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Tests of Short Memory With Thick-Tailed Errors

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  • Christine Amsler
  • Peter Schmidt

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.

Suggested Citation

  • Christine Amsler & Peter Schmidt, 2011. "Tests of Short Memory With Thick-Tailed Errors," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(3), pages 381-390, November.
    • Handle: RePEc:taf:jnlbes:v:30:y:2011:i:3:p:381-390
    DOI: 10.1080/07350015.2012.669668
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