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Testing for long memory in the presence of a general trend

Part of: Limit theorems Inference from stochastic processes Applications Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Liudas Giraitis ,
Piotr Kokoszka  and
Remigijus Leipus
Liudas Giraitis*
Affiliation:
London School of Economics
Piotr Kokoszka*
Affiliation:
University of Liverpool
Remigijus Leipus*
Affiliation:
Vilnius University
*
∗ Postal address: Department of Economics, London School of Economics, Houghton Street, London WC2A 2AE, UK. Email address: l.giraitis@lse.ac.uk
∗∗ Postal address: Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, UK.
∗∗∗ Postal address: Department of Mathematics and Informatics, Vilnius University, Naugarduko 24, Vilnius 2600, Lithuania.
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Abstract

The paper studies the impact of a broadly understood trend, which includes a change point in mean and monotonic trends studied by Bhattacharya et al. (1983), on the asymptotic behaviour of a class of tests designed to detect long memory in a stationary sequence. Our results pertain to a family of tests which are similar to Lo's (1991) modified R/S test. We show that both long memory and nonstationarity (presence of trend or change points) can lead to rejection of the null hypothesis of short memory, so that further testing is needed to discriminate between long memory and some forms of nonstationarity. We provide quantitative description of trends which do or do not fool the R/S-type long memory tests. We show, in particular, that a shift in mean of a magnitude larger than N -½, where N is the sample size, affects the asymptotic size of the tests, whereas smaller shifts do not do so.

Keywords

Long memorytrendchange point

MSC classification

Primary: 62M10: Time series, auto-correlation, regression, etc.
Secondary: 62P20: Applications to economics 60G10: Stationary processes 60G50: Sums of independent random variables; random walks 60F17: Functional limit theorems; invariance principles

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 38 , Issue 4 , December 2001 , pp. 1033 - 1054
Copyright
Copyright © by the Applied Probability Trust 2001 

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