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Student’s t mixture models for stock indices. A comparative study

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  • Massing, Till
  • Ramos, Arturo

Abstract

We perform a comparative study for multiple equity indices of different countries using different models to determine the best fit using the Kolmogorov–Smirnov statistic, the Anderson–Darling statistic, the Akaike information criterion and the Bayesian information criteria as goodness-of-fit measures. We fit models both to daily and to hourly log-returns. The main result is the excellent performance of a mixture of three Student’s t distributions with the numbers of degrees of freedom fixed a priori (3St). In addition, we find that the different components of the 3St mixture with small/moderate/high degree of freedom parameter describe the extreme/moderate/small log-returns of the studied equity indices.

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  • Massing, Till & Ramos, Arturo, 2021. "Student’s t mixture models for stock indices. A comparative study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 580(C).
    • Handle: RePEc:eee:phsmap:v:580:y:2021:i:c:s0378437121004167
    DOI: 10.1016/j.physa.2021.126143
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    as
    1. Felipe Aparicio & Javier Estrada, 2001. "Empirical distributions of stock returns: European securities markets, 1990-95," The European Journal of Finance, Taylor & Francis Journals, vol. 7(1), pages 1-21.
    2. Kon, Stanley J, 1984. "Models of Stock Returns-A Comparison," Journal of Finance, American Finance Association, vol. 39(1), pages 147-165, March.
    3. Till Massing, 2019. "What is the best Lévy model for stock indices? A comparative study with a view to time consistency," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 33(3), pages 277-344, September.
    4. Göncü, Ahmet & Karahan, Mehmet Oğuz & Kuzubaş, Tolga Umut, 2016. "A comparative goodness-of-fit analysis of distributions of some Lévy processes and Heston model to stock index returns," The North American Journal of Economics and Finance, Elsevier, vol. 36(C), pages 69-83.
    5. Canan G. Corlu & Alper Corlu, 2015. "Modelling exchange rate returns: which flexible distribution to use?," Quantitative Finance, Taylor & Francis Journals, vol. 15(11), pages 1851-1864, November.
    6. Blattberg, Robert C & Gonedes, Nicholas J, 1974. "A Comparison of the Stable and Student Distributions as Statistical Models for Stock Prices," The Journal of Business, University of Chicago Press, vol. 47(2), pages 244-280, April.
    7. Eom, Cheoljun & Kaizoji, Taisei & Scalas, Enrico, 2019. "Fat tails in financial return distributions revisited: Evidence from the Korean stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 526(C).
    8. Massing, Till & Puente-Ajovín, Miguel & Ramos, Arturo, 2020. "On the parametric description of log-growth rates of cities’ sizes of four European countries and the USA," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
    9. Madan, Dilip B & Seneta, Eugene, 1990. "The Variance Gamma (V.G.) Model for Share Market Returns," The Journal of Business, University of Chicago Press, vol. 63(4), pages 511-524, October.
    10. Sieczka, Paweł & Hołyst, Janusz A., 2008. "Statistical properties of short term price trends in high frequency stock market data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(5), pages 1218-1224.
    11. Kjersti Aas & Ingrid Hobaek Haff, 2006. "The Generalized Hyperbolic Skew Student's t-Distribution," Journal of Financial Econometrics, Oxford University Press, vol. 4(2), pages 275-309.
    12. Cassidy, Daniel T., 2011. "Describing n-day returns with Student’s t-distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(15), pages 2794-2802.
    13. Bucsa, G. & Jovanovic, F. & Schinckus, C., 2011. "A unified model for price return distributions used in econophysics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(20), pages 3435-3443.
    14. Drożdż, S. & Forczek, M. & Kwapień, J. & Oświe¸cimka, P. & Rak, R., 2007. "Stock market return distributions: From past to present," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 383(1), pages 59-64.
    15. Stephen Chan & Jeffrey Chu & Saralees Nadarajah & Joerg Osterrieder, 2017. "A Statistical Analysis of Cryptocurrencies," JRFM, MDPI, vol. 10(2), pages 1-23, May.
    16. Zhang, Yuanyuan & Chu, Jeffrey & Chan, Stephen & Chan, Brandon, 2019. "The generalised hyperbolic distribution and its subclass in the analysis of a new era of cryptocurrencies: Ethereum and its financial risk," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 526(C).
    17. Praetz, Peter D, 1972. "The Distribution of Share Price Changes," The Journal of Business, University of Chicago Press, vol. 45(1), pages 49-55, January.
    18. Gillemot, L. & Töyli, J. & Kertesz, J. & Kaski, K., 2000. "Time-independent models of asset returns revisited," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 282(1), pages 304-324.
    19. S. Drozdz & M. Forczek & J. Kwapien & P. Oswiecimka & R. Rak, 2007. "Stock market return distributions: from past to present," Papers 0704.0664, arXiv.org.
    20. Jeffrey Chu & Saralees Nadarajah & Stephen Chan, 2015. "Statistical Analysis of the Exchange Rate of Bitcoin," PLOS ONE, Public Library of Science, vol. 10(7), pages 1-27, July.
    21. Cassidy, Daniel T. & Hamp, Michael J. & Ouyed, Rachid, 2010. "Pricing European options with a log Student’s t-distribution: A Gosset formula," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(24), pages 5736-5748.
    22. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    23. repec:dau:papers:123456789/3569 is not listed on IDEAS
    24. Saralees Nadarajah & Emmanuel Afuecheta & Stephen Chan, 2015. "A note on "Modelling exchange rate returns: which flexible distribution to use?"," Quantitative Finance, Taylor & Francis Journals, vol. 15(11), pages 1777-1785, November.
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