Testing Symmetry of a NIG Distribution

Abstract

Heavy-tailed and skewed distributions have recently appeared in many empirical financial studies and many researchers have found that the normal inverse Gaussian (NIG) distribution fits these stylized nonnormal data well and is at the same time analytically tractable. In this article, we propose a likelihood ratio test (LRT) for symmetry of a NIG distribution. Due to the complexity of the likelihood function, an EM type algorithm proposed by Karlis (2002) is used to find the maximum likelihood estimates of the NIG distribution. The conclusions from a simulation study show that the LRT is usually able to achieve the desired significance levels and the testing power increases as the asymmetry increases, i.e., the proposed LRT is successful in detecting the asymmetric behavior of the NIG distribution.