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An Analytical EM Algorithm for Sub-Gaussian Vectors

Author

Listed:
  • Audrius Kabašinskas

    (Faculty of Mathematics and Natural Sciences, Kaunas University of Technology, 51368 Kaunas, Lithuania)

  • Leonidas Sakalauskas

    (Šiauliai Academy, Vilnius University, 76352 Šiauliai, Lithuania)

  • Ingrida Vaičiulytė

    (Faculty of Business and Technologies, Šiauliai State College, 76241 Šiauliai, Lithuania)

Abstract

The area in which a multivariate α -stable distribution could be applied is vast; however, a lack of parameter estimation methods and theoretical limitations diminish its potential. Traditionally, the maximum likelihood estimation of parameters has been considered using a representation of the multivariate stable vector through a multivariate normal vector and an α -stable subordinator. This paper introduces an analytical expectation maximization (EM) algorithm for the estimation of parameters of symmetric multivariate α -stable random variables. Our numerical results show that the convergence of the proposed algorithm is much faster than that of existing algorithms. Moreover, the likelihood ratio (goodness-of-fit) test for a multivariate α -stable distribution was implemented. Empirical examples with simulated and real world (stocks, AIS and cryptocurrencies) data showed that the likelihood ratio test can be useful for assessing goodness-of-fit.

Suggested Citation

  • Audrius Kabašinskas & Leonidas Sakalauskas & Ingrida Vaičiulytė, 2021. "An Analytical EM Algorithm for Sub-Gaussian Vectors," Mathematics, MDPI, vol. 9(9), pages 1-20, April.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:9:p:945-:d:542075
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    References listed on IDEAS

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