Test of fit for a Laplace distribution against heavier tailed alternatives
Over the last decade there has been a marked interest in a Laplace distribution and its properties and generalizations, especially in the framework of financial applications. Such an interest has led to a revision and discussion of available goodness-of-fit procedures for a Laplace distribution. Indeed, since most of the studies which employ the Laplace distribution are concerned with modelling heavy tailed patterns, the modern class of possible alternatives is way broader than just testing the Laplace vs. normal distribution. In this paper we propose a new test of fit for a Laplace distribution against deviations with heavier tails than that of the reference Laplace distribution. The proposed goodness-of-fit procedure is based on sample skewness and kurtosis and a robust L1 estimator of scale about a sample median. The developed test statistic is shown to asymptotically follow a [chi]2-distribution with two degrees of freedom. Performance of the new goodness-of-fit test is illustrated by simulations and a case study.
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- Markus Haas & Stefan Mittnik & Marc Paolella, 2006.
"Modelling and predicting market risk with Laplace-Gaussian mixture distributions,"
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- Thorsten Thadewald & Herbert Buning, 2007. "Jarque-Bera Test and its Competitors for Testing Normality - A Power Comparison," Journal of Applied Statistics, Taylor & Francis Journals, vol. 34(1), pages 87-105.
- Stefan Mittnik & Marc Paolella & Svetlozar Rachev, 1998. "Unconditional and Conditional Distributional Models for the Nikkei Index," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 5(2), pages 99-128, May.
- Best, D.J. & Rayner, J.C.W. & Thas, O., 2008. "Comparison of some tests of fit for the Laplace distribution," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5338-5343, August.
- Linden, Mikael, 2001. "A Model for Stock Return Distribution," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 6(2), pages 159-169, April.
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- Ole E. Barndorff-Nielsen, 1997. "Processes of normal inverse Gaussian type," Finance and Stochastics, Springer, vol. 2(1), pages 41-68. Full references (including those not matched with items on IDEAS)
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