ESTIMATING WEAK GARCH REPRESENTATIONS

Using an approach based on linear conditional expectations, we define a class of weak ARMA-GARCH representations. The generality of the clas s is illustrated through a collection of examples. We propose a two-st age estimation procedure based on the minimization of sums of squared linear-predictions errors. Strong consistency and asymptotic normality of the estimator are established under ergodic and mixing assumptions . (C) Academie des Sciences/Elsevier, Paris.