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Biometrika 2001 88(4):1089-1104; doi:10.1093/biomet/88.4.1089
© 2001 by Biometrika Trust
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Bayesian semiparametric inference on long-range dependence

Brunero Liseo1, Domenico Marinucci1 and Lea Petrella1

1 Dipartimento di Studi Geoeconomici, Statistici, Storici per l'Analisi Regionale, Università di Roma "La Sapienza", Via del Castro Laurenziano 9, 00161 Roma, Italybrunero{at}pow2.sta.uniroma1.itmarinucc{at}scec.eco.uniroma1.itpetrella{at}scec.eco.uniroma1.it

We develop a Bayesian semiparametric procedure for the analysis of stationary long-range dependent time series.We use frequency domain methods to partition the infinite-dimensional parameter space into regions where genuine prior information on the form of the spectral density is available, and others where vague prior beliefs are adopted; the solution to the partition problem, 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 on the spectral density of a stationary process. Asymptotic properties of our technique and comparisons with frequentist approaches are also considered; the suggested procedure is finally implemented via Markov chain Monte Carlo methods on simulated and real data.

Key Words: Bayesian semiparametric methods; Frequency domain analysis; Long-range dependence; Markov chain Monte Carlo

Received July 1999. Revised June 2001


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