Testing for Long Memory

30 Pages Posted: 10 Oct 2006

See all articles by David Harris

David Harris

University of Melbourne - Department of Economics

Brendan P.M. McCabe

University of Liverpool - Management School (ULMS)

Stephen J. Leybourne

University of Nottingham

Date Written: February 10, 2006

Abstract

This paper introduces a new test statistic for the null hypothesis of short memory against long memory alternatives. The novelty of our statistic is that it is based on only high order sample autocovariances and by construction eliminates the effects of nuisance parameters typically induced by short memory autocorrelation. For practically relevant situations where the short memory process is not directly observed, but instead appears as the disturbance term in a deterministic linear regression model, we are able to demonstrate that our residual-based statistic has an asymptotic standard normal distribution under the null hypothesis. We also establish consistency of the statistic under long memory alternatives. The finite sample properties of our procedure are compared to other well-known tests in the literature via Monte Carlo simulations. These show that the empirical size properties of the new statistic can be very robust compared to existing tests and also that it competes well in terms of power.

Keywords: Short memory, long memory, fractional processes, asymptotic normality

JEL Classification: C22

Suggested Citation

Harris, David and McCabe, Brendan P.M. and Leybourne, Stephen J., Testing for Long Memory (February 10, 2006). Available at SSRN: https://ssrn.com/abstract=936267 or http://dx.doi.org/10.2139/ssrn.936267

David Harris (Contact Author)

University of Melbourne - Department of Economics ( email )

Melbourne, 3010
Australia

Brendan P.M. McCabe

University of Liverpool - Management School (ULMS) ( email )

Chatham Street
Liverpool, L69 7ZH
United Kingdom

Stephen J. Leybourne

University of Nottingham ( email )

University Park
School of Economics
Nottingham NG7 2RD
United Kingdom
+44 (0)115 9515478 (Phone)
+44 (0)115 951 4159 (Fax)

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