Statistical Properties of Microstructure Noise
基于高频数据，在非参数设定下估计微观结构噪声的（联合）矩，允许价格过程有跳跃、观测时间不规则、噪声与价格相关且具有日内特征，并证明了估计量的一致性和中心极限定理。
We study the estimation of (joint) moments of microstructure noise based on high frequency data. The estimation is conducted under a nonparametric setting, which allows the underlying price process to have jumps, the observation times to be irregularly spaced, and the noise to be dependent on the price process and to have diurnal features. Estimators of arbitrary orders of (joint) moments are provided, for which we establish consistency as well as central limit theorems. In particular, we provide estimators of autocovariances and autocorrelations of the noise. Simulation studies demonstrate excellent performance of our estimators in the presence of jumps, irregular observation times, and even rounding. Empirical studies reveal (moderate) positive autocorrelations of microstructure noise for the stocks tested.