The class of generalized hyperbolic (GH) distributions is generated by a mean-variance mixture of a multivariate Gaussian with a generalized inverse Gaussian (GIG) distribution. This rich family of GH distributions includes some well-known heavy-tailed and symmetric multivariate distributions, including the Normal Inverse Gaussian and some members of the family of scale-mixture of skew-normal distributions. The class of GH distributions has received considerable attention in finance and signal processing applications. In this paper, we propose the likelihood ratio (LR) test to test hypotheses about the skewness parameter of a GH distribution. Due to the complexity of the likelihood function, the EM algorithm is used to find the maximum likelihood estimates both in the complete model and the reduced model. For comparative purposes and due to its simplicity, we also consider the Gradient (G) test. A simulation study shows that the LR and G tests are usually able to achieve the desired significance levels and the testing power increases as the asymmetry increases. The methodology developed in the paper is applied to two real datasets.
We acknowledge the partial financial support from Project Fondecyt 1150325 (Chile), FAPEMIG (Brazil) and CNPq (Brazil).
"Hypotheses tests on the skewness parameter in a multivariate generalized hyperbolic distribution." Braz. J. Probab. Stat. 35 (3) 630 - 655, August 2021. https://doi.org/10.1214/21-BJPS502