Local linear estimator for stochastic differential equations driven by $\alpha$-stable Lévy motions

Abstract

We study the local linear estimator for the drift coefficient of stochastic differential equations driven by $\alpha$-stable Lévy motions observed at discrete instants letting $T\to \infty$. Under regular conditions, we derive the weak consistency and central limit theorem of the estimator. Compare with Nadaraya-Watson estimator, the local linear estimator has a bias reduction whether kernel function is symmetric or not under different schemes.

15 pages