Robust Bayesian analysis for autoregressive models

Abstract

Abstract Time series data sometimes show violation of normal assumptions. For cases wherethe assumption of normality is untenable, more exible models can be adopted toaccommodate heavy tails. The exponential power distribution (EPD) is considered aspossible candidate for errors of time series model that may show violation of normalassumption. Besides, the use of exible models for errors like EPD might be able toconduct the robust analysis. In this paper, we especially consider EPD as the exibledistribution for errors of autoregressive models. Also, we represent this distribution asscale mixture of uniform and this form enables ecient Bayesian estimation via Markovchain Monte Carlo (MCMC) methods.Keywords: Autoregressive model, exponential power distribution, Gibbs sampler, ro-bustness. 1. Introduction Real data often show violation of normal assumptions. Heavy-tailed distributions are fre-quently encountered in empirical studies. For cases where the assumption of normality isuntenable, more exible models can be adopted to accommodate heavy tails. The exponen-tial power distribution (EPD) is considered as possible candidate for errors of time seriesmodel that may show violation of normal assumption. Besides, the use of exible modelsfor errors like EPD might be able to conduct the robust analysis. An exponential powerdistribution had been studied by Box and Tiao (1992) in the context of robustness studies.The exponential power density is given by (1.1)f(xj;˙;p) =12p