An Analytical EM Algorithm for Sub-Gaussian Vectors

【Author】 Kabasinskas, Audrius; Sakalauskas, Leonidas; Vaiciulyte, Ingrida

【Source】MATHEMATICS

【影响因子】2.592

【Abstract】The area in which a multivariate alpha-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 alpha-stable subordinator. This paper introduces an analytical expectation maximization (EM) algorithm for the estimation of parameters of symmetric multivariate alpha-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 alpha-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; alpha-stable distribution; crypto-currency

【发表时间】2021 MAY

【收录时间】2022-01-02

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