A Regularized Vector Autoregressive Hidden Semi-Markov Model, with Application to Multivariate Financial Data

A regularized vector autoregressive hidden semi-Markov model is developed to analyze multivariate financial time series with switching data generating regimes. Furthermore, an augmented EM algorithm is proposed for parameter estimation by embedding regularized estimators for the state-dependent covariance matrices and autoregression matrices in the M-step. The performance of the proposed regularized estimators is evaluated both in the simulation experiments and on the New York Stock Exchange financial portfolio data.