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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.

Bias reduction estimation for drift coefficient in diffusion models with jumps