基于分形自仿射的混沌时间序列预测

从混沌与分形的关系出发，基于奇怪吸引子的分形结构和时间序列的自仿射特性，提出了一种混沌时间序列的预测方法.采用迭代函数系统跟踪混沌的局部运动轨迹，由此确定统计意义上仿射性能最优的时间序列段，并根据吸引子定理和拼贴定理建立预测模型.以Mackey-Glass混沌系统、脑电信号和Lorenz混沌系统等三种混沌系统为例进行预测试验，结果表明本方法能对混沌时间序列进行准确预测，且对混沌时间序列先验知识要求少，具有广泛的实用性. 关键词： 自仿射 迭代函数系统 混沌时间序列 预测

Prediction of chaotic time series based on fractal self-affinity

Based on the fractal structure of strange attractor and self-affine property of time series, a method is proposed for predicting chaotic time series. The algorithm first exploits the iterative function system to track current chaotic trajectory and selects the segment which possesses the best self-affine property of the time series statistically. Then the prediction model is constructed according to attractor and coverage theorem. To illustrate the performance of the proposed model, simulations are performed on the chaotic Mackey-Glass time series, EEG signal and Lorenz chaotic system. The results show that the chaotic time series are accurately predicted, which demonstrates the effectiveness of the model.