Markov-switching autoregressive models for wind time series

Abstract

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

A Markov-Switching Vector Autoregressive Stochastic Wind Generator for Multiple Spatial and Temporal Scales

“…For example, the ability of a model to duplicate the length of stormy and calm periods is investigated in [36]. For each of the simulation scenarios outlined in Section 3, we are interested in replicating the following features of the observed data:…”

“…Most models focus primarily on simulating wind speed or wind power for one temporal sampling frequency, with a few exceptions that model the wind vector [29,32,35]. Some more advanced approaches that use Markov-switching autoregressive [36] or vector autoregressive models have been proposed [20] with the underlying assumption that many locations tend to observe one of a few prevailing wind regimes, and characteristics within these regimes may differ dramatically [37,38].…”

Bayesian Estimation of Multivariate Autoregressive Hidden Markov Model with Application to Breast Cancer Biomarker Modeling

“…In fact, the autoregressive assumption in HMM has shown its advantage over regular HMM that cannot catch the strong dependence between successive observations (e.g., Ref. [9]). A similar model to ours can be found in Ref.…”

Marginal distribution of Markov-switching VAR processes

“…Thanks to their ability to fit time series subject to changes in pattern, these models have entertained a large success in empirical works over a wide variety of disciplines. They have been applied for instance in macroeconomics to the analysis of the business cycle (Hamilton, 1989;McConnell and Perez-Quiros, 2000) and monetary policy (Sims and Zha, 2006), in finance to asset pricing (Cecchetti et al, 1990(Cecchetti et al, , 1993, in environmental science to characterize wind time series (Ailliot and Monbet, 2012), in medicine for clinical monitoring (Gordon and Smith, 1990), in speech recognition (Juang and Rabiner, 1985), as well as in many other fields. General discussions and additional references can be found in West and Harrison (1997), Kim and Nelson (1999), Scott (2002), Fruhwirth-Schnatter (2006), and Ang and Timmermann (2011).…”