Capturing Measurement Error Bias in Volatility Forecasting by Realized GARCH Models

This paper proposes generalisations of the Realized GARCH model, in three different directions. First, heteroskedasticity of the noise term in the measurement equation is modelled letting the variance of the measurement error to vary over time as a function of an estimator of the Integrated Quarticity obtained from intra-daily returns. Second, to account for attenuation bias effects, volatility dynamics are allowed to depend on the accuracy of the realized measure letting the response coefficient of the lagged realized measure be a function of the time-varying variance of the volatility measurement error. Therefore, the model tends to assign more weight to lagged volatilities when they are measured more accurately. Finally, a further extension is proposed by introducing an additional explanatory variable into the measurement equation, aiming to quantify the bias due to the effect of jumps.