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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
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    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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    File URL: http://www.tandfonline.com/doi/abs/10.1080/0266476032000053736
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    Bibliographic Info

    Article provided by Taylor & Francis Journals in its journal Journal of Applied Statistics.

    Volume (Year): 30 (2003)
    Issue (Month): 6 ()
    Pages: 635-667

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    Handle: RePEc:taf:japsta:v:30:y:2003:i:6:p:635-667

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    1. Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
    2. James G. MacKinnon, 1990. "Critical Values for Cointegration Tests," Working Papers 1227, Queen's University, Department of Economics.
    3. Peter C.B. Phillips, 1989. "Time Series Regression with a Unit Root and Infinite Variance Errors," Cowles Foundation Discussion Papers 897R, Cowles Foundation for Research in Economics, Yale University, revised Aug 1989.
    4. Tucker, Alan L, 1992. "A Reexamination of Finite- and Infinite-Variance Distributions as Models of Daily Stock Returns," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(1), pages 73-81, January.
    5. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    6. B. Mandelbrot, 1972. "Statistical Methodology For Nonperiodic Cycles: From The Covariance To Rs Analysis," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 1, number 3, pages 259-290 National Bureau of Economic Research, Inc.
    7. Dennis Jansen & Casper de Vries, 1988. "On the frequency of large stock returns: putting booms and busts into perspective," Working Papers 1989-006, Federal Reserve Bank of St. Louis.
    8. repec:cup:etheor:v:6:y:1990:i:1:p:44-62 is not listed on IDEAS
    9. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-72, June.
    10. Niels Haldrup & Peter Lildholdt, . "On the Robustness of Unit Root Tests in the Presence of Double Unit Roots," Economics Working Papers 2000-1, School of Economics and Management, University of Aarhus.
    11. Benoit Mandelbrot, 1967. "The Variation of Some Other Speculative Prices," The Journal of Business, University of Chicago Press, vol. 40, pages 393.
    12. Chan, Ngai Hang & Tran, Lanh Tat, 1989. "On the First-Order Autoregressive Process with Infinite Variance," Econometric Theory, Cambridge University Press, vol. 5(03), pages 354-362, December.
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    1. repec:ebl:ecbull:v:3:y:2008:i:38:p:1-10 is not listed on IDEAS

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