カオス時系列データの予測のためのパラメータ最適化手法

Abstract

A new method is proposed for predicting chaotic time series based on a local approximation. In the local approximation, a time series is embedded in a state space using delay coordinates and a local predictor is constructed using the nearest neighbors of the current state. The embedding dimension and the number of the nearest neighbors are significant parameters affecting the prediction accuracy. The proposed method aims to select the optimal parameters of the embedding dimension and the nearest neighbor number so as to minimize the prediction error. The efficacy of the proposed method is demonstrated using chaotic time series generated by the Hénon map and the Ikeda map.