Estimation of Long Memory in the Presence of a Smooth Nonparametric Trend

28 Pages Posted: 3 Nov 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

Gabriel Lang

INRA-AgroParisTech - Department Mathematical Modeling

Philippe Soulier

Université d'Évry

Date Written: July 2002

Abstract

We consider semi parametric estimation of the long-memory parameter of a stationaryprocess in the presence of an additive nonparametric mean function. We use a semi parametric Whittle type estimator, applied to the tapered, differenced series. Since the mean function is not necessarily apolynomial of finite order, no amount of differencing will completely remove the mean. We establish a central limit theorem for the estimator of the memory parameter, assuming that a slowly increasing number of low frequencies are trimmed from the estimator's objective function. We find in simulationsthat tapering and trimming are essential for the good performance of the estimator in practice.

Keywords: Nonparametric regression, long-range dependence, tapering, periodogram

Suggested Citation

Hurvich, Clifford M. and Lang, Gabriel and Soulier, Philippe, Estimation of Long Memory in the Presence of a Smooth Nonparametric Trend (July 2002). Statistics Working Papers Series, Vol. , pp. -, 2002. Available at SSRN: https://ssrn.com/abstract=1293617

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

Gabriel Lang

INRA-AgroParisTech - Department Mathematical Modeling

AgroParisTech
16 rue Claude Bernard
Paris, Cedex 05 F-75231
France

Philippe Soulier

Université d'Évry ( email )

F-91025 Evry Cedex
France
33 (0)1 69 47 02 28 (Phone)
33 (0)1 69 47 02 18 (Fax)

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