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

Valérie Monbet (1, 2) , Pierre Ailliot (3)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 ASPI - Applications of interacting particle systems to statistics
3 LMBA - Laboratoire de Mathématiques de Bretagne Atlantique

Multivariate 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.

Mots clés: sparse; penalized likelihood; Markov Switching Vector Autoregressive process; SCAD; dimension reduction

Domaines: Statistiques [math.ST]

Valérie Monbet, Pierre Ailliot. Sparse vector Markov switching autoregressive models. Application to multivariate time series of temperature. Computational Statistics and Data Analysis, 2017, 108, pp.40-51. ⟨10.1016/j.csda.2016.10.023⟩. ⟨hal-01250058v2⟩