Nonparametric estimation of jump characteristics under market microstructure noise

This article proposes a simple nonparametric method to estimate the jump characteristics in asset price with noisy high-frequency data. We combine the pre-averaging approach and the threshold technique to identify the jumps, and then propose the pre-averaging threshold estimators for the number and sizes of jumps occurred. We further present the asymptotic properties of the proposed estimators. The Monte Carlo simulation shows that the estimators are robust to microstructure noise and work very well especially when the data frequency is ultra-high. Finally, an empirical example further demonstrates the power of the proposed method.