Bayesian estimation and unit root tests for Random Coefficient AutoRegressive models

Abstract

Random Coefficient AutoRegressive (RCAR) models are obtained by introducing random coefficients to an AR or more generally ARMA model. These models have second order properties similar to that of ARCH and GARCH models. In this article, we consider a Bayesian approach to estimate RCAR models. We study the frequentist performance of the Bayes estimators and show that they have good coverage properties. We propose a couple of Bayesian testing criteria for the unit root hypothesis of first order RCAR models: one is based on the Posterior Interval, and the other one is based on the Bayes Factor. Using extensive simulation studies, we evaluate the performance of the Bayesian tests and show the impact of using different priors. In the end, we present a real life example involving the daily stock volume transaction data to illustrate the proposed methods.