Bayesian estimation for first-order autoregressive model with explanatory variables

In this article, we develop a Bayesian analysis in autoregressive model with explanatory variables. When σ² is known, we consider a normal prior and give the Bayesian estimator for the regression coefficients of the model. For the case σ² is unknown, another Bayesian estimator is given for all unknown parameters under a conjugate prior. Bayesian model selection problem is also being considered under the double-exponential priors. By the convergence of ρ-mixing sequence, the consistency and asymptotic normality of the Bayesian estimators of the regression coefficients are proved. Simulation results indicate that our Bayesian estimators are not strongly dependent on the priors, and are robust.