Non-parametric estimation of time varying AR(1)–processes with local stationarity and periodicity

Abstract : Extending the ideas of [7], this paper aims at providing a kernel based non-parametric estimation of a new class of time varying AR(1) processes (Xt), with local stationarity and periodic features (with a known period T), inducing the definition Xt = at(t/nT)X t−1 + ξt for t ∈ N and with a t+T ≡ at. Central limit theorems are established for kernel estima-tors as(u) reaching classical minimax rates and only requiring low order moment conditions of the white noise (ξt)t up to the second order.
Type de document :
Article dans une revue
Electronic journal of statistics , Shaker Heights, OH : Institute of Mathematical Statistics, 2018, 12 (2), pp.2323 - 2354. 〈10.1214/18-EJS1459〉
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-01527749
Contributeur : Jean-Marc Bardet <>
Soumis le : samedi 10 novembre 2018 - 09:30:38
Dernière modification le : mardi 13 novembre 2018 - 01:14:33

Fichiers

nonstationarity28062018.pdf
Fichiers produits par l'(les) auteur(s)

Licence


Distributed under a Creative Commons Paternité 4.0 International License

Identifiants

Collections

Citation

Jean-Marc Bardet, Paul Doukhan. Non-parametric estimation of time varying AR(1)–processes with local stationarity and periodicity. Electronic journal of statistics , Shaker Heights, OH : Institute of Mathematical Statistics, 2018, 12 (2), pp.2323 - 2354. 〈10.1214/18-EJS1459〉. 〈hal-01527749v3〉

Partager

Métriques

Consultations de la notice

11

Téléchargements de fichiers

8