Variance reduction estimation for return models with jumps using gamma asymmetric kernels

Abstract

This paper discusses Nadaraya-Watson estimators for the unknown coefficients in second-order diffusion model with jumps constructed with Gamma asymmetric kernels. Compared with existing nonparametric estimators constructed with Gaussian symmetric kernels, local constant smoothing using Gamma asymmetric kernels possesses some extra advantages such as boundary bias correction, variance reduction and resistance to sparse design points, which is validated through theoretical details and finite sample simulation study. Under the regular conditions, the weak consistency and the asymptotic normality of these estimators are presented. Finally, the statistical advantages of the nonparametric estimators are depicted through 5-minute high-frequency data from Shenzhen Stock Exchange in China.

Nonparametric Threshold Estimation for Drift Function in Jump–Diffusion Model of Interest Rate Using Asymmetric Kernel

“…Secondly, the variance of the gamma asymmetric kernel threshold estimator is inversely proportional to the design x for "interior x", which indicates that Estimator (4) is resistant to sparse design point x. One can refer to Song et al [22] for more theoretical details.…”

Nonparametric Estimation for Second-Order Jump-Diffusion Model in High Frequency Data

“…The modified proof of Theorem 2 in Hanif [21] is similar to that of Theorem 1, so we omit it. One can refer to Song [44] for similar procedure.…”