Nonparametric Estimation of Jump Characteristics under Market Microstructure Noise

By exploiting financial high frequency data, we nonparametrically estimate the jump characteristic in the presence of market microstructure noise. Our estimator is based on the realized range increments and threshold technique. Besides, the bias caused by microstructure noise can be estimated and removed, if it is modeled as ask-bid spread, which is a used frequently assumption. We further present the asymptotic properties of the proposed estimator. Simulation studies show the estimator works well under microstructure noise. Finally, the estimator is also applied to the real data.