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Compound distributions for financial returns

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Listed:
  • Emmanuel Afuecheta
  • Artur Semeyutin
  • Stephen Chan
  • Saralees Nadarajah
  • Diego Andrés Pérez Ruiz

Abstract

In this paper, we propose six Student’s t based compound distributions where the scale parameter is randomized using functional forms of the half normal, Fréchet, Lomax, Burr III, inverse gamma and generalized gamma distributions. For each of the proposed distribution, we give expressions for the probability density function, cumulative distribution function, moments and characteristic function. GARCH models with innovations taken to follow the compound distributions are fitted to the data using the method of maximum likelihood. For the sample data considered, we see that all but two of the proposed distributions perform better than two popular distributions. Finally, we perform a simulation study to examine the accuracy of the best performing model.

Suggested Citation

  • Emmanuel Afuecheta & Artur Semeyutin & Stephen Chan & Saralees Nadarajah & Diego Andrés Pérez Ruiz, 2020. "Compound distributions for financial returns," PLOS ONE, Public Library of Science, vol. 15(10), pages 1-25, October.
    • Handle: RePEc:plo:pone00:0239652
    DOI: 10.1371/journal.pone.0239652
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    References listed on IDEAS

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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. M. C. Jones & M. J. Faddy, 2003. "A skew extension of the t‐distribution, with applications," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 159-174, February.
    3. Bauwens, Luc & Laurent, Sebastien, 2005. "A New Class of Multivariate Skew Densities, With Application to Generalized Autoregressive Conditional Heteroscedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 346-354, July.
    4. 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.
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