Problèmes d'Estimation et de Prévision d’un Processus AR à Noyau de Convolution

Abstract

In this thesis we are interested in the estimation of a functional autoregressive process on [0,1] by the sieves method . We show results on the existence and the almost sure convergence of sieves estimate of the parameter operator of a first order Hilbertian autoregressive process in a particular case and then we generalize them. We also give an explicit form of this estimate in the Gaussian case. We illustrate the performance of this method by simulations studies and real-life applications. The results obtained corroborate the theoretical results.