适用于高必要嵌入维的混沌时间序列预测算法

针对现有的混沌时间序列预测算法－－延迟坐标状态空间重构法不能对必要嵌入维较高的奇异吸引子进行有效预测问题，分析表明了高嵌入维时预测精度下降的原因在于 构空间的全局Ｌｙａｐｕｎｏｖ指数谱的变化。通过引入仿射变换，改善了高维重构空间的全局Ｌｙａｐｕｎｏｖ指数谱的性状，并由此给出了适用于高必要嵌入维的预测算法。仿真结果很好地支持了这一设想。

RECONSTRUCTING HIGH DIMENSION PHASE SPACE: AN IMPROVED APPROACH TO CHAOTIC TIME SERIES FORECASTING

Though a popular and widely used forecast algorithm for chaotic time series, the delay coordinate method in some extent leaves much to be desired. For example,our experiment and literature indicate that the forecast precision of algorithm would almost monotonously descend after it reaches the peak value at a certain embedding dimension. On the other hand,there is a theoretical demand that the embedding dimension should be greater than the twice box-counting dimension of the chaotic attractor in the full phase space. The demand infers that the current algorithm is not fit to reconstruct the high dimension strange attractor- In this paper we prove that the cause of the precision descent with the increase of embedding dimension should be due to the change of the universal Lyapunov exponent spectrum. Therefore,we introduce an affine transform to improve the character of the Lyapunov exponent spectrum. Moreover,we propose an improved forecast algorithm for the high essential embedding dimension. The outcome of computer simulation perfectly support our idea.