Non-informative priors in the case of Gaussian long-memory processes

Abstract

In this paper, we consider an asymptotic Bayesian analysis for Gaussian processes with long memory. First, we determine the asymptotic expansion of the posterior density based on a normal approximation. This expansion leads to the construction of Bayesian confidence regions such as highest posterior density regions and to the determination of matching prior. Then, we generalize Clarke and Barron's result in the long-memory set-up. More precisely, we establish the asymptotic expansion of the Kullback-Leibler distance between the true density and the marginal density of the observations. As in the independent and identically distributed case, this result gives an asymptotic justification of Berger and Bernardo's algorithm to obtain reference priors.