Bayesian Analysis of Extended Auto Regressive Model with Stochastic Volatility

Abstract

This paper proposes an extension of the autoregressive model with stochastic volatility error. The Bayes analysis of the proposed model using vague priors for the parameters of the conditional mean equation and informative prior for the parameters of conditional volatility equation is done. The Gibbs sampler with intermediate Metropolis steps is used to find out posterior inferences for the parameters of autoregressive model and independent Metropolis–Hastings algorithm is used to simulate the volatility of the mean equation. The two data sets in the form of gross domestic product growth rate of India at constant prices and exchange rate of Indian rupees relative to US dollar are considered for numerical illustration. These data are used after assuring the stationarity by differencing the data once. The retrospective as well as prospective short term predictions of the data are provided based on the two simple components of the general autoregressive process. The findings based on the real data are expected to assist the policy makers and managers to make economic and business strategies more precisely.