Model Selection for Broadband Semiparametric Estimation of Long Memory in Time Series

31 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

Date Written: March 1999

Abstract

We study the properties of Mallows’ CL criterion for selecting a fractional exponential (FEXP) model for a Gaussian long-memory time series. The aim is to minimize the mean squared error of a corresponding regression estimator dFEXP of the memory parameter, d. Under conditions which do not require that the data were actually generated by a FEXP model, it is known that the mean squared error MSE = E[dFEXP – d]² can converge to zero as fast as (log n)/n, where n is the sample size, assuming that the number of parameters grows slowly with n in a deterministic fashion. Here, we suppose that the number of parameters in the FEXP model is chosen so as to minimize a local version of CL, restricted to frequencies in a neighborhood of zero. We show that, under appropriate conditions, the expected value of the local CL is asymptotically equivalent to MSE. A combination of theoretical and simulation results give guidance as to the choice of the degree of locality in CL.

Suggested Citation

Hurvich, Clifford M., Model Selection for Broadband Semiparametric Estimation of Long Memory in Time Series (March 1999). NYU Working Paper No. 2451/14783. Available at SSRN: https://ssrn.com/abstract=1290961

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

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