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

Abstract

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.