X-13ARIMA-SEATS Seasonal Adjustment Program

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

---

• Back to Seasonal Adjustment Papers page
• Download PDF file (about 321K)

---

⁽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.