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Bandwidth selection for functional time series prediction

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  • Antoniadis, Anestis
  • Paparoditis, Efstathios
  • Sapatinas, Theofanis

Abstract

We propose a method to select the bandwidth for functional time series prediction. The idea underlying this method is to calculate the empirical risk of prediction using past segments of the observed series and to select as value of the bandwidth for prediction the bandwidth which minimizes this risk. We prove an oracle bound for the proposed bandwidth estimator showing that it mimics, asymptotically, the value of the bandwidth which minimizes the unknown theoretical risk of prediction based on past segments. We illustrate the usefulness of the proposed estimator in finite sample situations by means of a small simulation study and compare the resulting predictions with those obtained by a leave-one-curve-out cross-validation estimator used in the literature.

Suggested Citation

  • Antoniadis, Anestis & Paparoditis, Efstathios & Sapatinas, Theofanis, 2009. "Bandwidth selection for functional time series prediction," Statistics & Probability Letters, Elsevier, vol. 79(6), pages 733-740, March.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:6:p:733-740
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    References listed on IDEAS

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    1. Frédéric Ferraty & Aldo Goia & Philippe Vieu, 2002. "Functional nonparametric model for time series: a fractal approach for dimension reduction," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 11(2), pages 317-344, December.
    2. 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.
    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. Chagny, Gaëlle & Roche, Angelina, 2016. "Adaptive estimation in the functional nonparametric regression model," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 105-118.
    2. Sophie Bercu & Fr�d�ric Proïa, 2013. "A SARIMAX coupled modelling applied to individual load curves intraday forecasting," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(6), pages 1333-1348, June.
    3. Alexander Aue & Diogo Dubart Norinho & Siegfried Hörmann, 2015. "On the Prediction of Stationary Functional Time Series," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 378-392, March.

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