Tests of Short Memory With Thick-Tailed Errors

Christine Amsler and Peter Schmidt

Journal of Business & Economic Statistics, 2011, vol. 30, issue 3, 381-390

Abstract: In this article, we consider the robustness to fat tails of four stationarity tests. We also consider their sensitivity to the number of lags used in long-run variance estimation, and the power of the tests. Lo's modified rescaled range (MR/S) test is not very robust. Choi's Lagrange multiplier (LM) test has excellent robustness properties but is not generally as powerful as the Kwiatkowski--Phillips--Schmidt--Shin (KPSS) test. As an analytical framework for fat tails, we suggest local-to-finite variance asymptotics, based on a representation of the process as a weighted sum of a finite variance process and an infinite variance process, where the weights depend on the sample size and a constant. The sensitivity of the asymptotic distribution of a test to the weighting constant is a good indicator of its robustness to fat tails. This article has supplementary material online.

Date: 2011
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DOI: 10.1080/07350015.2012.669668

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