Deep Switching State Space Model (DS$^3$M) for Nonlinear Time Series Forecasting with Regime Switching

2021-06-04

AI Summary

To address complex time-series forecasting challenges characterized by strong nonlinear dependencies and irregular state transitions, this paper proposes a generative Deep Switching State Space Model (DSSSM) that jointly incorporates discrete latent variables—modeling dynamic regime shifts—and continuous latent variables—capturing stochastic evolution. The model employs a Markov chain to govern regime transitions, enhances temporal modeling via RNNs, and parameterizes nonlinear transition and emission distributions using multi-layer perceptrons, thereby enabling both interpretable regime discovery and high-accuracy long-horizon forecasting. Empirical evaluations across diverse domains—including healthcare, economics, transportation, meteorology, and energy—demonstrate statistically significant reductions in prediction error compared to state-of-the-art baselines. Notably, the model successfully uncovers economically meaningful latent regimes, validating its interpretability and practical utility. This work advances both the theoretical foundations and real-world applicability of deep probabilistic time-series modeling.

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 in offering insightful understanding into the underlying stochastic phenomena. To tackle these challenges, we introduce a novel modeling framework known as the Deep Switching State Space Model (DS$^3$M). This framework is engineered to make accurate forecasts for such time series while adeptly identifying the irregular regimes hidden within the dynamics. These identifications not only have significant economic ramifications but also contribute to a deeper understanding of the underlying phenomena. 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 effectiveness and regime identification capabilities of DS$^3$M through short- and long-term forecasting tests on a wide array of simulated and real-world datasets, spanning sectors such as healthcare, economics, traffic, meteorology, and energy. Experimental results reveal that DS$^3$M outperforms several state-of-the-art models in terms of forecasting accuracy, while providing meaningful regime identifications.

Problem

• Complex Time Series Prediction
• Pattern Change
• Accuracy Enhancement

Innovation

• Deep Switching State Space Model (DS$^3$M)
• Recurrent Neural Networks
• Irregular Time Series Prediction