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Testing new property of elliptical model for stock returns distribution

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  • Petr Koldanov

Abstract

Wide class of elliptically contoured distributions is a popular model of stock returns distribution. However the important question of adequacy of the model is open. There are some results which reject and approve such model. Such results are obtained by testing some properties of elliptical model for each pair of stocks from some markets. New property of equality of $\tau$ Kendall correlation coefficient and probability of sign coincidence for any pair of random variables with elliptically contoured distribution is proved in the paper. Distribution free statistical tests for testing this property for any pair of stocks are constructed. Holm multiple hypotheses testing procedure based on the individual tests is constructed and applied for stock markets data for the concrete year. New procedure of testing the elliptical model for stock returns distribution for all years of observation for some period is proposed. The procedure is applied for the stock markets data of China, USA, Great Britain and Germany for the period from 2003 to 2014. It is shown that for USA, Great Britain and Germany stock markets the hypothesis of elliptical model of stock returns distribution could be accepted but for Chinese stock market is rejected for some cases.

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  • Petr Koldanov, 2019. "Testing new property of elliptical model for stock returns distribution," Papers 1907.10306, arXiv.org.
    • Handle: RePEc:arx:papers:1907.10306
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    References listed on IDEAS

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    1. Rémy Chicheportiche & Jean-Philippe Bouchaud, 2012. "The Joint Distribution Of Stock Returns Is Not Elliptical," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(03), pages 1-23.
    2. Rémy Chicheportiche & Jean-Philippe Bouchaud, 2012. "The joint distribution of stock returns is not elliptical," Post-Print hal-00703720, HAL.
    3. R'emy Chicheportiche & Jean-Philippe Bouchaud, 2010. "The joint distribution of stock returns is not elliptical," Papers 1009.1100, arXiv.org, revised Jun 2012.
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    Cited by:

    1. Koldanov, A. & Koldanov, P. & Semenov, D., 2021. "Confidence set for connected stocks of stock market," Journal of the New Economic Association, New Economic Association, vol. 50(2), pages 12-34.

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