Signal Simplification Is Not Predictive Simplification: Diagnosing Residual Neural Forecasting in Short-Horizon Volatility

Bingqi Lian; Linfeng Cheng; Mei Lu; Jerry Wu

cs.LGOct 2, 2026

Signal Simplification Is Not Predictive Simplification: Diagnosing Residual Neural Forecasting in Short-Horizon Volatility

Authors: Bingqi Lian, Linfeng Cheng, Mei Lu, Jerry Wu

Organizations: Science Academy, College of Computer, Mathematical, and Natural Sciences, University of Maryland, College Park, MD 20742, USA · Department of Electrical and Computer Engineering, University of Maryland, College Park, MD 20742, USA

Abstract

Hybrid statistical-neural pipelines often assume that a successful statistical first stage leaves a cleaner and more learnable residual target. We examine that assumption in short-horizon volatility forecasting through a signal-forecast-system diagnostic framework. Across five liquid U.S. assets, a volatility-aligned HAR-style model outperforms AR, MA, and ARIMA. Within expanding training windows, the pre-standardization fitted residual process used to construct residual-LSTM sequences has about 82% lower variance than the corresponding target and near-zero lag-1 autocorrelation; independently, rolling pseudo-out-of-sample HAR errors show about 74% variance reduction and similarly weak lag-1 dependence. Residual-only LSTM augmentation nevertheless raises mean squared error from 0.3049 to 0.3594 on average, with deterioration on every asset. Pure LSTM records the lowest selected pseudo-out-of-sample MSE, 0.2649, while the residual hybrid requires substantially more end-to-end runtime without improving accuracy. We describe this pattern as forecaster-preconditioner asymmetry: first-stage forecasting success and statistical residual simplification need not translate into useful downstream neural preconditioning.

Figures & tables

Model	MSE	MAE	$R^{2}_{\mathrm{OOS}}$	QLIKE	Wins
AR	0.5785	0.4733	-0.7620	-6.8708	0
MA	0.5421	0.4791	-0.6513	-6.9024	0
ARIMA	0.5854	0.4770	-0.7829	-6.8701	0
HAR-style	0.3049	0.3125	0.0697	-7.0875	0
Pure LSTM	0.2649	0.2900	0.1931	-7.1059	5
HAR-style+LSTM	0.3594	0.3609	-0.0974	-7.0656	0

Table 1: Grouped forecasting results across five assets. Wins denotes the number of assets on which a model attains the lowest selected MSE.

Figure 1: Cross-asset MSE for the six-model design. Individual points show assets; diamonds denote cross-asset means.

	Training fitted residuals			Rolling POOS errors
Asset	Var. Red.	ACF(1)	ACF(6)	Var. Red.	ACF(1)	ACF(6)
SPY	0.8596	0.0067	-0.3303	0.7726	-0.0113	-0.3584
QQQ	0.8420	0.0064	-0.3424	0.7258	-0.0577	-0.4070
IWM	0.8144	0.0001	-0.3872	0.7565	-0.0434	-0.3754
AMD	0.7918	0.0123	-0.3400	0.7136	-0.0275	-0.3772
XOM	0.7897	0.0192	-0.3521	0.7536	0.0162	-0.3329

Table 2: HAR-Style Residual Signal Diagnostics. Training entries are asset-level means across expanding refit windows; POOS entries use sequential rolling forecast errors.

Figure 2: Rolling pseudo-out-of-sample HAR-style forecast-error diagnostics. Left: forecast-error variance reduction by asset. Right: cross-asset mean forecast-error autocorrelation at lags 1–6.

Asset	Pure LSTM	HAR-style	HAR-style+LSTM	$\Delta$ MSE
SPY	0.2711	0.3071	0.3443	+0.0372
QQQ	0.2552	0.3175	0.3644	+0.0469
IWM	0.2263	0.2612	0.3192	+0.0580
AMD	0.2538	0.2959	0.3599	+0.0641
XOM	0.3180	0.3430	0.4093	+0.0663

Table 3: Asset-Level Core Diagnostic Comparison

Figure 3: Marginal effect of residual LSTM augmentation. $\Delta$ MSE is HAR-style+LSTM minus HAR-style; positive values indicate deterioration.

Layer	Diagnostic	Result
Forecast	HAR-style MSE	0.3049
Signal	Training fitted-residual var. reduction	81.95%
Signal	Training fitted-residual ACF(1)	0.0089
Signal	Training fitted-residual ACF(6)	-0.3504
Signal	Rolling error variance reduction	74.44%
Signal	Rolling error ACF(1)	-0.0247

Table 4: Forecaster–Preconditioner Asymmetry Summary

Comparison	Mean Diff.	Median $p$	$p<0.05$	$N$
HAR-style+LSTM vs HAR-style	+0.0545	$<0.001$	5	5
HAR-style vs AR	-0.2736	$<0.001$	5	5
HAR-style vs MA	-0.2372	$<0.001$	5	5
HAR-style vs ARIMA	-0.2805	$<0.001$	5	5
HAR-style+LSTM vs Pure LSTM	+0.0945	$<0.001$	5	5

Table 5: Focused Asset-Level Diebold–Mariano Comparisons (MSE Loss; Newey–West Lag 6)

Model	End-to-End Runtime (s)	MSE
AR	221.39	0.5785
MA	471.51	0.5421
ARIMA	159.14	0.5854
HAR-style	2.87	0.3049
Pure LSTM	336.40	0.2649
HAR-style+LSTM	353.12	0.3594

Table 6: Accuracy–Efficiency Summary

Figure 4: Accuracy–efficiency trade-off across the six models. Lower-left is preferred. HAR-style+LSTM is less accurate than both HAR-style and Pure LSTM while retaining neural-scale runtime.

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Financial volatility is regime dependent, yet incorporating regime information into neural networks can also destabilize training. This paper asks where such information should enter a neural cross-sectional volatility forecasting model. We study five-day realized-volatility forecasts for 1,027 U.S. equities using a rolling walk-forward evaluation framework in which information, model capacity, hyperparameter tuning, and random seeds are matched across architectures. We propose RG-ResMoE, a regime-gated residual mixture-of-experts architecture in which regime information is used only for expert routing rather than for direct forecasting. The base predictor models volatility from stock features, while a gating network uses regime state variables to route residual corrections. RG-ResMoE consistently outperforms a capacity-matched MLP in both forecasting accuracy and training stability in the main U.S. study. Similar gains are observed on an independent Japanese panel. The integration pathway is decisive: appending the same regime variables directly to the forecasting input degrades both predictive performance and training stability, whereas restricting them to the routing gate improves accuracy and Value-at-Risk calibration. Hard routing consistently underperforms soft routing. The results suggest that, in compact neural volatility forecasting models, the primary value of mixture-of-experts models lies less in increasing model capacity than in controlling how nonstationary regime information influences prediction.

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