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

International audienceMultivariate time series are of interest in many fields including economics and environment. The dynamical processes occurring in these domains often exhibit regimes 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. In this paper we propose to use a Smoothly Clipped Absolute DEviation (SCAD) penalization of the likelihood to shrink the parameters. The Expectation Maximization algorithm build for maximizing the penalized likelihood is described in details and tested on daily mean temperature time series

Markov-switching autoregressive models for wind time series

International audienceIn this paper, non-homogeneous Markov-Switching Autoregressive (MS-AR) models are proposed to describe wind time series. In these models, several au-toregressive models are used to describe the time evolution of the wind speed and the switching between these different models is controlled by a hidden Markov chain which represents the weather types. We first block the data by month in order to remove seasonal components and propose a MS-AR model with non-homogeneous autoregressive models to describe daily components. Then we discuss extensions where the hidden Markov chain is also non-stationary to handle seasonal and inter-annual fluctuations. The different models are fitted using the EM algorithm to a long time series of wind speed measurement on the Island of Ouessant (France). It is shown that the fitted models are interpretable and provide a good description of im-portant properties of the data such as the marginal distributions, the second-order structure or the length of the stormy and calm periods