Revisiting Dynamical System-Based Financial Forecasting: The Role of Smoothing Methods

Abstract

This study examines the role of causal smoothing in dynamical system-based financial forecasting by integrating an asymmetric backward Savitzky-Golay (SG) filter into the new Price Reversion Model (nPRM) and comparing it with conventional moving-average preprocessing on the S&P 500 index. Despite the theoretical advantages of SG filtering in noise suppression and analytical derivative estimation, the original nPRM achieves a lower one-step-ahead forecasting error on the S&P 500 index, indicating that, within this causal nPRM framework, noise reduction and predictability enhancement need not coincide. This discrepancy is attributed to the larger dynamic range of SG-derived coefficient estimates, which weakens the gradient control mechanism and amplifies instability at market turning points. Both nPRM variants substantially outperform an LSTM baseline, highlighting the robustness of lightweight dynamical models with interpretable time-varying coefficients under limited and noisy financial data conditions.