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Leptokurtic moment-parameterized elliptically contoured distributions with application to financial stock returns

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  • Luca Bagnato
  • Antonio Punzo
  • Maria Grazia Zoia

Abstract

This article shows how multivariate elliptically contoured (EC) distributions, parameterized according to the mean vector and covariance matrix, can be built from univariate standard symmetric distributions. The obtained distributions are referred to as moment-parameterized EC (MEC) herein. As a further novelty, the article shows how to polynomially reshape MEC distributions and obtain distributions, called leptokurtic MEC (LMEC), having probability density functions characterized by a further parameter expressing their excess kurtosis with respect to the parent MEC distributions. Two estimation methods are discussed: the method of moments and the maximum likelihood. For illustrative purposes, normal, Laplace, and logistic univariate densities are considered to build MEC and LMEC models. An application to financial returns of a set of European stock indexes is finally presented.

Suggested Citation

  • Luca Bagnato & Antonio Punzo & Maria Grazia Zoia, 2022. "Leptokurtic moment-parameterized elliptically contoured distributions with application to financial stock returns," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 51(2), pages 486-500, January.
    • Handle: RePEc:taf:lstaxx:v:51:y:2022:i:2:p:486-500
    DOI: 10.1080/03610926.2020.1751202
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    Cited by:

    1. Ryan P. Browne & Luca Bagnato & Antonio Punzo, 2024. "Parsimony and parameter estimation for mixtures of multivariate leptokurtic-normal distributions," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 18(3), pages 597-625, September.

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