Estimation of Garch Models from the Autocorrelations of the Squares of a Process by Richard T. Baillie

This paper shows how the parameters of a stable GARCH(1, 1) model can be estimated from the autocorrelations of the squared process. Speci®cally, the method applies a minimum distance estimator (MDE) to the sample autocorrelations of the squared realization. The asymptotic ef®ciency of the estimator is calculated from using the ®rst g autocorrelations. The estimator can be surprisingly ef®cient for quite small numbers of autocorrelations and, in some cases, can be more ef®cient than the quasi maximum likelihood estimator (QMLE). Also, the estimated process can better ®t the pattern of observed autocorrelations of squared returns than those from models estimated by maximum likelihood estimation (MLE). The estimator is applied to a series of hourly exchange rate returns, which are extremely non Gaussian.