Robust nonparametric estimation for the volatility of financial market

The occurrence of a macroeconomic policy would lead to a jump of financial data and the presence of jump behaviors might make the statistical methods for high-frequency sampling data to face new challenges. This paper will use the threshold function technique to disentangle the continuous part and the jump part from the high frequency financial data. Moreover, in the financial practices, the abnormal observations contained in the data could cause bias from nonparametric estimation based on least squares. The paper will employ the local M estimation to provide a robust estimator for the unknown diffusion coefficient of the diffusion model with jumps under high frequency sampling data. Under certain conditions for the initial values, this paper further considers one-step local M estimation for the unknown diffusion coefficient which can reduce the calculation quantity under the estimation efficiency. The Monte Carlo numerical simulation results verify that compared with the local linear threshold estimator, the threshold one-step local M estimator is more accurate and more robust. Finally, the threshold one-step local M estimator in this paper is applied to the Shanghai composite index of 2015 and 2020 in China and the Nasdaq index of 2020 in USA, which illustrates the method considered in this paper possesses good finite sample properties.