Title: 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.