Estimation of the integrated volatility using noisy high-frequency data with jumps and endogeneity
ABSTRACT In this paper, we investigate a new estimator of the integrated volatility of Itô semimartingales in the presence of both market microstructure noise and jumps when sampling times are endogenous. In the first step, our estimation wipes off the effects of the microstructure noise, and in the second step our estimator shrinks the effects of jumps. We provide consistency of the estimator when the jumps have finite variation and infinite variation and establish a central limit theorem for the estimator in a general endogenous time setting when the jumps only have finite variation. Simulation illustrates the performance of the proposed estimator.