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1\section{Conclusion}2\label{sec:conclusion}34We asked whether a compact, transferable, multi-resolution Transformer can learn minute-level structure that5improves calibrated forecasts of the next 5 to 60 minutes, and we tested the question against matched baselines,6with proper scoring rules, on \num{234} million one-minute bars of 300 U.S. stocks and ETFs, with sixty unseen7instruments and an untouched year. The answers are precise. Minute-level history improves distributional forecasts8over a trailing-scale random walk by about four percent of CRPS at every horizon, for every model, and the9improvement is a volatility improvement: no model has directional skill or economic content after costs. The10sequence models win at five minutes; a heterogeneous autoregression of realised variance with a Student-$t$11matched to residual kurtosis wins, and is better calibrated, from fifteen minutes on. The multi-resolution context12that defines the architecture adds at most a tenth of a percent in sample and nothing out of sample; model size does13not matter between 3.5 and 20.7 million parameters; regime conditioning adds nothing; coherent paths add nothing14because the next hour's minute returns are conditionally independent given the recent history. Pooled training15transfers to unseen instruments without penalty. And a model that reads only the trailing volatility and the clock16recovers nine tenths of what the full model knows.1718The central empirical statement of this paper is therefore not that a Transformer predicts financial markets. It is19that, for liquid U.S. instruments at the one-minute scale and with bars as the only input, the universal intraday20representation worth learning is small: a scale, a clock, a heavy tail, and a few tenths of a percent of residual21structure that sequence models and variance regressions extract in different proportions at different horizons.22Two directions follow from the limitations rather than from the results: order-book or quote data, which the23literature suggests carry the microstructure signal that bars lack, and the delisted instruments that this24universe could not include. The package, the protocol and the null results are released so that both can be25tested the same way.26
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