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.