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Best linear predictor of a C[0,1]-valued functional autoregressive process

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  • Kada Kloucha, Meryem
  • Mourid, Tahar

Abstract

We establish exponential bounds and the a.s. convergence of the best linear predictor BLP of a C[0,1]-valued autoregressive process. Simulation studies on real series illustrate the performance of the BLP and show competitive results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:150:y:2019:i:c:p:114-120
    DOI: 10.1016/j.spl.2019.03.003
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    References listed on IDEAS

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    1. Fatiha Mokhtari & Tahar Mourid, 2003. "Prediction of Continuous Time Autoregressive Processes via the Reproducing Kernel Spaces," Statistical Inference for Stochastic Processes, Springer, vol. 6(3), pages 247-266, October.
    2. Berhoune, Kamila & Bensmain, Nawel, 2018. "Sieves estimator of functional autoregressive process," Statistics & Probability Letters, Elsevier, vol. 135(C), pages 60-69.
    3. Anestis Antoniadis & Efstathios Paparoditis & Theofanis Sapatinas, 2006. "A functional wavelet–kernel approach for time series prediction," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(5), pages 837-857, November.
    4. Yao, Fang & Muller, Hans-Georg & Wang, Jane-Ling, 2005. "Functional Data Analysis for Sparse Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 577-590, June.
    5. Bosq, D., 2014. "Computing the best linear predictor in a Hilbert space. Applications to general ARMAH processes," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 436-450.
    6. Kargin, V. & Onatski, A., 2008. "Curve forecasting by functional autoregression," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2508-2526, November.
    7. Besnik Pumo, 1998. "Prediction of Continuous Time Processes by C[0,1]‐Valued Autoregressive Process," Statistical Inference for Stochastic Processes, Springer, vol. 1(3), pages 297-309, October.
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