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Resumen de Functional Nonparametric Model for Time Series: a Fractal Approach for Dimension Reduction

Philippe Vieu Árbol académico, Frédéric Ferraty Árbol académico, Aldo Goia Árbol académico

  • 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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