Prediction of weakly locally stationary processes by auto-regression

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-01269137
Contributor : François Roueff <>
Submitted on : Friday, January 12, 2018 - 5:08:32 PM
Last modification on : Friday, June 7, 2019 - 11:18:38 AM
Long-term archiving on : Saturday, May 5, 2018 - 7:11:05 PM

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François Roueff, Andres Sanchez-Perez. Prediction of weakly locally stationary processes by auto-regression. ALEA : Latin American Journal of Probability and Mathematical Statistics, Instituto Nacional de Matemática Pura e Aplicada, 2018, 15, pp.1215-1239. ⟨http://alea.math.cnrs.fr/articles/v15/15-45.pdf⟩. ⟨10.30757/ALEA.v15-45⟩. ⟨hal-01269137v3⟩

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