We consider a continuous time random process with functional autoregressive representation. We state statistical results on a mean functional estimator determining a minimum distance estimator of the period giving consistency and a limit law stated in Mourid and Benyelles [13]. Then we discuss...

We consider Banach space-valued autoregressive processes. For this class of processes we give sufficient conditions for absolute regularity and strong mixing properties that are useful in limit theorems and statistics.

We consider the estimation of the operator of one-order functional autoregressive process by the sieves method of Grenander in the case of dependent random variables framework. We show the almost sure convergence in Hilbert-Schmidt norm when the operator is of kernel type in Gaussian case...