Periodic autoregressive models with closed skew-normal innovations

Abstract

This paper is concerned with the estimation problem of a periodic autoregressive model with closed skew-normal innovations. The closed skew-normal (CSN) distribution has some useful properties similar to those of the Gaussian distribution. Maximum likelihood (ML), Maximum a posteriori (MAP) and Bayesian approaches are proposed and compared in order to estimate the model parameters. For the Bayesian approach, the Gibbs sampling algorithm and for computing the ML and MAP estimations, the expectation–maximization algorithms are performed. The simulation studies are then conducted to compare the frequentist average losses of competing estimators and to study the asymptotic properties of the given estimators. The proposed model and methods developed in this paper are also applied to a real time series. The accuracy of the CSN and Gaussian models is compared by cross validation criterion.