An EM algorithm for maximum likelihood estimation of Barndorff-Nielsen's generalized hyperbolic distribution

Abstract

We present an EM algorithm for Maximum Likelihood (ML) estimation of the location, structure matrix, skew or drift, and shape parameters of Barndorff-Nielsen's Generalized Hyperbolic distribution, which is the Gaussian Location Scale mixture (or Normal Variance Mean Mixture) with Generalized Inverse Gaussian (GIG) scale mixing distribution. We use the GLSM representation along with the closed form posterior expectations possible with the GIG distribution to derive an EM algorithm for computing ML parameter estimates.