Bayesian semiparametric inference on long-range dependence

We develop a Bayesian semiparametric procedure for the analysis of stationa ry long-range dependent time series, We use frequency domain methods to par tition the infinite-dimensional parameter space into regions where genuine prior information on the form of the spectral density is available, and oth ers where vague prior beliefs are adopted; the solution to the partition pr oblem, which is equivalent to bandwidth choice from a frequentist point of view, is obtained via Bayes factors. We derive a tight characterisation of the class of admissible noninformative priors for nonparametric inference o n the spectral density of a stationary process. Asymptotic properties of ou r technique and comparisons with frequentist approaches are also considered ; the suggested procedure is finally implemented via Markov chain Monte Car lo methods on simulated and real data.