Locally stationary processes prediction by auto-regression

François Roueff (1) , Andres Sanchez-Perez (1)

1 LTCI - Laboratoire Traitement et Communication de l'Information

In this contribution we introduce 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 es-timator 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. For TVAR, the predictor naturally obtained from the estimator also exhibits an optimal minimax convergence rate.

Mots clés: locally stationary time series; auto-regression coefficients; time varying autoregressive processes; minimax-rate prediction

Domaines: Statistiques [math.ST]

François Roueff, Andres Sanchez-Perez. Locally stationary processes prediction by auto-regression. 2016. ⟨hal-01269137v1⟩