Gibbs Sampling in AR Models with Random Walk Priors

Abstract

The paper analyses univariate autoregressive AR(p) models with tightness prior. The framework of the model is the conjugate normal linear model where the prior distribution is assumed to be a random walk process. The deviation from the prior distribution is measured by the tightness (hyper-) parameter λ. It is shown how the estimation of the starting values can be incorporated into the Gibbs sampling scheme. We demonstrate this approach with simulated and economic time series. It is found that for typical economic sample size the sampling fluctuations influence the posterior distribution considerably and informative prior distributions seem to be useful, especially for prediction.