TY - JOUR
T1 - Leptokurtic moment-parameterized elliptically contoured distributions with application to financial stock returns
AU - Bagnato, Luca
AU - Punzo, Antonio
AU - Zoia, Maria
PY - 2022
Y1 - 2022
N2 - 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.
AB - 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.
KW - Elliptical distributions
KW - excess kurtosis
KW - financial returns
KW - moments
KW - orthogonal polynomials
KW - Elliptical distributions
KW - excess kurtosis
KW - financial returns
KW - moments
KW - orthogonal polynomials
UR - http://hdl.handle.net/10807/156095
U2 - 10.1080/03610926.2020.1751202
DO - 10.1080/03610926.2020.1751202
M3 - Article
SN - 0361-0926
VL - 51
SP - 486
EP - 500
JO - Communications in Statistics - Theory and Methods
JF - Communications in Statistics - Theory and Methods
ER -