Predicting financial stock returns remains challenging due to their inherent nonlinearity, non-stationarity, and sensitivity to market microstructure noise. Existing approaches typically rely on either econometric filtering techniques or deep learning models in isolation, limiting their ability to jointly capture latent dynamics and complex temporal dependencies. This study proposes a hybrid Extended Kalman Filter–Long Short-Term Memory (EKF–LSTM) framework that integrates nonlinear state-space filtering with deep sequential learning. The EKF component performs nonlinear state estimation and denoises to extract latent signals from noisy observations, while the LSTM network models nonlinear temporal dependencies in the filtered series. The proposed framework is evaluated using data from multiple international markets, including China, the United States, and Europe, providing cross-market evidence of model robustness. Empirical results show that the EKF–LSTM model consistently outperforms benchmark models (ARIMA, standalone EKF, LSTM, and GRU) across standard statistical metrics, including RMSE, MAE, and mean directional accuracy (MDA). In addition, the model delivers economically meaningful improvements under a long-only trading strategy, achieving higher risk-adjusted returns and lower maximum drawdowns relative to benchmark strategies. Diebold–Mariano tests further confirm that these performance gains are statistically significant. Overall, the findings demonstrate that integrating nonlinear state-space filtering with deep learning provides a robust and effective framework for financial time-series forecasting. However, the results should be interpreted with caution due to the limited sample size and the simplifying assumptions underlying the trading strategy.
Tian et al. (Sat,) studied this question.