The asymptotic distribution of the Gaussian quasi-maximum likelihood estimator (QMLE) is obtained for a wide class of asymmetric GARCH models with exogenous covariates. The true value of the parameter is not restricted to belong to the interior of the parameter space, which allows us to derive...

Regularity conditions are given for the consistency of the Poisson quasi-maximum likelihood estimator of the conditional mean parameter of a count time series. The asymptotic distribution of the estimator is studied when the parameter belongs to the interior of the parameter space and when it...