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.
Model Performance
Across five liquid U.S. assets, a volatility-aligned HAR-style model outperforms AR, MA, and ARIMA.
Residual Process Analysis
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
Residual-only LSTM augmentation nevertheless raises mean squared error from 0.3049 to 0.3594 on average, with deterioration on every asset.
Pure LSTM vs. Residual Hybrid
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.
Forecaster-Preconditioner Asymmetry
We describe this pattern as forecaster-preconditioner asymmetry: first-stage forecasting success and statistical residual simplification need not translate into useful downstream neural preconditioning.