20162016-04-21 , Faculty of Mathematics, Kyushu University
We address parametric estimation of both trend and scale coefficients of a pure-jump Levy driven univariate stochastic differential equation (SDE) model based on high-frequency data over a fixed time period. The conventional Gaussian quasi-maximum likelihood estimator is known to be inconsistent. In this paper, under the assumption that the driving Levy process is locally stable, we propose a novel quasi-likelihood function based on the small-time non-Gaussian stable approximation of the unknown transition density. The resulting estimator is shown to be asymptotically mixed-normally distributed and remarkably more efficient than the Gaussian quasi-maximum likelihood estimator. We need neither ergodicity nor existence of finite moments. Compared with the existing methods for estimating SDE models, the proposed quasi-likelihood enables us to achieve better performance in a unified manner for a wide range of the driving Levy processes.