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

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.

Keywords:

• Diffusion process with jumps
• expected risk return
• nonparametric estimation
• consistency and asymptotic normality
• interest rate

MSC 2010::

• primary 62G20
• 62M05
• Secondary 60J75
• 62P20

JEL CLASSIFICATION::

• C13
• C14
• C22

Data availability statement

The dataset for the empirical analysis is available as a supplementary file, which can also be derived from the following resource available in the public domain: http://www.shibor.org/shibor/web/DataService.jsp

Additional information

Funding

This research work is supported by National Natural Science Foundation of China (11901397), Ministry of Education, Humanities and Social Sciences project (18YJCZH153), National Statistical Science Research Project (2018LZ05), Youth Academic Backbone Cultivation Project of Shanghai Normal University (310-AC7031-19-003021), General Research Fund of Shanghai Normal University (SK201720) and Key Subject of Quantitative Economics (310-AC7031-19-004221) and Academic Innovation Team (310-AC7031-19-004228) of Shanghai Normal University.