Adaptive Regime-Switching Forecasts with Distribution-Free Uncertainty: Deep Switching State-Space Models Meet Conformal Prediction

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 (DS$^3$M) 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 improved band efficiency.