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Estimation of nonlinear autoregressive models using design-adapted wavelets

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Abstract

We estimate nonlinear autoregressive models using a design-adapted wavelet estimator. We show two properties of the wavelet transform adapted to an autoregressive design. First, in an asymptotic setup, we derive the order of the threshold that removes all the noise with a probability tending to one asymptotically. Second, with this threshold, we estimate the detail coefficients by soft-thresholding the empirical detail coefficients. We show an upper bound on thel 2-risk of these soft-thresholded detail coefficients. Finally, we illustrate the behavior of this design-adapted wavelet estimator on simulated and real data sets.

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Authors and Affiliations

  1. Solar Physics Department, Royal Observatory of Belgium, Avenue Circulaire 3, B-1180, Brussels, Belgium

    Véronique Delouille

  2. Institut de statistique, Université catholique de Louvain, Voie du Roman Pays, 20, B-1348, Louvain-la-Neuve, Belgium

    Rainer Von Sachs

Authors
  1. Véronique Delouille
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  2. Rainer Von Sachs
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Additional information

Financial support from the contract ‘Projet d'Actions de Recherche Concertées’ nr. 98/03-217 from the Belgian government, and from the IAP research network nr. P5/24 of the Belgian State (Federal Office for Scientific, Technical and Cultural Affairs) is gratefully acknowledged.

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Delouille, V., Von Sachs, R. Estimation of nonlinear autoregressive models using design-adapted wavelets. Ann Inst Stat Math 57, 235–253 (2005). https://doi.org/10.1007/BF02507024

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  • DOI: https://doi.org/10.1007/BF02507024

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