期刊
TEST
卷 11, 期 2, 页码 317-344出版社
SPRINGER
DOI: 10.1007/BF02595710
关键词
fractal dimension; functional data; kernel estimator; mixing processes; nonparametric regression; semi-normed linear space
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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