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Hier finden Sie wissenschaftliche Publikationen aus den FraunhoferInstituten. An adaptive sparse grid approach for time series prediction
 Garcke, J.; Griebel, M.: Sparse grids and applications Berlin: Springer, 2013 (Lecture notes in computational science and engineering 88) ISBN: 3642317022 ISBN: 9783642317026 ISBN: 9783642317033 DOI: 10.1007/9783642317033 S.130 

 Englisch 
 Aufsatz in Buch 
 Fraunhofer SCAI () 
Abstract
A real valued, deterministic and stationary time series can be embedded in a  sometimes highdimensional  real vector space. This leads to a onetoone relationship between the embedded, time dependent vectors in Rd and the states of the underlying, unknown dynamical system that determines the time series. The embedded data points are located on an mdimensional manifold (or even fractal) called attractor of the time series. Takens' theorem then states that an upper bound for the embedding dimension d can be given by d <= 2m + 1.The task of predicting future values thus becomes, together with an estimate on the manifold dimension m, a scattered data regression problem in d dimensions. In contrast to most of the common regression algorithms like support vector machines (SVMs) or neural networks, which follow a databased approach, we employ in this paper a sparse gridbased discretization technique. This allows us to efficiently handle huge amounts of training data in moderate dimensions. Extensions of the basic method lead to space and dimensionadaptive sparse grid algorithms. They become useful if the attractor is only located in a small part of the embedding space or if its dimension was chosen too large.We discuss the basic features of our sparse grid prediction method and give the results of numerical experiments for time series with both, synthetic data and real life data.