Propriétés asymptotiques des estimateurs du gradient et du gradient moyennisé pour les modèles autorégressifs stables

Abstract

We consider a stable autoregressive model of order p. We establish, for the gradient estimator, a central limit theorem, a law of the iterated logarithm and an almost sure central limit theorem; a quadratic strong law of large numbers is proved for the estimation and for the associated prediction. Then we give a new estimator, the averaged gradient estimator, which is computed more easily than the classical least squares estimator, and enjoys the same optimal asymptotic properties as the latter.