Markov switching multiple-equation tensor regressions

A new flexible tensor model for multiple-equation regressions that accounts for latent regime changes is proposed. The model allows for dynamic coefficients and multi-dimensional covariates that vary across equations. The coefficients are driven by a common hidden Markov process that addresses structural breaks to enhance the model 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. Theoretical results are derived to help with the choice of the hyperparameters. An efficient Markov chain Monte Carlo (MCMC) algorithm based on random scan Gibbs and back-fitting strategy is designed with priority placed on 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 compared to the current benchmark, Lasso regression.