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We develop a Bayesian procedure for analyzing stationary long-range dependent processes. Specifically, we consider the fractional exponential model (FEXP) to estimate the memory parameter of a stationary long-memory Gaussian time series. Further, the method we propose is hierarchical and integrates over all possible models, thus reducing underestimation of uncertainty at the model-selection stage. Additionally, we establish Bayesian consistency of the memory parameter under mild conditions on the data process. Finally the suggested procedure is investigated on simulated and real data.
Adaptive model selection, Bayesian model averaging; FEXP; Hierarchical Bayes; Long-range dependence, Reversible Jump; Markov Chain Monte Carlo; Spectral density
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