Sparse vector Markov switching autoregressive models. Application to multivariate time series of temperature

Multivariate time series are of interest in many fields including economics and environment. The dynamical processes occurring in these domains often exhibit a mixture of different dynamics so that it is common to describe them using Markov Switching vector autoregressive processes. However the estimation of such models is difficult even when the dimension is not so high because of the number of parameters involved. A Smoothly Clipped Absolute Deviation penalization of the likelihood is proposed to shrink the parameters towards zeros and regularize the inference problem which is generally ill-posed. The Expectation Maximization algorithm built for maximizing the penalized likelihood is described in detail and tested on simulated data and real data consisting of daily mean temperature.