Plug-In Selection of the Number of Frequencies in Regression Estimates of the Memory Parameter of a Long-Memory Time Series

11 Pages Posted: 31 Oct 2008

See all articles by Clifford M. Hurvich

Clifford M. Hurvich

Stern School of Business, New York University; New York University (NYU) - Department of Information, Operations, and Management Sciences

Rohit Deo

Stern School of Business, New York University

Date Written: July 1998

Abstract

We consider the problem of selecting the number of frequencies, m, in a log-periodogram regression estimator of the memory parameter d of a Gaussian long-memory time series. It is known that under certain conditions the optimal m, minimizing the mean squared error of the corresponding estimator of d, is given by m(opt) = Cn4/5, where n is the sample size and C is a constant. In practice, C would be unknown since it depends on the properties of the spectral density near zero frequency. In this paper, we propose an estimator of C based again on a log-periodogram regression and derive its consistency. We also derive an asymptotically valid confidence interval for d when the number of frequencies used in the regression is deterministic and proportional to n4/5. In this case, squared bias cannot be neglected since it is of the same order as the variance. In a Monte Carlo study, we examine the performance of the plug-in estimator of d, in which m is obtained by using the estimator of C in the formula for m(opt) above. We also study the performance of a bias-corrected version of the plug-in estimator of d. Comparisons with the choice m = n½ frequencies, as originally suggested by Geweke and Porter-Hudak.

Keywords: Periodogram, bandwith

Suggested Citation

Hurvich, Clifford M. and Deo, Rohit, Plug-In Selection of the Number of Frequencies in Regression Estimates of the Memory Parameter of a Long-Memory Time Series (July 1998). NYU Working Paper No. 2451/14773. Available at SSRN: https://ssrn.com/abstract=1290234

Clifford M. Hurvich (Contact Author)

Stern School of Business, New York University ( email )

44 West 4th Street
New York, NY 10012-1126
United States

New York University (NYU) - Department of Information, Operations, and Management Sciences

44 West Fourth Street
New York, NY 10012
United States

Rohit Deo

Stern School of Business, New York University ( email )

44 West Fourth Street
New York, NY 10012
United States

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