Estimateur crible de l'opérateur d'un processus ARB(1)

We consider the sieve estimator of the operator of a Banach autoregressive process. We show the almost sure convergence when the operator is 2-summing, strictly 2-integral, afterwards 2-nuclear for the adequate norms. To cite this article: F. Rachedi, T. Mourid, C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Prediction of Continuous Time Autoregressive Processes via the Reproducing Kernel Spaces

We study the statistical prediction of a continuous time stochastic process admitting a functional autoregressive representation. We construct an approximation of Parzen's optimal predictor in reproducing kernel spaces framework. This approach did not require an estimation of the operator of the autoregressive representation. This revised version was published online in August 2006 with corrections to the Cover Date.     

Statistiques d'une saisonnalité perturbée par un processus a représentation autorégressiveStatistics of seasonality perturbed by time continuous processes with autoregressive representation

We consider limit theorems for an estimator of a seasonality when it is perturbed by a time continuous process admitting a Banach autoregressive representation. From the compact iterated logarithm law we derive confidence regions for a(·) in the Banach space of continuous functions. When a(·) belongs to a finite dimensional subspace, we study the estimation of a(·) by projection and we estimate the dimension when it is unknown. To cite this article: T. Mourid, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 909–912.     

Prédiction des processus à temps continu autorégressifs via les espaces à noyau reproduisantPrediction of autoregressive processes via the reproducing kernel spaces

We study the statistical prediction of a continuous time stochastic process admitting a functional autoregressive representation. We construct an approximation of Parzen's optimal predictor in reproducing kernel spaces framework. To cite this article: F. Mokhtari, T. Mourid, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 65–70