Markov Switching Multiple-equation Tensor Regressions

We propose a new flexible tensor model for multiple-equation regression that accounts for latent regime changes. The model allows for dynamic coefficients and multi-dimensional covariates that vary across equations. We assume the coefficients are driven by a common hidden Markov process that addresses structural breaks to enhance the model flexibility and preserve parsimony. We introduce a new Soft PARAFAC hierarchical prior 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. We developed theoretical results to help hyperparameter choice. An efficient MCMC algorithm based on random scan Gibbs and back-fitting strategy is developed to achieve better computational scalability of the posterior sampling. The validity of the MCMC algorithm is demonstrated theoretically, and its computational efficiency is studied using numerical experiments in different parameter settings. The effectiveness of the model framework is illustrated using two original real data analyses. The proposed model exhibits superior performance when compared to the current benchmark, Lasso regression.