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Prediction of weakly locally stationary processes by auto-regression
- François Roueff #1, Andrés Sánchez Pérez #1
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Laboratoire Traitement et Communication de l'Information [Paris] (LTCI)
- Télécom ParisTech
- CNRS : UMR5141
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- References
- ALEA : Latin American Journal of Probability and Mathematical Statistics, 2018, vol. 15, pp. 1215–1239
- 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.
- Keywords
- time varying autoregressive processes;minimax-rate prediction;locally stationary time series;auto-regression coefficients
- Category
- Article in peer reviewed Journal
- Research Area(s)
- Mathematics/Statistics
- Identifier(s)
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DOI 10.30757/ALEA.v15-45
HAL ref. hal-01269137
Bibliographic key roueff:hal-01269137
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- Last update
- on january 25, 2019 by Francois Roueff
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