Nonparametric estimation for i.i.d. Gaussian continuous time moving average models. - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Statistical Inference for Stochastic Processes Année : 2021

Nonparametric estimation for i.i.d. Gaussian continuous time moving average models.

Résumé

We consider a Gaussian continuous time moving average model X(t) = t 0 a(t − s)dW (s) where W is a standard Brownian motion and a(.) a deterministic function locally square integrable on R +. Given N i.i.d. continuous time observations of (Xi(t)) t∈[0,T ] on [0, T ], for i = 1,. .. , N distributed like (X(t)) t∈[0,T ] , we propose nonparametric projection estimators of a 2 under different sets of assumptions, which authorize or not fractional models. We study the asymptotics in T, N (depending on the setup) ensuring their consistency, provide their nonparametric rates of convergence on functional regularity spaces. Then, we propose a data-driven method corresponding to each setup, for selecting the dimension of the projection space. The findings are illustrated through a simulation study.
Fichier principal
Vignette du fichier
CARMA-HAL.pdf (768.12 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-02546705 , version 1 (18-04-2020)

Identifiants

Citer

Fabienne Comte, Valentine Genon-Catalot. Nonparametric estimation for i.i.d. Gaussian continuous time moving average models.. Statistical Inference for Stochastic Processes, 2021, 24 (1), pp.149-177. ⟨10.1007/s11203-020-09228-y⟩. ⟨hal-02546705⟩
154 Consultations
136 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More