Prediction of weakly locally stationary processes by auto-regression - IMT - Institut Mines-Télécom Accéder directement au contenu
Article Dans Une Revue ALEA : Latin American Journal of Probability and Mathematical Statistics Année : 2018

Prediction of weakly locally stationary processes by auto-regression

Résumé

In this contribution we introduce weakly locally stationary time series through the local approximation of the non-stationary covariance structure by a stationary one. This allows us to define autoregression coefficients in a non-stationary context, which, in the particular case of a locally stationary Time Varying Autoregressive (TVAR) process, coincide with the generating coefficients. We provide and study an estimator of the time varying autoregression coefficients in a general setting. The proposed estimator of these coefficients enjoys an optimal minimax convergence rate under limited smoothness conditions. In a second step, using a bias reduction technique, we derive a minimax-rate estimator for arbitrarily smooth time-evolving coefficients, which outperforms the previous one for large data sets. In turn, for TVAR processes, the predictor derived from the estimator exhibits an optimal minimax prediction rate.
Fichier principal
Vignette du fichier
article.pdf (324.32 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-01269137 , version 1 (05-02-2016)
hal-01269137 , version 2 (25-01-2017)
hal-01269137 , version 3 (12-01-2018)

Identifiants

Citer

François Roueff, Andres Sanchez-Perez. Prediction of weakly locally stationary processes by auto-regression. ALEA : Latin American Journal of Probability and Mathematical Statistics, 2018, 15, pp.1215-1239. ⟨10.30757/ALEA.v15-45⟩. ⟨hal-01269137v3⟩
323 Consultations
413 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More