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A Bayesian Approach to Estimating the Long Memory Parameter

Scott Holan(1), Tucker S. McElroy(2), Sounak Chakraborty(3)

ABSTRACT:

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.

KEYWORDS:

Adaptive model selection, Bayesian model averaging; FEXP; Hierarchical Bayes; Long-range dependence, Reversible Jump; Markov Chain Monte Carlo; Spectral density





(1) Scott Holan is a professor in the Department of Statistics, University of Missouri-Columbia.

(2) Tucker S. McElroy is Mathematical Statistican, Center for Statistical Research and Methodology U. S. Census Bureau, 4600 Silver Hill Road, Washington, DC 20233. email : Tucker.S.McElroy@census.gov

(3) Sounak Chakraborty is a professor in the Department of Statistics, University of Missouri-Columbia.



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Source: U.S. Census Bureau | Center for Statistical Research and Methodology | (301) 763-1649 (or x12@census.gov) |  Last Revised: November 19, 2012