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Highly flexible distributions to fit multiple frequency financial returns

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  • BenSaïda, Ahmed
  • Slim, Skander

Abstract

Financial data are usually studied via low flexible distributions, independently of the frequency of the data, due to their simplicity and analytical tractability. In this paper we analyze two highly flexible five-parameter distributions into fitting financial returns, these are the skewed generalized t (SGT) and the generalized hyperbolic (GH). Applications carried on two exchange rates (Euro–Dollar and Dollar–Yen), and two indexes (S&P 500 and Nikkei 225) over four frequencies: weekly, daily, 30-min and 5-min, confirm the superiority of the SGT and GH in approximating the distribution of a given data at a remarkable precision. Moreover, as we move from higher to lower frequency, the distribution’s overall shape does indeed change radically, and the estimated parameters refute the tendency to normality, which calls into question the aggregational Gaussianity’s stylized fact.

Suggested Citation

  • BenSaïda, Ahmed & Slim, Skander, 2016. "Highly flexible distributions to fit multiple frequency financial returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 442(C), pages 203-213.
    • Handle: RePEc:eee:phsmap:v:442:y:2016:i:c:p:203-213
    DOI: 10.1016/j.physa.2015.09.021
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    1. Panayiotis Theodossiou, 1998. "Financial Data and the Skewed Generalized T Distribution," Management Science, INFORMS, vol. 44(12-Part-1), pages 1650-1661, December.
    2. Eling, Martin, 2014. "Fitting asset returns to skewed distributions: Are the skew-normal and skew-student good models?," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 45-56.
    3. McDonald, James B. & Xu, Yexiao J., 1995. "A generalization of the beta distribution with applications," Journal of Econometrics, Elsevier, vol. 69(2), pages 427-428, October.
    4. Fajardo, José & Farias, Aquiles, 2009. "Multivariate affine generalized hyperbolic distributions: An empirical investigation," International Review of Financial Analysis, Elsevier, vol. 18(4), pages 174-184, September.
    5. 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.
    6. Theodossiou, Panayiotis & McDonald, James B. & Hansen, Christian B., 2007. "Some Flexible Parametric Models for Partially Adaptive Estimators of Econometric Models," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 1, pages 1-20.
    7. Tina Hviid Rydberg, 2000. "Realistic Statistical Modelling of Financial Data," International Statistical Review, International Statistical Institute, vol. 68(3), pages 233-258, December.
    8. McDonald, James B. & Newey, Whitney K., 1988. "Partially Adaptive Estimation of Regression Models via the Generalized T Distribution," Econometric Theory, Cambridge University Press, vol. 4(3), pages 428-457, December.
    9. David Scott & Diethelm Würtz & Christine Dong & Thanh Tran, 2011. "Moments of the generalized hyperbolic distribution," Computational Statistics, Springer, vol. 26(3), pages 459-476, September.
    10. Anagnostidis, Panagiotis & Emmanouilides, Christos J., 2015. "Nonlinearity in high-frequency stock returns: Evidence from the Athens Stock Exchange," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 421(C), pages 473-487.
    11. Marsaglia, George & Marsaglia, John, 2004. "Evaluating the Anderson-Darling Distribution," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 9(i02).
    12. Antypas, Antonios & Koundouri, Phoebe & Kourogenis, Nikolaos, 2013. "Aggregational Gaussianity and barely infinite variance in financial returns," Journal of Empirical Finance, Elsevier, vol. 20(C), pages 102-108.
    13. Richard D. F. Harris & C. Coskun Küçüközmen, 2001. "The Empirical Distribution of UK and US Stock Returns," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 28(5‐6), pages 715-740, June.
    14. Hansen, Bruce E, 1994. "Autoregressive Conditional Density Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(3), pages 705-730, August.
    15. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    16. Turan Bali & Panayiotis Theodossiou, 2007. "A conditional-SGT-VaR approach with alternative GARCH models," Annals of Operations Research, Springer, vol. 151(1), pages 241-267, April.
    17. BenSaïda, Ahmed, 2015. "The frequency of regime switching in financial market volatility," Journal of Empirical Finance, Elsevier, vol. 32(C), pages 63-79.
    18. Kumar, Dilip, 2014. "Long range dependence in the high frequency USD/INR exchange rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 396(C), pages 134-148.
    19. James Mcdonald & Richard Michelfelder & Panayiotis Theodossiou, 2010. "Robust estimation with flexible parametric distributions: estimation of utility stock betas," Quantitative Finance, Taylor & Francis Journals, vol. 10(4), pages 375-387.
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    1. Brendan K. Beare & Juwon Seo, 2022. "Stochastic arbitrage with market index options," Papers 2207.00949, arXiv.org, revised Jul 2022.
    2. Ahmed BenSaïda & Houda Litimi, 2021. "Financial contagion across G10 stock markets: A study during major crises," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 26(3), pages 4798-4821, July.
    3. Luo, Min & Kontosakos, Vasileios E. & Pantelous, Athanasios A. & Zhou, Jian, 2019. "Cryptocurrencies: Dust in the wind?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 1063-1079.
    4. BenSaïda, Ahmed, 2018. "The contagion effect in European sovereign debt markets: A regime-switching vine copula approach," International Review of Financial Analysis, Elsevier, vol. 58(C), pages 153-165.
    5. Dangxing Chen, 2019. "Does the leverage effect affect the return distribution?," Papers 1909.08662, arXiv.org, revised Sep 2019.
    6. Ahmed BenSaïda, 2021. "The Good and Bad Volatility: A New Class of Asymmetric Heteroskedastic Models," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 83(2), pages 540-570, April.
    7. Sikora, Grzegorz & Michalak, Anna & Bielak, Łukasz & Miśta, Paweł & Wyłomańska, Agnieszka, 2019. "Stochastic modeling of currency exchange rates with novel validation techniques," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1202-1215.
    8. Szarek, Dawid & Bielak, Łukasz & Wyłomańska, Agnieszka, 2020. "Long-term prediction of the metals’ prices using non-Gaussian time-inhomogeneous stochastic process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).
    9. Slim, Skander & Koubaa, Yosra & BenSaïda, Ahmed, 2017. "Value-at-Risk under Lévy GARCH models: Evidence from global stock markets," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 46(C), pages 30-53.
    10. Ahmed BenSaïda & Sabri Boubaker & Duc Khuong Nguyen & Skander Slim, 2018. "Value‐at‐risk under market shifts through highly flexible models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 37(8), pages 790-804, December.

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