Integrated volatility estimation: the case of observed noise variables

Abstract

We propose a new estimator of the integrated volatility in presence of observed noise variables, measured, for example, by the trading volume or the bid-ask-spread. We find that, under specific conditions, the proposed estimator is consistent and the error, adjusted for the noise effects, between the proposed estimator and the integrated volatility has the same asymptotic distribution of the realized volatility estimator under no noise effects. Finally, our results are validated by a simulation and an empirical study.