A Tale of Two Averagings: Estimating the Integrated Volatility Using 'Pooled' High-Frequency Data

Abstract

In estimating the integrated volatility using high-frequency data, it is well documented that the presence of the microstructure noise causes big challenge. In this paper, as demonstrated by the motivational simulation study, the common feature of multiple observations brings an additional problem to the estimation of the integrated volatility. It becomes one more source of bias in addition to the microstructure noise. In this paper, we propose a multiplicity- adjusted and noise-corrected preaveraging estimator which is proved to be consistent and have asymptotic normal distribution. Our approach is also easily extended to the case when the latent process has jumps. Extensive comparisons with empirical procedures in dealing with microstructure noise and/or multiple transactions show that our newly proposed estimator is superior over others. Yet surprisingly, in some cases, our estimator performs even better than the ideal estimator which assumes the transaction times within a single time stamp are observable. Simulation studies justify our theory and we also implement our estimator to some real data sets.