The signal and the noise volatilities

Abstract

This paper explores the volatility forecasting implications of a model in which the high-frequency market microstructure noise is related to the true underlying volatility. The contribution of this paper is to propose a theoretical framework under which the realized variance, based on the highest frequency to compute returns, may improve volatility forecasting if the noise variance is an affine function of the fundamental volatility. In this new setting, we extend the work of Andersen et al. (2011) and quantify the predictive ability of several measures of integrated variance. We find that the traditional realized variance based on the highest frequency returns outperforms alternative realized measures. We also evaluate the usefulness of our approach by conducting an empirical application and show several improvements resulting from the assumption of time-varying noise variance.