A Comparison of the Bayesian and Non-Bayesian Approaches for the Periodic AR Models Based on the SMSN Innovations

• Published in: Iranian journal of science (Online) Vol. 46; no. 2; pp. 615 - 630
• Main Authors: Manouchehri, T, Nematollahi, A R
• Format: Journal Article
• Language: English
• Published: Shiraz Springer Nature B.V 01.04.2022
• Subjects: Algorithms; Autoregressive models; Bayesian analysis; Innovations; Mathematical models; Mixtures; Parameter estimation; Sensitivity analysis; Skewed distributions; Time series
• ISSN: 2731-8095; 2731-8109
• DOI: 10.1007/s40995-022-01266-w

We consider here a periodic autoregressive model with scale mixtures of skew-normal innovations. The class of scale mixtures of skew-normal distributions is a general and quite flexible class of error distributions, which is often used for statistical procedures of analyzing symmetrical and asymmetrical data. Our aim is to compare some well-known parameter estimation methods of periodic autoregressive time series with scale mixtures of skew-normal error terms. The maximum likelihood, maximum a posterior, and Bayesian estimation methods are then developed by using the expectation–conditional maximization algorithms and the Gibbs sampling algorithm. The numerical results obtained by means of simulation studies are reported to examine and compare the proposed methods. A prior sensitivity analysis is also developed to study the effect of changes in the priors. Moreover, a web-based shiny app called “PAR(1) Model Analysis” is developed here, for modeling, estimation, and prediction in the periodic autoregressive time series using the proposed technique. Finally, the proposed methods are applied to some quarterly UK macroeconomic variables.