Time Varying Heteroskedastic Realized GARCH models for tracking measurement error bias in volatility forecasting

Abstract

This paper proposes generalisations of the Realized GARCH model by Hansen et al. (2012), in three different directions. First, heteroskedasticity in the noise term in the measurement equation is allowed, since this is generally assumed to be time-varying as a function of an estimator of the Integrated Quarticity for intra-daily returns. Second, in order to account for attenuation bias effects, the volatility dynamics are allowed to depend on the accuracy of the realized measure. This is achieved by letting the response coefficient of the lagged realized measure depend on the time-varying variance of the volatility measurement error, thus giving more weight to lagged volatilities when they are more accurately measured. Finally, a further extension is proposed by introducing an additional explanatory variable into the measurement equation, aiming to quantify the bias due to effect of jumps and measurement errors