A1482
Title: Efficient estimation of stable-Levy SDEs with constant scale coefficient
Authors: Alexandre Brouste - Le Mans University (France)
Laurent Denis - Le Mans University (France)
Thi Bao Tram Ngo - University of Evry Val d Essonne (France) [presenting]
Abstract: The joint parametric estimation of the drift coefficient, the scale coefficient, and the jump activity index in stochastic differential equations driven by a symmetric stable Levy process are considered based on high-frequency observations. Firstly, the LAMN property for the corresponding Euler-type scheme is proven, and lower bounds for the estimation risk in this setting are deduced. Therefore, when the approximation scheme experiment is asymptotically equivalent to the high-frequency observation of the solution of the considered stochastic differential equation, these bounds can be transferred. Secondly, since the maximum likelihood estimator can be time-consuming for large samples, an alternative to Le Cam's one-step procedure is proposed in the general setting. It is based on an initial guess estimator, which is a combination of generalized variations of the trajectory for the scale and the jump activity index parameters and a maximum likelihood type estimator for the drift parameter. This proposed one-step procedure is shown to be fast, asymptotically normal, and even asymptotically efficient when the scale coefficient is constant. In addition, the performances in terms of asymptotic variance and computation time on samples of finite size are illustrated with simulations.
