A0364
Title: Locally stable approximation of SDE: Numerical algorithms in yuimaStable
Authors: Hiroki Masuda - University of Tokyo (Japan)
Lorenzo Mercuri - University of Milan (Italy) [presenting]
Abstract: The purpose is to analyze the numerical aspects related to the estimation of an ergodic Markovian stochastic differential equation (SDE) driven by a locally stable Levy process. The likelihood function constructed on the small-time stable approximation of the transition density (QSMLE) leads to an estimator with appropriate asymptotic behavior. To the best of knowledge, the joint estimation of drift, jump coefficients, and stability index has only been considered in recent literature. However, in previous works, the problem of filtering noise from the data has not been discussed from either a theoretical or numerical point of view. A two-step procedure is considered. First, the drift, the jump coefficient, and the stability parameters are estimated jointly. Consequently, the filtered increments are reconstructed with the possibility of estimating the Levy measure parameters for the underlying noise. To this aim, the transition stable-density is numerically evaluated in QSMLE using different Gauss-like quadrature methods. Finally, the new classes and methods implemented in yuimaStable for the estimation of these SDEs are discussed with simulated and real high-frequency data.
