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