Regime-switching factor models for high-dimensional matrix time series

In this article, we introduce a regime-switching matrix factor model in which the mean, loading matrix, and noise processes change with different regimes, regulated by a hidden Markov chain. We devise an iterative algorithm to estimate parameters of the matrix factor model, starting with an initial estimation of Markov states to estimate the factor loadings and dimensions of latent factors based on eigenanalysis, and subsequently utilizing the Viterbi algorithm to estimate the Markov states, and repeat the procedures until the convergence criterion is satisfied. Furthermore, we establish the asymptotic properties of the parameter estimates and demonstrate that the convergence rate can be improved by the presence of strong factors in stages with weak factors, as supported by numerical simulations. Empirical studies on nine indicators of 10 component stocks in Energy industry of S&P 500 show that the regime-switching matrix factor model is reasonable since it successfully distinguishes between two scenarios of market states which are stable and volatile downward with high and low frequency, respectively, and also works better than the matrix factor model according to RSS/TSS.