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Functional nonparametric model for time series: a fractal approach for dimension reduction

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In this paper we propose a functional nonparametric model for time series prediction. The originality of this model consists in using as predictor a continuous set of past values. This time series problem is presented in the general framework of regression estimation from dependent samples with regressor valued in some infinite dimensional semi-normed vectorial space. The curse of dimensionality induced by our approach is overridden by means of fractal dimension considerations. We give asymptotics for a kernel type nonparametric predictor linking the rates of convergence with the fractal dimension of the functional process. Finally, our method has been implemented and applied to some electricity consumption data.

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Authors and Affiliations

  1. Dip. di Scienze Economiche e Metodi Quantitativi, Università degli Studi del Piemonte orientale, Novara, Italia

    Aldo Goia

  2. Laboratone de Statistique et Probabilités, Université Paul Sabatier, 118 route de Narbonne, bat. 1R1, 31062, Toulouse Cedex, France

    Frédéric Ferraty & Philippe Vieu

Authors
  1. Frédéric Ferraty
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  2. Aldo Goia
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  3. Philippe Vieu
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Correspondence to Frédéric Ferraty.

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Ferraty, F., Goia, A. & Vieu, P. Functional nonparametric model for time series: a fractal approach for dimension reduction. Test 11, 317–344 (2002). https://doi.org/10.1007/BF02595710

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  • DOI: https://doi.org/10.1007/BF02595710

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