Parametric estimation of a bivariate stable Levy process

We propose a parametric model for a bivariate stable Levy process based on a Levy copula as a dependence model. We estimate the parameters of the full bivariate model by maximum likelihood estimation. As an observation scheme we assume that we observe all jumps larger than some epsilon > 0 and base our statistical analysis on the resulting compound Poisson process. We derive the Fisher information matrix and prove asymptotic normality of all estimates when the truncation point epsilon -> 0. A simulation study investigates the loss of efficiency because of the truncation. (c) 2011 Elsevier Inc. All rights reserved.