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ON DISTINGUISHING BETWEEN RANDOM WALK AND CHANGE IN THE MEAN ALTERNATIVES

Published online by Cambridge University Press:  01 April 2009

Alexander Aue ,
Lajos Horváth ,
Marie Hušková  and
Shiqing Ling
Alexander Aue*
Affiliation:
University of California, Davis
Lajos Horváth
Affiliation:
University of Utah
Marie Hušková
Affiliation:
Charles University
Shiqing Ling
Affiliation:
Hong Kong University of Science and Technology
*
*Address correspondence to Alexander Aue, Department of Statistics, University of California, Davis, One Shields Avenue, Davis, CA 95616, USA; e-mail: alexaue@wald.ucdavis.edu.
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Abstract

We study test procedures that detect structural breaks in underlying data sequences. In particular, we wish to discriminate between different reasons for these changes, such as (1) shifting means, (2) random walk behavior, and (3) constant means but innovations switching from stationary to difference stationary behavior. Almost all procedures presently available in the literature are simultaneously sensitive to all three types of alternatives.

The test statistics under investigation are based on functionals of the partial sums of observations. These cumulative sum–type (CUSUM-type) statistics have limit distributions if the mean remains constant and the errors satisfy the central limit theorem but tend to infinity in the case when any of the alternatives (1), (2), or (3) holds. On removing the effect of the shifting mean, however, divergence of the test statistics will only occur under the random walk behavior, which in turn enables statisticians not only to detect structural breaks but also to specify their causes.

The results are underlined by a simulation study and an application to returns of the German stock index DAX.

Type
ARTICLES
Information
Econometric Theory , Volume 25 , Issue 2 , April 2009 , pp. 411 - 441
Copyright
Copyright © Cambridge University Press 2009

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