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

Luca Bagnato, Maria Zoia, Antonio Punzo

Research output: Contribution to journalArticle

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.
Original languageEnglish
Pages (from-to)1-15
Number of pages15
JournalCOMMUNICATIONS IN STATISTICS. THEORY AND METHODS
DOIs
Publication statusPublished - 2020

Keywords

  • Elliptical distributions
  • excess kurtosis
  • financial returns
  • moments
  • orthogonal polynomials

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