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

TL;DR

This paper introduces a local linear smoothing method using Gamma asymmetric kernels to estimate moments in second-order jump-diffusion models, offering advantages like bias correction and variance reduction, validated through simulations and financial data application.

Contribution

It proposes a novel local linear estimation technique with Gamma asymmetric kernels for jump-diffusion models, enhancing bias correction and variance reduction capabilities.

Findings

Establishes weak consistency and asymptotic normality of estimators.

Demonstrates advantages of variable bandwidth and boundary bias correction.

Validates method with finite sample simulations and financial data.

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.