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Sieves estimator of functional autoregressive process

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  • Berhoune, Kamila
  • Bensmain, Nawel

Abstract

We provide a general theory for the sieves estimation of the Hilbert autoregressive process operator presented by Mourid and Bensmain. The existence, explicit form and consistency of the estimate are established. Simulation studies and real-life series illustrate its performance.

Suggested Citation

  • Berhoune, Kamila & Bensmain, Nawel, 2018. "Sieves estimator of functional autoregressive process," Statistics & Probability Letters, Elsevier, vol. 135(C), pages 60-69.
    • Handle: RePEc:eee:stapro:v:135:y:2018:i:c:p:60-69
    DOI: 10.1016/j.spl.2017.11.008
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    References listed on IDEAS

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    1. Mourid, Tahar & Bensmain, Nawel, 2006. "Sieves estimator of the operator of a functional autoregressive process," Statistics & Probability Letters, Elsevier, vol. 76(1), pages 93-108, January.
    2. Philippe C. Besse & Herve Cardot & David B. Stephenson, 2000. "Autoregressive Forecasting of Some Functional Climatic Variations," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(4), pages 673-687, December.
    3. Antoniadis, Anestis & Sapatinas, Theofanis, 2003. "Wavelet methods for continuous-time prediction using Hilbert-valued autoregressive processes," Journal of Multivariate Analysis, Elsevier, vol. 87(1), pages 133-158, October.
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    Cited by:

    1. Kada Kloucha, Meryem & Mourid, Tahar, 2019. "Best linear predictor of a C[0,1]-valued functional autoregressive process," Statistics & Probability Letters, Elsevier, vol. 150(C), pages 114-120.

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