Local Nonparametric Estimation for Second-Order Jump-Diffusion Model Using Gamma Asymmetric Kernels

Abstract: This paper discusses the local linear smoothing to estimate the unknown first and second infinitesimal moments in second-order jump-diffusion model based on Gamma asymmetric kernels. Under the mild conditions, we obtain the weak consistency and the asymptotic normality of these estimators for both interior and boundary design points. Besides the standard properties of the local linear estimation such as simple bias representation and boundary bias correction, the local linear smoothing using Gamma asymmetric kernels possess some extra advantages such as variable bandwidth, variance reduction and resistance to sparse design, which is validated through finite sample simulation study. Finally, we employ the estimators for the return of some high frequency financial data.