Estimation for multivariate stable distributions with generalized empirical likelihood

Abstract

This paper considers the generalized empirical likelihood (GEL) method for estimating the parameters of the multivariate stable distribution. The GEL method is considered to be an extension of the generalized method of moments (GMM). The multivariate stable distributions are widely applicable as they can accommodate both skewness and heavy tails. We treat the spectral measure, which summarizes scale and asymmetry, by discretization. In order to estimate all the model parameters simultaneously, we apply the estimating function constructed by equating empirical and theoretical characteristic functions. The efficacy of the proposed GEL method is demonstrated in Monte Carlo studies. An illustrative example involving daily returns of market indexes is also included.