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Prediction of weakly locally stationary processes by auto-regression

François Roueff #1, Andrés Sánchez Pérez #1
#1 Laboratoire Traitement et Communication de l'Information [Paris] (LTCI)
  • Télécom ParisTech
  • CNRS : UMR5141
ALEA : Latin American Journal of Probability and Mathematical Statistics, 2018, vol. 15, pp. 1215–1239

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.

time varying autoregressive processes;minimax-rate prediction;locally stationary time series;auto-regression coefficients
Article in peer reviewed Journal
Research Area(s)
DOI 10.30757/ALEA.v15-45
HAL ref. hal-01269137
Bibliographic key roueff:hal-01269137
Last update
on january 25, 2019 by Francois Roueff

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