluating}, closed-form CRPS for15the Student-$t$ family as implemented in \texttt{scoringRules} \citep{jordan2019evaluating, taillardat2016calibrated},16threshold-weighted variants \citep{gneiting2011comparing}, and multivariate energy and variogram scores17\citep{scheuerer2015variogram}. Inference on loss differentials follows \citet{diebold1995comparing},18\citet{harvey1997testing}, \citet{giacomini2006tests} and \citet{hansen2011model}.1920\paragraph{Deep learning for financial microstructure and time series.}21\citet{sirignano2019universal} documented that a single neural model trained on pooled limit-order-book data transfers22across stocks---the closest antecedent of our ``universal'' question, although with order-book inputs that we do not23have. DeepLOB \citep{zhang2019deeplob} and deep order-flow imbalance models \citep{kolm2023deep} also use quote-level24data. With bars only, the relevant architectures are the generic sequence models: temporal convolutions25\citep{bai2018tcn}, DeepAR-style autoregressive likelihood models \citep{salinas2020deepar}, N-BEATS26\citep{oreshkin2020nbeats}, and Transformer variants \citep{vaswani2017attention, wen2023transformers}. Patch27tokenisation \citep{nie2023patchtst} and variable-as-token inversion \citep{liu2024itransformer} are the28Transformer designs we adapt; \citet{zeng2023transformers} is the reminder that linear baselines are competitive.29Pretrained foundation models for time series \citep{ansari2024chronos, das2024timesfm} promise zero-shot30forecasting but assume a single real-valued series without missingness masks or multi-resolution context; we discuss31in Section~\ref{sec:design} why they are not evaluated here. Diffusion-based multivariate forecasters32\citep{rasul2021autoregressive} are a possible Stage-B alternative that we do not pursue given their compute cost.33Surveys of financial machine learning \citep{gu2020empirical, kelly2023financial, lim2021time} stress the34evaluation pitfalls we try to avoid: overlapping samples, survivorship, look-ahead, and multiple testing35\citep{lopez2018advances, bailey2014deflated}.3637\paragraph{Dependence across horizons.}38Coherent joint paths require a dependence model. Copulas separate marginals from dependence39\citep{sklar1959, patton2006modelling}; our Stage~B uses a Gaussian copula with a low-rank-plus-diagonal40correlation over the sixty future minutes, trained on the probability-integral transforms of the observed41targets with the marginals frozen.42
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