Regime-aware causal Bayesian forecasting for non-stationary time series
Non-stationary time series are common in many real-world domains, including infectious disease spread, where the underlying relationships between variables evolve over time. However, most existing forecasting methods assume stationarity and fail to capture changing causal dynamics. To address this challenge, we propose the Causal Regime Bayesian (CaReBayes) forecasting framework, which integrates regime detection, causal discovery, and Bayesian forecasting within a unified approach. CaReBayes segments time series into regimes using temporal causal discovery, fits a Bayesian structural autoregressive model for each regime, classifies the current regime, then performs regime-specific forecasting with uncertainty quantification. The framework introduces methodological advances: a grid-search procedure for automated regime-dependent causal discovery, a classification method that assigns future observations to regimes based on learned Bayesian structures, and regime-conditioned Bayesian structural forecasting. Across both synthetic and Ontario COVID-19 time series data, CaReBayes outperforms benchmark models for time series forecasting. In addition to improved forecasting performance, it produces regime-dependent causal graphs that summarize candidate structural relationships in the system, enhancing interpretability.