Recent literature has shown that incorporating realized measures based on high frequency data into volatility forecasting models can allow for substantial gains in terms of forecasting accuracy. Nevertheless, there are still some open issues related to the latent nature of volatility itself. Said differently, any volatility measure is naturally affected by a heteroskedastic estimation error that can have complex effects on the identification of the volatility dynamics. Furthermore the presence of jumps could introduce an additional source of uncertainty and bias into the estimated volatilities. Neglecting to properly account for these features can lead to biased  and inefficient volatility forecasts.

Following this line of research we propose two different extensions of the Realized GARCH (RGARCH) model of Hansen, Huang and Shek (2012) that allow to correct for both the attenuation bias originated from the time varying volatility measurement error as well as for the effect of jumps. The first class of specifications we consider extends the standard RGARCH model since it allows for i) heteroskedastic measurement errors ii) time varying volatility persistence iii) a jump component in the measurement equation. The second class of specifications aims at achieving the same tasks by combining realized measures based on information at different frequencies. The weights of the combination are designed to be a function of the amount of noise due to measurement error and jumps. In this latter case the idea is to use the fitted model as a framework for adaptively determining, in a fully data driven fashion, an optimized volatility measure that allows to gain for each time point the optimal bias variance\tradeoff.

The merits of the proposed model specifications are illustrated through an application to a set of stocks traded on the XETRA market.