An Analytical EM Algorithm for Sub-Gaussian Vectors

Audrius Kabašinskas, Leonidas Sakalauskas and Ingrida Vaičiulytė
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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

Mathematics, 2021, vol. 9, issue 9, 1-20

Abstract: The area in which a multivariate ? -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 ? -stable subordinator. This paper introduces an analytical expectation maximization (EM) algorithm for the estimation of parameters of symmetric multivariate ? -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 ? -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.

Keywords: EM algorithm; maximum likelihood method; statistical modeling; ?-stable distribution; crypto-currency (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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