Reinforcement learning driven periodic kernel fusion for probabilistic forecasting of market dynamic

Yawei Dong, He Jiang(通讯作者）,Bo Zeng, Sheng Pan

Abstract

Probabilistic forecasting of financial time series is essential for risk management and asset pricing, yet remains challenging due to non-stationarity, multi-scale temporal dynamics, and distributional drift. To address these challenges, this study proposes a reinforcement learning-enhanced probabilistic forecasting framework, termed the Probabilistic Periodic Sequence Drift Predictor (P-PSDP). The proposed model integrates Fourier-based periodic feature extraction with a subsequence kernel fusion mechanism that combines convolutional weighted pooling and gating operations to capture multi-scale temporal dependencies. Furthermore, the residual transformation is reformulated as a state-dependent decision process and optimized through reinforcement learning, where a policy network dynamically regulates representation updates to adapt to evolving market regimes. This design enables adaptive control of information flow at the representation level rather than relying solely on static parameter updates. Experiments on four real-world financial datasets demonstrate that P-PSDP consistently achieves superior probabilistic forecasting performance. Under a 90% coverage level, the proposed method improves the prediction interval coverage probability (PICP) by approximately 2–4% while reducing the prediction interval normalized average width (PINAW) by up to 30% compared with strong baselines. In multi-step forecasting settings, the model achieves lower mean pinball loss and exhibits greater stability over long horizons. Diebold-Mariano tests further confirm that these improvements are statistically significant at the 95% confidence level. These results indicate that reinforcement learning-based adaptive representation control improves robustness to distributional shifts in financial time series forecasting.