Bayesian Analysis of AR(1) Model

Abstract

The first-order autoregressive process, AR (1), has been widely used and implemented in time series analysis. Different estimation methods have been employed in order to estimate the autoregressive parameter. This article focuses on subjective Bayesian estimation as opposed to objective Bayesian estimation and frequentist procedures. The truncated normal distribution is considered as a prior, to impose stationarity. The posterior distribution as well as the Bayes estimator are derived. A comparative study between the newly derived estimator and other existing estimation methods (frequentist) is employed in terms of simulation and real data. Furthermore, a posterior sensitivity analysis is performed based on four different priors; g prior, natural conjugate prior, Jeffreys' prior and truncated normal prior and the performance is compared in terms of Highest Posterior Density Region criterion.