UQO Working Papers · WP41 · v1.1
Multi-Resolution Context in Intraday Probabilistic Return Forecasting: A Pre-Registered, Matched-Budget Measurement on 300 U.S. Instruments
CHRONOS-X: a Multi-Resolution Patch Transformer against matched baselines, 5 to 60 minutes ahead, 2018–2025
- Year
- 2026
- First release
- November 2026
- Latest revision
- November 2026
- Publication status
- Working paper
- Pages
- 82
- Figures
- 5
- Tables
- 74
- Equations
- 1
- References
- 69
- Words
- 41,913
Multi-resolution context lowers scaled CRPS by 0.081–0.214 % against a one-minute-only twin in 2024, a detectable but small effect that the untouched 2025 year does not confirm
A Multi-Resolution Patch Transformer, its matched one-minute-only twin and ten baselines sharing the same information set are scored with proper scoring rules and day-cluster inference on 234 million one-minute bars of 300 U.S. stocks and ETFs, 2018–2025. The findings are negative for the architecture: a minute-scale Student-t HAR-RV matches the neural models at five minutes and leads by 0.21–0.49 % from fifteen minutes on, no location forecast has economic content after costs, and a rank-4 copula adds nothing. The universe is close to a survivor sample of liquid instruments.
Abstract
Does multi-resolution context improve calibrated probabilistic forecasts of equity and ETF returns 5–60 minutes ahead? We test five pre-registered hypotheses with a Multi-Resolution Patch Transformer, its one-minute-only twin and ten baselines on 234 million one-minute bars of 300 instruments, with day-cluster inference. Over five seeds at a 12,000-step budget the contrast is −0.081 to −0.214 % of scaled CRPS, every seed pair negative: the pre-stated rule supports the hypothesis in 2024 at small magnitude; on 2025 these checkpoints keep the sign but fail it. A minute-scale Student-t HAR-RV matches the neural models at five minutes and leads by 0.21–0.49 % afterwards. Pooled training beats refitted baselines on unseen instruments only at five minutes, without penalty; no location forecast has economic content after costs; a rank-4 copula adds nothing. The full model gains 1.54 % and 0.30 % of scaled CRPS over a calibrated Student-t random walk at 5 and 60 minutes.
Key findings
−0.081 % to −0.214 %
scaled CRPS of the multi-resolution model against its one-minute-only twin, five to sixty minutes ahead, mean of five seeds at 12,000 steps on the 2024 development test; negative in every seed pair, pre-stated seed-aware rule met at 4 of 4 horizons, 1.5–3.4 times the seed half-band
−0.046 % to −0.116 %
the same contrast on the untouched 2025 year, scored once: the sign is kept at every horizon but the t across seeds stays below its 2.78 threshold, so the 2024 verdict does not replicate (a failure to detect, not a detected absence)
1.54 % / 0.30 %
gain of the full 12,000-step model in scaled CRPS over a Student-t random walk with scale and tail calibrated on 2023, at 5 and 60 minutes; against a Gaussian random walk the gain is 2.50–4.14 %, most of it the heavy tail and the scale
0.21–0.49 %
lead of a minute-scale HAR-RV with a kurtosis-matched Student-t over the neural models from fifteen minutes on; at five minutes the two differ by −0.07 % (Holm p = 0.148)
−0.20 % (5 min only)
zero-shot contrast with HAR-RV refitted on the 60 held-out instruments' own histories (Holm p = 7.66e−05), indistinguishable from fifteen minutes on; transfer itself costs nothing, for unseen liquid survivors
0 of 224 cells
net-positive cells of the economic test on pooled instruments in 2025 with a one-minute execution delay (5 in 2024 against about 11.2 expected false positives); neural directional accuracy is 0.499–0.502, linear and tree models reach 0.518 at five minutes
0.00025
mean off-diagonal correlation implied by the rank-4 Gaussian copula, numerically the identity: joint paths add nothing, while the model's own PIT scores show lag-one dependence of −0.069 and second-moment dependence of 0.095 that the copula cannot represent
Scientific contributions
- A pre-registered, matched measurement, not a new state of the art
- Five hypotheses written before any model was trained are tested at a matched architecture, information set and training budget; the result is a multi-resolution effect that is statistically detectable in 2024, negligible beside what the heavy tail and the scale contribute, and absent from the untouched 2025 year.
- Baselines that share the information set exactly
- A random walk with a trailing scale (Gaussian and calibrated Student-t), seasonal volatility, EWMA, minute-scale HAR-RV, GARCH(1,1)-t, ridge, elastic net, LightGBM, an MLP and a TCN with the same Student-t head, built under one consistent retransformation; from fifteen minutes on HAR-RV is both sharper and better calibrated than the sequence models.
- Inference that respects overlapping intraday windows
- The trading day is the cluster: a day-cluster t on the loss differential, checked by a Diebold–Mariano test on daily mean differentials, Holm adjustment inside named families, model confidence sets per horizon, and a five-seed replication of the central hypothesis because one seed cannot separate an architectural effect from training noise.
- Verdicts on transfer, regime conditioning and joint paths
- Pooled training transfers to unseen liquid instruments without penalty but beats refitted baselines only at five minutes; regime statistics worsen stress-day calibration once the control does not receive them elsewhere (hypothesis rejected, opposite sign); a rank-4 Gaussian copula adds nothing to independent sampling.
- Measurements the protocol produced unplanned
- The dependence of the model's PIT scores across future minutes, the share of the random-walk gain attributable to a calibrated heavy tail rather than to minute-level structure, and the behaviour of the nulls on the 66 instruments the availability filter removed.
Methodology
Methodology (5)
Multi-Resolution Patch Transformer
At each origin the model reads the last 390 one-minute bars, five days of 5-minute aggregates and twenty days of 30-minute aggregates, tokenised in patches into a shared pre-norm Transformer encoder; a direct decoder with sixty future-calendar queries emits a Student-t marginal per future minute. Inputs are strictly causal and scale-free, and the model carries no ticker identity. Small (3.5 million parameters) and Base (20.7 million) presets perform alike at the 12,000-step budget.
Matched-architecture control and seed study
The one-minute-only twin has the same width, depth and optimiser steps and 7.4 % fewer parameters; both twins are retrained with four further seeds at 12,000 steps and followed along a warm-restart learning curve that early stopping ended at 34,000 steps.
Proper scoring rules
CRPS, weighted interval score, quantile losses, coverage, PIT diagnostics, QLIKE and tail Brier scores for the cumulative return, and energy and variogram scores for joint paths; never price-level errors.
Unconfounded controls
Regime conditioning is tested on 24 stress days against a control that receives the regime statistics through no input; a second-stage rank-4 Gaussian copula is scored against independent sampling of the same marginals; the economic test covers the predictive median of all 7 location models with a one-minute execution delay.
Leakage gate
A test perturbs every bar after the origin and asserts that no input changes; a quarantined fixture that deliberately uses the next bar is rejected by the same test.
Research data
- FinData OS lakehouse: FirstRate Data one-minute bars, 2018–2025
- 233,958,776 exported one-minute bars of 300 U.S. stocks and ETFs over 2,011 sessions, of which 220,142,835 fall in regular hours, from the author's private lakehouse under a private-use licence; audited for timestamp conventions, session boundaries, early closes, daylight-saving time, missing minutes and splits. No raw bar leaves the compute node.
- Universe and held-out sets
- 300 instruments drawn at the end of 2017 from 2,147 candidates meeting point-in-time liquidity rules, stratified by asset class, dollar volume, volatility and sector, with 60 held out entirely. An availability filter of 80 % regular-hours coverage over 2018–2025 is computed ex post; the 66 candidates it removes although they pass on the training years are scored as a second held-out set.
- Splits and evaluation origins
- Training 2018–2022 (586,202 training origins), validation 2023, development test 2024 (986,468 origins over 251 sessions on 240 pooled instruments, every 15 minutes from 10:00; 250,322 on the held-out instruments) and an untouched final period 2025 (1,008,425 origins over 249 sessions), scored once per final model.
Reproducibility
- The repository contains the chronos_x package (data connector, calendar, quality checks, grids, models, training, scoring, inference, baselines), the numbered scripts and frozen configurations behind every result, the test suite, the universe manifests with their hashes and the provenance record of every API call.
- Every table, figure and number in the text is generated from the saved results; a synthetic cache in the exact data schema lets anyone run the entire pipeline without a licence.
- Raw bars, grids and per-origin returns never leave the compute node. The per-origin score arrays behind the inferential exhibits (171 files, 27.6 GB, no returns or bars) are held in a restricted archive available from the author under the FirstRate licence terms.
- Reproduction tolerances are measured: tables regenerated from the committed aggregates are byte-identical, the deterministic baselines reproduce exactly on a different chip, and a retrained neural model reproduces to within the five-seed band. All runs used Apple Silicon (MPS) without mixed precision.
Quality control
This paper went through a multi-stage quality control. The manuscript published here is the revised version; the record below reports the assessment before and after revision, what quality control changed and the limitations the paper states.
- Weighted total
- 58.467.2+8.8
- Decision
- Major revision
- Scientific integrity
- Pass
- Reproducibility
- R2Partially reproduced
- Maturity
- BOne revision cycle from submission
- Revised branch
- wp41_uqo @ d76e207
Assessment before and after revision
Before quality controlAfter revision
What quality control changed
Quality control had the baselines rebuilt under one consistent retransformation, replaced origin-level Diebold–Mariano statistics with day-cluster inference, and added a five-seed replication scored once on 2025. The paper now presents a small 2024 effect that 2025 does not confirm, withdraws the neural lead at five minutes, and describes its universe as filtered ex post.
- Multi-resolution hypothesis: a single-seed reading → five seeds, supported in 2024 at −0.081 to −0.214 % of scaled CRPS, not replicated on the untouched 2025 year
- Neural lead over HAR-RV at five minutes: attributed to the baseline construction → −0.07 % (Holm p = 0.148) under a consistent retransformation, with HAR-RV ahead by 0.21–0.49 % from fifteen minutes on
- Transfer hypothesis: one verdict → two clauses, beating refitted baselines supported only at five minutes, no transfer penalty supported
- Regime conditioning: confounded control → control receiving the statistics through no input; hypothesis rejected with the opposite sign
- Joint paths: the copula is numerically the identity and the claim that future minutes are conditionally independent is withdrawn; PIT dependence exists and is unmodelled
- Universe: point-in-time selection → disclosed ex-post availability filter, with the 66 excluded instruments scored as a second held-out set
Limitations stated in the paper
- The universe is close to a survivor sample: the 80 % coverage filter reads the evaluation years and delisted instruments are under-represented, so the results describe liquid instruments that survived the window.
- One training budget and few seeds: the verdict on multi-resolution context holds at a matched 12,000-step budget, ablations at 4,000 steps are single-seed numbers, and the 2025 non-replication is a failure to detect rather than a detected absence.
- HAR-RV, ridge, elastic net and LightGBM are fitted once on 2018–2022 and frozen; pretrained time-series foundation models were not evaluated.
- The joint-path verdict is specific to a rank-4 Gaussian copula with constant correlation; regular hours only, bars as the only input, and no quote data for the cost assumptions.
Research artifacts
Version history
| Version | Date | Description | File |
|---|---|---|---|
| v1.1current | November 2026 | Revised after quality control | PDF · 82 p. |