Maximum a-posteriori estimation of autoregressive processes based on finite mixtures of scale-mixtures of skew-normal distributions

Abstract

This article investigates maximum a-posteriori (MAP) estimation of autoregressive model parameters when the innovations (errors) follow a finite mixture of distributions that, in turn, are scale-mixtures of skew-normal distributions (SMSN), an attractive and extremely flexible family of probabilistic distributions. The proposed model allows to fit different types of data which can be associated with different noise levels, and provides a robust modelling with great flexibility to accommodate skewness, heavy tails, multimodality and stationarity simultaneously. Also, the existence of convenient hierarchical representations of the SMSN random variables allows us to develop an EM-type algorithm to perform the MAP estimates. A comprehensive simulation study is then conducted to illustrate the superior performance of the proposed method. The new methodology is also applied to annual barley yields data. © 2016 Informa UK Limited, trading as Taylor & Francis Group.