GARCH Model Estimation Using Estimated Quadratic Variation

We consider estimates of the parameters of GARCH models obtained using auxiliary information on latent variance which may be available from higher-frequency data, for example from an estimate of the daily quadratic variation such as the realized variance. We obtain consistent estimates of the parameters of the infinite ARCH representation via a regression using the estimated quadratic variation, without requiring that it be a consistent estimate; that is, variance information containing measurement error can be used for consistent estimation. We obtain GARCH parameters using a minimum distance estimator based on the estimated ARCH parameters. With LAD estimation of the truncated ARCH approximation, we show that consistency and asymptotic normality can be obtained using a general result on LAD estimation in truncated models of infinite-order processes. We provide simulation evidence on small-sample performance for varying numbers of intra-day observations.