# Volatility Forecasting when the Noise Variance Is Time-Varying

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This paper explores the volatility forecasting implications of a model in which the friction in high-frequency prices is related to the true underlying volatility. The contribution of this paper is to propose a framework under which the realized variance may improve volatility forecasting if the noise variance is related to the true return volatility. The realized variance is defined as the sum of the squared intraday returns. When based on high-frequency returns, the realized variance would be non-informative for the true volatility under the standard framework. In this new setting, we revisit the results of Andersen et al. (2011) and quantify the predictive ability of several measures of integrated variance. Importantly, the time-varying aspect of the noise variance implies that the forecast of the integrated variance is different from the forecast of a realized measure. We characterize this difference, which is time-varying, and propose a feasible bias correction. We assess the usefulness of our approach for realistic models, then study the empirical implication of our method when dealing with forecasting integrated variance or trading options. The empirical results for Alcoa stock show several improvements resulting from the assumption of time-varying noise variance.

JEL Code(s): C, C1, C14, C5, C51, C58