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The impact of fat-tailed distributions on some leading unit roots tests

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  • K. D. Patterson
  • S. M. Heravi

Abstract

There is substantial evidence that many time series associated with financial and insurance claim data are fat-tailed, with a (much) higher probability of " outliers' compared with the normal distribution. However, standard tests, or variants of them, for the presence of unit roots assume a normal distribution for the innovations driving the series. Application of the former to the latter therefore involves an inconsistency. We assess the impact of this inconsistency and provide information on its impact on inference when innovations are drawn from the Cauchy and sequence of t(v) distributions. A simple prediction that fat tails will uniformly lead to over-sizing of standard tests (because the fatness in the tail translates to the test distribution) turns out to be incorrect: we find that some tests are over-sized but some are under-sized. We also consider size retention and the power of the Dickey-Fuller pivotal and normalized bias test statistics and weighted symmetric versions of these tests. To make the unit root testing procedure feasible, we develop an entropy-based test for some fat-tailed distributions and apply it to share prices from the FTSE100.

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  • K. D. Patterson & S. M. Heravi, 2003. "The impact of fat-tailed distributions on some leading unit roots tests," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(6), pages 635-667.
    • Handle: RePEc:taf:japsta:v:30:y:2003:i:6:p:635-667
    DOI: 10.1080/0266476032000053736
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    Cited by:

    1. Fatma Ozgu Serttas, 2018. "Infinite-Variance Error Structure in Finance and Economics," International Econometric Review (IER), Econometric Research Association, vol. 10(1), pages 14-23, April.
    2. repec:ebl:ecbull:v:3:y:2008:i:38:p:1-10 is not listed on IDEAS
    3. D. M. Mahinda Samarakoon & Keith Knight, 2009. "A Note on Unit Root Tests with Infinite Variance Noise," Econometric Reviews, Taylor & Francis Journals, vol. 28(4), pages 314-334.
    4. Shafique Ur Rehman & Touqeer Ahmad & Wu Dash Desheng & Amirhossein Karamoozian, 2024. "Analyzing selected cryptocurrencies spillover effects on global financial indices: Comparing risk measures using conventional and eGARCH-EVT-Copula approaches," Papers 2407.15766, arXiv.org.
    5. Serttas, Fatma Ozgu, 2010. "Essays on infinite-variance stable errors and robust estimation procedures," ISU General Staff Papers 201001010800002742, Iowa State University, Department of Economics.
    6. K. Patterson & Saeed Heravi, 2003. "Weighted symmetric tests for a unit root: response functions, power, test dependence and test conflict," Applied Economics, Taylor & Francis Journals, vol. 35(7), pages 779-790.

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