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.

KEYWORDS:

• Autoregressive models
• ECME algorithm
• finite mixture distributed innovations
• maximum a-posteriori probabilities
• non-Gaussian time series
• SMSN family

Acknowledgment

The authors would like to thank the anonymous reviewers for their suggestions, corrections and encouragement, which helped us to improve the earlier versions of the manuscript.