Regime-aware causal Bayesian forecasting for non-stationary time series

Quantile-adaptive distributional Granger causal model for high-dimensional time series

Hierarchical Bayesian autoregressive smooth transition time series models

Hierarchical Bayesian smooth transition autoregressive models provide accurate forecasts by accommodating nonlinear regime-switching dynamics while delivering robust uncertainty quantification, which makes them well suited for infectious disease surveillance and public health decision-making in resource-limited, high-uncertainty settings.

Conditional Regime Analog Forecasting with Trajectories: A Nonparametric Framework for Multivariate Probabilistic

We propose Conditional Regime Analog Forecasting with Trajectories (CRAFT), a nonparametric framework for multivariate probabilistic time-series prediction. The method constructs paired backward and forward trajectory profiles from cumulative multi-horizon returns, learns recurrent low-dimensional regime labels in both spaces using singular value decomposition, change-point segmentation, and segment clustering, and estimates a backward-to-forward conditional regime correspondence. Forecast distributions are obtained by sampling historically realized future trajectory profiles according to a composite compatibility score that combines future-regime correspondence with similarity to the current backward trajectory profile. Unlike parametric vector autoregressions or Gaussian state-space models, CRAFT preserves empirical cross-sectional and multi-horizon dependence by resampling complete future paths. We describe the estimator, its diagnostics, and a reproducible simulation benchmark comparing CRAFT with direct analog resampling, SVD analogs, unconditional bootstrap, OLS VAR bootstrap, and random-forest forecasts.

Bayesian Modeling and Forecasting of Double Seasonal Vector Autoregressive Processes

A wide range of real-world multivariate time series encountered in practice exhibit two simultaneous and interacting seasonal cycles, for example hourly electricity demand, intraday financial prices, and sub-daily traffic volumes. Existing Bayesian frameworks for vector autoregressive (VAR) processes accommodate at most a single seasonal periodicity, leaving no established methodology for the double seasonal case commonly observed in high-frequency multivariate data. This paper bridges that gap by introducing the double seasonal VAR (DSVAR) models, which extend the univariate double seasonal literature to a coherent multivariate setting. These models are defined through a multiplicative triple autoregressive operator that naturally accommodates the second seasonal cycle. Under a Gaussian error assumption, we derive a comprehensive and analytically convenient Bayesian framework for both modeling and forecasting of DSVAR processes. We consider two prior families: a conjugate matrix normal-Wishart prior which yields exact closed-form inference, and a Jeffreys’ non-informative prior. Under each prior, we derive the marginal posterior distribution of the coefficient matrix as a matrix-t distribution and the marginal posterior of the precision matrix as a Wishart distribution. Moreover, we derive the predictive distribution of future observations as a multivariate-t with an exact analytic form, together with its highest predictive density regions. The methodology is validated through a Monte Carlo simulation experiment and applied to hourly electricity loads in Czech Republic and Germany, two physically interconnected markets with pronounced intraday and intraweek seasonal cycles. Benchmark comparisons against standard VAR, single-seasonal VAR, and univariate seasonal AR models confirm the substantial forecasting gains delivered by the proposed DSVAR framework at both short and long horizons.

Causal Local States: Scalable Simultaneous Causal Network Inference and Forecasting for Dynamical Systems

Reconstruction of the underlying networks with high fidelity and forecasts on par with a model that is supplied with the true network are achieved, providing a step toward explainable and scalable forecasting of complex systems.

Causal Machine Learning for Macroeconomic Forecasting Under Structural Breaks and Economic Uncertainty

Macroeconomic forecasting has become increasingly challenging in environments characterized by structural breaks, nonlinear dynamics, and elevated economic uncertainty. Traditional econometric forecasting models frequently experience substantial predictive deterioration during periods of financial crises, geopolitical instability, and rapidly evolving macroeconomic conditions due to their reliance on assumptions of parameter stability and linear economic relationships. In response to these limitations, this study proposes an integrated causal machine learning framework designed to improve macroeconomic forecasting performance under structural instability and uncertainty. The proposed framework combines structural break detection techniques, machine learning algorithms, causal inference methodologies, and Explainable Artificial Intelligence (XAI) tools within a unified empirical architecture. More specifically, the study integrates Bai–Perron structural break analysis, Markov-Switching regime identification, Double Machine Learning (DML), Causal Forest estimation procedures, and SHAP-based explainability techniques. The empirical analysis employs a U.S. macroeconomic time-series dataset covering major crisis episodes, including the 2008 Global Financial Crisis, the COVID-19 pandemic, and the 2022 inflation shock. The dataset combines inflation, monetary, financial, energy-market, and uncertainty indicators obtained from publicly available U.S. macroeconomic databases. The empirical findings demonstrate that causal machine learning models significantly outperform conventional econometric frameworks such as VAR and TVP-VAR models, as well as standard machine learning algorithms including Random Forest (RF), XGBoost, and LSTM networks. The Double Machine Learning framework generates the strongest forecasting performance across all forecasting horizons, economic regimes, and robustness specifications. The results further reveal that macroeconomic relationships are highly regime-dependent and strongly influenced by uncertainty indicators, financial volatility, oil price shocks, and monetary policy dynamics. Explainability analysis additionally shows that uncertainty measures and energy market variables become dominant drivers of inflation forecasts during crisis periods characterized by elevated instability. The study contributes to the growing literature on macroeconomic forecasting by bridging econometric forecasting theory, causal inference methodologies, machine learning techniques, and explainable artificial intelligence within a unified forecasting framework. The findings provide important implications for central banks, policymakers, and financial institutions seeking more adaptive, transparent, and robust forecasting systems under uncertain macroeconomic environments.