Source-linked AI summary
A Compact Selective State-Space Model for Cross-Sectional Stock Return Ranking from Raw Intraday Bars
Mingju Chen, Enze Zhang
TL;DR
Raw financial inputs vary in scale and can encourage models to exploit price levels or rewarded styles rather than stock-specific dynamics. STRATA addresses these issues with a learnable multi-scale residual stem and staggered selective state-space backbone, evaluated after style residualisation. On a held-out year, it leads six parameter-matched sequence baselines on all four reported metrics, while the executable first-price spread is indistinguishable from zero.
Problem
Raw price series are non-stationary and differ greatly across stocks, while raw rank correlations can reflect rewarded style exposures instead of stock-specific predictive information.
Method
STRATA maps raw five-minute bars to cross-sectional rankings using a five-branch residual stem, four staggered selective state-space blocks, and style-residualised evaluation against eight price-volume factors.
Results
STRATA leads six parameter-matched sequence baselines on all four metrics; its rank IC is 0.0728, and every day-level paired rank-IC comparison has p < 0.001.
Takeaways & Limitations
The results support raw-input sequence modeling with STRATA’s bundled design under style-residualised predictive evaluation, while its lead is not explained by greater exposure to the controls.
Takeaways & Limitations
The eight-factor style set omits valuation, profitability, growth, leverage, and industry controls, so residualised metrics are upper bounds under stricter risk adjustment.
Abstract
from arXiv · showhide
We present STRATA (Staggered-Timescale Residual Architecture), a 244,633-parameter sequence model that maps five trading days of raw five-minute bar and order-book data directly to a next-day cross-sectional return ranking, with no hand-crafted features. The raw-input setting has a structural obstacle: price series are non-stationary and differ across stocks by orders of magnitude, so a model easily latches onto price level rather than dynamics. STRATA addresses it with a stem of five branches--four learnable causal depthwise convolutions whose effective kernels are initialised to sum to zero, plus one cross-field linear contrast--followed by four selective state-space blocks whose decay biases are staggered across the stack and a four-path readout. Because a score that merely tilts toward common style factors scores well on raw rank correlations, every model's scores are residualised against eight price-volume style factors before any metric is computed. Trained on four years of data covering roughly one thousand mid-capitalisation Chinese A-shares and evaluated once on a held-out year, STRATA reaches a style-residualised rank information coefficient of 0.0728 (information ratio 1.128, signal long-short Sharpe 12.85), ahead of six parameter-matched sequence baselines on all four reported metrics; on rank IC the day-level paired gap against every baseline is significant at p < 0.001, and among the arms competitive on predictive power STRATA's scores are the least explained by the controls. The close-to-close target opens before the score exists: measured instead from the first executable price, the decile spread is indistinguishable from zero, while the ordering of the seven architectures is unchanged and STRATA's margin widens.
1 Introduction
STRATA targets raw-input cross-sectional return ranking while addressing price-level heterogeneity and style confounding. Its multi-scale residual stem, staggered state-space backbone, and controlled evaluation protocol define the proposed approach.
- Motivation: Raw-input models must overcome price levels that vary widely across stocks and drift over time, despite being nearly uninformative about next-day returns.
- Motivation: Raw rank correlations can reflect rewarded style exposures rather than stock-specific predictive information.
- Approach: STRATA evaluates raw fields under restricted preprocessing and residualises every score against eight price-volume style factors before computing metrics.
- Architecture: Its stem uses four zero-sum-initialised causal depthwise convolution branches plus a cross-field contrast to learn level-robust, multi-scale residual representations.
- Architecture: Four selective state-space blocks use staggered decay biases, while a four-path readout summarises sequences across effective horizons.
- Evaluation: STRATA is compared with six parameter-matched sequence architectures under shared data, training, and evaluation conditions.
2 Related Work
Related work frames STRATA as a raw-bar alternative to engineered quantitative signals and as a combination of established sequence-modeling and learnable decomposition ideas. Its distinctive position is a causal, learnable residual front-end paired with sequence architectures for cross-sectional ranking.
- Cross-sectional return prediction: Quantitative equity prediction commonly uses formulaic price-volume expressions or engineered feature tables, while learned factor models retain factor structure with latent variables.
- Sequence architectures: Recurrent networks, causal convolutions, attention, linear maps, and selective state-space models are established sequence-modeling alternatives for time-series data.
- Learnable decomposition front-ends: Zero-sum convolution kernels originated as high-pass filters in image forensics, and STRATA transfers the idea to causal raw price sequences.
- Learnable decomposition front-ends: STRATA’s stem is causal, depthwise, fully learnable, and multi-scale, producing deviations from each channel’s recent history without hand-designed decomposition.
3 Model
STRATA maps five days of raw five-minute fields to a cross-sectional stock score through a causal, multi-timescale architecture. Its protocol uses minimal shared preprocessing and a close-to-close next-day target, while acknowledging that part of this target precedes score availability.
- Problem setup: The input window contains five complete trading days, ending with the signal day’s final five-minute bar, and uses 25 raw fields per bar.The default tensor has T = 240 bars and F = 25 fields.
- Problem setup: The score is produced only after the final signal-day bar, while the adjusted close-to-close target includes an overnight segment before the score exists.Thus the target avoids look-ahead but is not an exactly replicable trading return.
- Preprocessing: Preprocessing applies fixed unit scaling, log(1 + x) to price and size fields, training-split standardisation, and post-standardisation zero-filling for missing entries.Inputs remain unadjusted; corporate-action adjustment enters only through the label.
- Self-referential stem: The five-branch stem combines four trainable depthwise temporal residual branches with one within-time cross-field linear contrast.The residual branches use causal convolutions; the cross-field branch is the only field-mixing operation.
- Self-referential stem: The multi-scale residual branches use receptive fields of 3, 12, and 48 bars, initially forming zero-sum high-pass kernels while remaining learnable after training.These correspond to 15, 60, and 240 minutes, with the largest spanning one trading session.
4 Experiments
The experiments evaluate STRATA and six parameter-matched sequence baselines on roughly one thousand Chinese A-shares using style-residualised metrics and a held-out 2024 test year. STRATA leads on all four metrics, with day-level rank-IC gaps significant against every baseline, while comparisons also expose temporal-structure effects and evaluation limitations.
- Data and splits: 2024 test-year evaluation covers 241 trading days of mid-capitalisation Chinese A-shares, with point-in-time membership and 48 five-minute bars per stock-day.The panel contains close to one thousand names per day and uses 25 raw fields per bar.
- Evaluation protocol: All reported metrics use scores residualised against eight causally computed price-volume style factors after non-finite filtering, symmetric winsorisation, and cross-sectional standardisation.The eight controls include size, nonlinear size, liquidity, realised volatility, momentum, beta, short-term reversal, and intraday volatility.
- Baselines: Six standard sequence encoders are compared with parameter counts within ±5% of STRATA’s 244,633 parameters under shared data, optimisation, epoch, and evaluation settings.The baselines are MLP, LSTM, GRU, TCN, Transformer, and Mamba; only complete encoder-plus-readout designs are compared.
- Main results: 0.0728 rank IC, 12.85 signal LS Sharpe, and 1.030 stress IC IR place STRATA ahead of the strongest baseline on each corresponding reported metric.STRATA’s rank IC is 14.9% above GRU’s 0.0634, its Sharpe is 17.7% above GRU’s 10.92, and its stress IC IR is 13.4% above GRU’s 0.909.
- Statistical comparisons: p < 0.001 day-level paired tests reject equality in rank IC against every baseline, whereas IC IR differences from GRU, Mamba, and LSTM are not significant across three seeds.The day-level analysis uses 241 paired daily cross-sectional ICs and Newey–West standard errors; the three-seed inference is comparatively coarse.
- Architectural comparisons: 0.0728 versus Mamba’s 0.0615 indicates an 18.5% gap for their bundled stem, decay-initialisation, and readout differences, while MLP’s 0.0485 trails every sequence model.The contribution of the stem and readout separately remains unisolated by ablation, and the shared recipe was developed with STRATA rather than tuned per architecture.
4.6 Style exposure of model scores
STRATA combines the highest residualised predictive rank IC with lower style-explained score variance than the sequence baselines. However, executable-session analysis shows that close-to-close long-short performance is not deployable from the signal timestamp, and the style controls remain incomplete.
- Style exposure and predictive performance: Residualisation reduces STRATA’s mean daily rank IC from 0.0893 to 0.0728 and raises IC IR from 0.919 to 1.128.The standard deviation also falls from 0.0973 to 0.0649; the same direction holds for every arm.
- Style exposure and predictive performance: 0.073 residualised rank IC: STRATA combines the highest predictive score with style R2 of 0.172, below all five sequence baselines at 0.180–0.220.MLP has lower style R2, 0.157, but is also the weakest predictor with residualised rank IC 0.049.
- Scope and deployment boundaries: The style analysis removes only eight price–volume controls, so omitted industry, valuation, profitability, growth and leverage exposures may explain additional score variation.The reported residualised metrics should therefore be read as upper bounds relative to stricter risk controls.
- Timing decomposition: The executable-session rank IC remains positive at 0.0215, but the decile spread reverses because stocks gapping down rebound more than stocks gapping up continue.STRATA’s top and bottom deciles both earn positive session returns, +6.0 and +7.5 bp per day respectively.
- Timing decomposition: −1.6 bp per day: STRATA’s executable-session long-short spread is indistinguishable from zero despite preserving the seven-arm ordering.Its Newey–West statistic is −0.37, while the weakest arms are significantly negative.
- Scope and deployment boundaries: The evidence covers one national equity market, one-day horizon and five-minute bars, while shared rather than per-arm tuning could narrow the reported gaps.A deployable strategy would additionally require executable returns, transaction costs, slippage, market-impact and borrowing constraints.
5 Conclusion
STRATA is a compact raw-input sequence model that outperforms six parameter-matched alternatives on style-residualised held-out-year metrics. The comparison supports model ranking, not a deployable trading-strategy interpretation.
- Conclusion: 244,633 parameters: STRATA maps raw five-minute bars to next-day cross-sectional rankings without hand-built input features.Its design combines a multi-scale zero-sum-initialised stem with a staggered selective state-space backbone.
- Conclusion: STRATA leads six parameter-matched alternatives on all four metrics, with every day-level paired rank-IC comparison significant at p < 0.001.Among the five sequence baselines, its score variance is least explained by the eight styles.
- Conclusion: 18.5% rank-IC gap: the Mamba comparison attributes the difference to bundled stem, decay-initialisation and readout changes, not isolated component effects.Component-level contributions require ablation.
- Conclusion: From the first executable price, STRATA’s relative rank-IC margin widens and architecture ordering is preserved, but its long-short spread is indistinguishable from zero.The results therefore support a prediction-model comparison rather than a deployable trading strategy.
A Corporate actions and the adjustment convention
Corporate-action adjustment is applied to the target while raw exchange quantities remain the model inputs. This keeps adjustment information from entering the input channels through the target convention.
- Adjustment convention: Raw prices, volumes and order-book quantities enter exactly as printed; corporate-action adjustment is applied only to the target.The adjustment contribution is defined multiplicatively over ex-dates on or before the relevant date.
- Adjustment convention: No adjustment factor appears among the 25 input fields, so an in-window ex-date remains a raw mechanical jump for the network to observe.An action first entering through the next-day adjustment affects only the label and cannot leak into the input.
B Stress-day detector: full specification
The stress-day detector standardises rolling market-return and volatility measures, thresholds a combined stress strength, and retains sufficiently long merged hot segments. Stress IC IR is then computed only on qualifying days.
- Inputs and strength: w = 10: the detector uses a ten-day window and standardises each series over its finite entries before combining stress measures.The available suffix is used when at least five finite returns are present.
- Thresholding and segmentation: h_j = max{Z(|c_j|), Z(v_j)} and τ is the 0.80 quantile of finite stress strengths.A day is hot when h_j ≥ τ; ties are included and non-finite strengths are cold.
- Thresholding and segmentation: g = 3 and m = 5: hot runs separated by at most three cold positions are merged, then only segments lasting at least five days are retained.The merge-before-length-filter order applies even when missing days occur.
- Stress metric: Stress IC IR is the mean divided by sample standard deviation of daily cross-sectional ICs inside the retained mask, reported only with at least 20 finite ICs.The detector is intentionally non-causal, uses returns only, and is identical across model arms.
C.1 Positive controls
The positive-control tests show that symmetric residualisation removes signals lying in the span of the controls, while asymmetric clipping creates residual artefacts.
- C.1 Positive controls: Symmetric clipping sends two control-span signals through the same residualisation pipeline before evaluating their residual ICs.The signals are rev5 = −strev and mom = momentum.
- C.1 Positive controls: Both symmetric residual ICs are within one standard error of zero, with R2_style = 1.000.
- C.1 Positive controls: +0.0152 and +0.0126 remain under asymmetric clipping, so symmetric clipping is necessary to prevent tail-induced residual artefacts.
C.2 Why the survival ratio is not identified
The survival ratio is not identified as a style-exposure measure because its value depends on which style loading is varied, even with the same alpha content.
- C.2 Why the survival ratio is not identified: Residualised-to-raw rank IC survival is not a style-exposure measure.
- C.2 Why the survival ratio is not identified: With fixed alpha content, increasing λ raises survival for strev but lowers it for −resvol.The tested style loadings have own ICs of −0.006 for strev and −0.060 for −resvol.
- C.2 Why the survival ratio is not identified: Style changes monotonically with |λ|, so opposite survival responses can occur as style loading changes.