Markov-switching autoregressive models for wind time series

In this paper, non-homogeneous Markov-Switching Autoregressive (MS-AR) models are proposed to describe wind time series. In these models, several autoregressive 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 interannual 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 important properties of the data such as the marginal distributions, the second-order structure or the length of the stormy and calm periods.