Abstract
Short-term prediction of the timeseries having chaotic behavior is to find some deterministic regularity in a phenomenon which was thought as noise or to beirregular and there by predict its state in the near future. For short-term rediction, the observed timeseries is reconstructed in a multi-dimensional state space according to the Takens' theorem of embedding. And local reconstruction is made by a set of vectors nearest to the latest vector. Proposed methods of this prediction are Gram-Schmidt's orthogonal method and tessellation method. However, the former method has a problem that it is hard to obtain high accuracy when the selected neighboring vector is not linearly independent. The latter method also has a problem that calculation time increases abruptly along with a rise in the dimension of reconstructed state space. For resolving such problems, this paper proposes the local fuzzy reconstruction method. And to verify the effectiveness of this method, we examine the result of its application to a short-term prediction of the logistic map and the Lorenz attractor which have a typical chaotic behavior.
