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Centering Drives Normalization Gains: Price-Offset Nuisances in Cross-Sectional Return Prediction
Mingju Chen, Qianhui Liu, Yui Lo, Yuanhang Liu
TL;DR
Cross-sectional return prediction from raw intraday bars may be sensitive to instrument-specific price offsets in transformed inputs. The paper tests offset removal against amplitude scaling and encoder changes using matched models and parameter-free transforms. Centering carries the reliable gains, which are mainly price-channel driven.
Problem
It is unclear whether normalization gains in raw-bar cross-sectional ranking come from removing transformed price offsets, rescaling amplitudes, or changing encoders.
Source: §1 · pp. 1–2Method
The study compares eight parameter-matched encoders with and without normalization, then uses parameter-free transforms and channel restrictions to separate offset removal from scaling.
Source: §1 · p. 2, §3.2 · p. 2, §3.3 · p. 2Results
All eight encoder effects are positive and survive Holm correction; among six stronger encoders, gains of 0.0376–0.0567 exceed the 0.0109 spread of normalized IC.
Source: §4.2 · p. 3Takeaways & Limitations
Centering carries the main effect, scale-only normalization does not help, and price-only standardization retains 93%–101% of the all-field gain.
Source: §4.3 · p. 4, §4.4 · p. 4The invariance is exact for additive offsets in transformed price channels, but raw-price scaling maps only approximately to a constant shift under log(1 + p), especially at low prices.
Source: §2 · p. 2
Abstract
from arXiv · showhide
Cross-sectional return prediction from raw intraday bars is sensitive to each instrument price level, an additive nuisance under a return-ranking hypothesis. We test whether removing this offset, rather than rescaling amplitudes or changing the encoder, explains gains on a point-in-time CSI~300 five-minute panel. We evaluate eight parameter-matched encoders with and without RevIN normalization; a parameter-free ladder then separates identity, scale-only, centering, last-value referencing, differencing, and standardization across all fields and restricted channels. Centering drives the reliable effect, while scale-only normalization does not help. All eight paired effects are positive and survive Holm correction on raw rank IC, after style residualization, and after further residualizing on short-term reversal. Among six stronger encoders, gains of 0.0376-0.0567 exceed the 0.0109 spread of normalized IC (0.0830-0.0939). Price-only standardization retains 93--101% of the all-field gain. These results place the main effect in transformed price-channel offset removal rather than amplitude scaling or encoder choice.
1. INTRODUCTION
The paper frames instrument price level as an additive nuisance in transformed inputs for cross-sectional return ranking, then tests whether offset removal explains normalization gains. It motivates controlled comparisons because architecture, representation, and training often change together.
1. INTRODUCTION
- Multiplying an instrument’s price path by a positive constant preserves its return label but shifts transformed price channels, motivating offset removal under a return-ranking hypothesis.The correspondence is exact after log x and approximate under log(1 + x).Source: §1 · p. 1
- The introduction illustrates the nuisance as a transformed-channel shift of about 180 within-window standard deviations when a path is scaled by c.The caption states the shift is exact for log p and approximate for log(1 + p).Source: Figure 1 · p. 1
- Existing cross-sectional models commonly use ratio-style inputs that hide price level, while changing architecture, representation, and training together makes their effects hard to separate.Prior normalization work addressed non-stationary forecasting or learned financial-series inputs, not the offset-versus-scale mechanism in raw-bar cross-sectional ranking.Source: §1 · p. 1
- The study tests whether removing transformed price-channel offsets, rather than scaling amplitudes or changing encoders, explains normalization gains on a point-in-time CSI 300 five-minute panel.It reports that centering carries the main effect, scale-only normalization does not help, and the gain is mainly price-channel driven.Source: §1 · p. 2
2. PROBLEM FORMULATION
The paper defines a point-in-time cross-sectional ranking task using each instrument’s preceding intraday window to score next-day returns. It evaluates predictions by daily rank IC.
2. PROBLEM FORMULATION
- Each instrument is represented by 240 preceding five-minute bars across six raw fields, with no hand-crafted factors or cross-asset features.The fields are open, high, low, close, volume, and traded amount, after training-only global log(1 + ·) preprocessing and standardization.Source: §2 · p. 2
- The target is the next-day close-to-close return, and the model maps each input window to a scalar score.The scoring model is an encoder followed by a linear score head.Source: §2 · p. 2
- Performance is the daily cross-sectional Spearman correlation between scores and labels, averaged over test days as rank IC.Because rank IC depends only on within-day ranks, the model is judged by the ordering it induces.Source: §2 · p. 2
- The hypothesis treats a per-instrument additive offset in transformed price channels as irrelevant to ranking, although raw-price scaling maps to an approximately constant shift at low prices.Mean removal is exactly invariant to the transformed-input offset, even though the log(1 + p) mapping from raw-price scaling is approximate.Source: §2 · p. 2
3. CONTROLLED DIAGNOSTIC FRAMEWORK
The diagnostic holds the prediction protocol fixed while varying normalization, transform, channel scope, or encoder-related factors one at a time. It compares parameter-matched models and uses shared inference procedures.
3. CONTROLLED DIAGNOSTIC FRAMEWORK
- The controlled framework fixes training-only preprocessing and the prediction pipeline while varying one factor: normalization, a ladder transform, or its channel scope.The pipeline uses one of eight parameter-matched encoders to produce cross-sectional scores.Source: §3 · p. 2, Figure 2 · p. 3
3.1. Learnable instance normalization
- The learnable normalization uses statistics from each sample’s backward-looking window and learned affine parameters, without output denormalization for dimensionless ranking scores.The main comparison uses the normalization half of RevIN.Source: §3.1 · p. 2
3.2. Parameter-free transform ladder
- The parameter-free ladder contrasts identity, scale-only, centering, last-value referencing, differencing, and standardization to separate offset removal from amplitude scaling.Centering, last-value referencing, and differencing remove an additive transformed-input offset; scale-only normalization leaves it intact.Source: §3.2 · p. 2
3.3. Channel-restricted transforms
- Transforms can be applied per sample and field to all six fields, the four price fields, or volume and traded amount, with unselected channels unchanged.Price-only scope tests the nuisance hypothesis; the volume/amount scope controls for generic conditioning.Source: §3.3 · p. 2
3.4. Matched-capacity controlled protocol
- The protocol compares eight encoders matched to 233,632 ± 5% trainable parameters, with three matched seeds per arm and fixed shared training components.The ladder and channel studies use a linear stem and GRU; the encoder set includes recurrent, convolutional, attention, state-space, and MLP models.Source: §3.4 · pp. 2–3
3.5. Statistical inference
- Inference compares daily IC within matched seeds and uses moving-block bootstrap intervals conditional on three seeds, Holm correction, and TOST with a 0.005 rank-IC margin.As a robustness check, scores are residualized on eight price-volume style proxies, including five-day short-term reversal; industry dummies are unavailable.Source: §3.5 · p. 3
4. EXPERIMENTS
Across eight parameter-matched encoders, normalization improves rank IC, with gains robust to style and short-term-reversal residualization. Ablations attribute the reliable effect mainly to centering transformed price fields, not scale-only normalization.
4.1. Datasets and implementation details
- The test uses CSI 300 five-minute bars, a 2019–2023 training / 2024 validation / 2025 test split, and training-only global preprocessing.The 2025 test covers 242 days; contrasts and the TOST margin were specified before inspecting its results.Source: §4.1 · p. 3, Table 1 · p. 3
4.2. Main results: normalization across encoders
- All eight encoders improve with normalization, and all effects survive Holm correction on raw, style-residualized, and reversal-residualized IC.Among six stronger encoders, gains are 0.0376–0.0567, larger than their 0.0109 normalized-IC spread.Source: §4.2 · p. 3, Figure 3 · p. 4
- Six stronger encoders exceed the stronger hand-crafted reversal factor by 0.028–0.039, while residualizing on both factors leaves all eight normalization effects significant at essentially unchanged magnitude.PatchTST, MLP, and the unnormalized GRU exceed neither factor.Source: §4.2 · p. 4
4.3. Ablation: centering versus scaling
- Centering gains +0.0287 on the linear stem and +0.0518 on GRU, while scale-only normalization changes IC by −0.0103 and −0.0028, respectively.Centering accounts for 56% and 100% of the respective full-standardization gains; last-value referencing and differencing have larger point estimates, but linear-stem differencing is unstable across seeds.Source: §4.3 · p. 4, Table 2 · p. 4
4.4. Ablation: field-specific effects
- Price-only standardization retains 93% of the linear-stem gain and 101% of the GRU gain; its advantage over volume/amount is +0.0428 and +0.0502, respectively.The volume/amount arm gains only +0.0051 and +0.0018, neither distinguishable from zero; centering alone reproduces the separation on GRU (+0.0519) and more modestly on the linear stem (+0.0142).Source: §4.4 · p. 4, Table 3 · p. 4
5. CONCLUSION
The controlled comparisons identify centering transformed price channels—not scale removal or encoder choice—as the main source of normalization gains. The evidence is limited to one market, bar frequency, test year, and three seeds.
5. CONCLUSION
- Centering carries the main effect, normalization gains exceed the spread among six stronger encoders, and price-channel offset removal—not scale-only normalization or short-term reversal—best fits the results.PatchTST and MLP nevertheless remain below the other six encoders after normalization under the shared protocol.Source: §5 · p. 4