Hierarchical Bayesian Estimation for Stationary Autoregressive Models Using Reversible Jump MCMC Algorithm

Abstract

The autoregressive model is a mathematical model that is often used to model data in different areas of life. If the autoregressive model is matched against the data then the order and coefficients of the autoregressive model are unknown. This paper aims to estimate the order and coefficients of an autoregressive model based on data. The hierarchical Bayesian approach is used to estimate the order and coefficients of the autoregressive model. In the hierarchical Bayesian approach, the order and coefficients of the autoregressive model are assumed to have a prior distribution. The prior distribution is combined with the likelihood function to obtain a posterior distribution. The posterior distribution has a complex shape so that the Bayesian estimator is not analytically determined. The reversible jump Markov Chain Monte Carlo (MCMC) algorithm is proposed to obtain the Bayesian estimator. The performance of the algorithm is tested by using simulated data. The test results show that the algorithm can estimate the order and coefficients of the autoregressive model very well. Research can be further developed by comparing with other existing methods.