Convoluted smoothed kernel estimation for drift coefficients in jump-diffusion models

Naiqi Liu, Kunyang Song, Yuping Song and Xiaochen Wang

Communications in Statistics - Theory and Methods, 2022, vol. 51, issue 21, 7354-7389

Abstract: The occurrence of economic policies and other sudden and large shocks often bring out jumps in financial data, which can be characterized through continuous-time jump-diffusion model. In this paper, we will adopt convoluted smoothed approach to estimate unknown drift function of the potentially nonstationary diffusion models with jumps under high frequency sampling data. With Gaussian approximation of locally square-integrable martingales, we will establish large sample properties for the underlying nonparametric estimators. Furthermore, we construct Monte Carlo simulation study through three examples for the better finite-sample properties such as reduction of mean-squared error compared with the existing estimators. Finally, our estimator is verified through the actual data of Shibor in China for better performance.

Date: 2022
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DOI: 10.1080/03610926.2021.1872641

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