Normal variance-mean mixtures (II) - a multivariate moment method

Abstract

A moment method for the multivariate variance-mean mixture model is considered. Besides mean and covariance the method uses the coskewness and cokurtosis tensors. Its algorithmic implementation depends upon the solution of a sextic equation. Explicit formulas for the normal inverse Gaussian, the gamma, the inverse gamma and the classical tempered stable mixing distributions are included. An application to the statistical estimation of bivariate stock market indices is given. The models are successfully fitted to seven bivariate daily data sets over different time periods. The goodness-of-fit of the margins are optimized and compared.