Deep switching state space model for nonlinear time series forecasting with regime switching

Abstract

Modern time series data often display complex nonlinear dependencies along with irregular regime-switching behaviors. These features present technical challenges in modeling, inference, and providing insightful understanding of the underlying stochastic phenomena. To tackle these challenges, we introduce the novel Deep Switching State Space Model (DS${}^3$M). In DS${}^3$M, the architecture employs discrete latent variables to represent regimes and continuous latent variables to account for random driving factors. By melding a Recurrent Neural Network (RNN) with a nonlinear Switching State Space Model (SSSM), we manage to capture the nonlinear dependencies and irregular regime-switching behaviors, governed by a Markov chain and parameterized using multilayer perceptrons. We validate the DS${}^3$M through short- and long-term forecasting on a wide array of simulated and real-world datasets, spanning sectors such as healthcare, economics, traffic, meteorology, and energy. Our results reveal that DS${}^3$M outperforms several state-of-the-art models in terms of forecasting accuracy, while providing meaningful regime identifications.