Bias reduction estimation for drift coefficient in diffusion models with jumps

Abstract

In this paper, we reconstruct the local linear threshold estimator for the drift coefficient of a semimartingale with jumps. Under mild conditions, we provide the asymptotic normality of our estimator in the presence of finite activity jumps whether the underlying process is Harris recurrent or positive recurrent. Simulation studies for different models show that our estimator performs better than previous research in finite samples, which can correct the boundary bias automatically. Finally, the estimator is illustrated empirically through the stock index from Shanghai Stock Exchange in China under 15-minute high sampling frequency.

Keywords:

• Jump-diffusion model
• local linear threshold estimator
• asymptotic normality
• bias correction
• high-frequency financial data

MSC 2010 subject classifications:

• 62G20
• 62M05
• secondary 60J75
• 62P20

Disclosure statement

No potential conflict of interest was reported by the author(s).

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.