Research Reports

A Bayesian Approach to Estimating the Long Memory Parameter

Scott Holan, Tucker McElroy, Sounak Chakraborty

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

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 {\it 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.

CITATION:

Source: U.S. Census Bureau, Statistical Research Division

Created: October 19, 2007
Last revised: October 19, 2007