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March 2009 A Bayesian approach to estimating the long memory parameter
Sounak Chakraborty, Scott Holan, Tucker McElroy
Bayesian Anal. 4(1): 159-190 (March 2009). DOI: 10.1214/09-BA406


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. In particular, we propose a hierarchical Bayesian model and make it fully adaptive by imposing a prior distribution on the model order. Further, we describe a reversible jump Markov chain Monte Carlo algorithm for variable dimension estimation and show that, in our context, the algorithm provides a reasonable method of model selection (within each repetition of the chain). Therefore, through an application of Bayesian model averaging, we incorporate all possible models from the FEXP class (up to a given finite order). As a result we reduce the underestimation of uncertainty at the model-selection stage as well as achieve better estimates of the long memory parameter. Additionally, we establish Bayesian consistency of the memory parameter under mild conditions on the data process. Finally, through simulation and the analysis of two data sets, we demonstrate the effectiveness of our approach.


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Sounak Chakraborty. Scott Holan. Tucker McElroy. "A Bayesian approach to estimating the long memory parameter." Bayesian Anal. 4 (1) 159 - 190, March 2009.


Published: March 2009
First available in Project Euclid: 22 June 2012

zbMATH: 1330.62136
MathSciNet: MR2486243
Digital Object Identifier: 10.1214/09-BA406

Keywords: Bayesian model averaging , FEXP , hierarchical Bayes , long-range dependence , reversible jump Markov chain Monte Carlo , Spectral density

Rights: Copyright © 2009 International Society for Bayesian Analysis


Vol.4 • No. 1 • March 2009
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