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

TL;DR

The paper introduces DS$^3$M, a deep learning framework combining RNNs and switching state space models to improve nonlinear time series forecasting and regime detection across diverse real-world datasets.

Contribution

It presents a novel deep switching state space model that captures nonlinear dependencies and regime switches, advancing time series modeling and interpretability.

Findings

Outperforms state-of-the-art models in forecasting accuracy.

Effectively identifies hidden regimes in complex datasets.

Validated on diverse real-world data including healthcare and economics.

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.