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Modern time series data often display complex nonlinear dependencies alongwith irregular regime-switching behaviors. These features present technicalchallenges in modeling, inference, and in offering insightful understandinginto the underlying stochastic phenomena. To tackle these challenges, weintroduce a novel modeling framework known as the Deep Switching State SpaceModel (DS$^3$M). This framework is engineered to make accurate forecasts forsuch time series while adeptly identifying the irregular regimes hidden withinthe dynamics. These identifications not only have significant economicramifications but also contribute to a deeper understanding of the underlyingphenomena. In DS$^3$M, the architecture employs discrete latent variables torepresent regimes and continuous latent variables to account for random drivingfactors. By melding a Recurrent Neural Network (RNN) with a nonlinear SwitchingState Space Model (SSSM), we manage to capture the nonlinear dependencies andirregular regime-switching behaviors, governed by a Markov chain andparameterized using multilayer perceptrons. We validate the effectiveness andregime identification capabilities of DS$^3$M through short- and long-termforecasting tests on a wide array of simulated and real-world datasets,spanning sectors such as healthcare, economics, traffic, meteorology, andenergy. Experimental results reveal that DS$^3$M outperforms severalstate-of-the-art models in terms of forecasting accuracy, while providingmeaningful regime identifications.

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