  We propose a class of estimators for the parameters of a GARCH(p,q) sequence.
  We show that our estimators are consistent and asymptotically normal under
mild conditions. The quasi-maximum likelihood and the likelihood estimators are
discussed in detail. We show that the maximum likelihood estimator is optimal.
If the tail of the distribution of the innovations is polynomial, even a
quasi-maximum likelihood estimator based on exponential density performs better
than the standard normal density-based quasi-likelihood estimator of Lee and
Hansen and Lumsdaine.
