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

• Autores: Philippe Vieu , Frédéric Ferraty , Aldo Goia
• Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 11, Nº. 2, 2002, págs. 317-344
• Idioma: inglés
• DOI: 10.1007/bf02595710
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• Resumen

  • 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.