Residual-Enhanced Adaptive Koopman Autoencoder: A Deep Latent Dynamics Model for Stock Prediction

Stock markets are complex dynamical systems shaped by macro fundamentals, policy, and investor behavior. Their evolution is non-stationary with recurrent market states and abrupt shocks, which challenges models that assume stable distributions. We tackle this problem with modern Koopman theory, which portrays complex dynamical systems and considers such nonstationary dynamics. Specifically, we propose REAKA, a Residual-Enhanced Adaptive Koopman Autoencoder for modeling stock-return dynamics in the latent space, with a residual path to capture higher-order nonlinearities. REAKA introduces an Adaptive Koopman Selector to adaptively choose the appropriate operator for different market conditions and a diffusion-based residual corrector to handle noise, abrupt shocks, and nonlinear effects beyond the limits of finite-dimensional Koopman linearization. By embedding these modules within an autoencoder, REAKA learns Koopman-invariant coordinates and advances dynamics in latent space. Experiments on real stock market data demonstrate that REAKA outperforms existing methods, significantly improving prediction accuracy and robustness in complex financial environments.