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

Hidden Markov model (HMM) has been a popular choice for financial time series modeling due to its advantage in capturing dynamic regimes. However, HMM's implicit assumption that the state duration follows a geometric distribution is too strong to hold in practice. In this work, we propose a regularized vector autoregressive hidden semi-Markov model to analyze multivariate financial time series. One challenge in such a model setting is that the number of parameters is too large to be reliably estimated unless the time series is extremely long. To address this issue, an augmented EM algorithm is developed for parameter estimation by using regularized estimators for the state-dependent covariance matrices and autoregression matrices in the M-step. The performance of the proposed model is evaluated in a simulation experiment, and demonstrated with the New York Stock Exchange financial portfolio data.