Local asymptotic normality for Student-Levy processes under high-frequency sampling

There is considerable interest in parameter estimation in Levy models. The maximum likelihood estimator is widely used because under certain conditions it enjoys asymptotic efficiency properties. The toolkit for Levy processes is the local asymptotic normality which guarantees these conditions. Although the likelihood function is not known explicitly, we prove local asymptotic normality for the location and scale parameters of the Student-Levy process assuming high-frequency data. In addition, we propose a numerical method to make maximum likelihood estimates feasible based on the Monte Carlo expectation-maximization algorithm. A simulation study verifies the theoretical results.