Regime transitions routinely break stationarity in time series, making calibrated uncertainty as important as point accuracy. We study distribution-free uncertainty for regime-switching forecasting by coupling Deep Switching State Space Models with Adaptive Conformal Inference (ACI) and its aggregated variant (AgACI). We also introduce a unified conformal wrapper that sits atop strong sequence baselines including S4, MC-Dropout GRU, sparse Gaussian processes, and a change-point local model to produce online predictive bands with finite-sample marginal guarantees under nonstationarity and model misspecification. Across synthetic and real datasets, conformalized forecasters achieve near-nominal coverage with competitive accuracy and generally improved band efficiency.

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.