Markov Switching Tensor Regressions

A new flexible tensor-on-tenor regression model that accounts for latent regime changes is proposed. The coefficients are driven by a common hidden Markov process that addresses structural breaks to enhance the model's flexibility and preserve parsimony. A new soft PARAFAC hierarchical prior is introduced to achieve dimensionality reduction while preserving the structural information of the covariate tensor. The proposed prior includes a new multi-way shrinking effect to address over-parametrization issues while preserving interpretability and model tractability. An efficient MCMC algorithm is introduced based on a random scan Gibbs and back-fitting strategy. The model framework’s effectiveness is illustrated using financial and commodity market volatility data. The proposed model exhibits superior performance compared to the current benchmark, Lasso regression.