Takens理论和小波分析在非线性预测中的应用

The Application of Takens Theory and Wavelets to Nonlinear Prediction

以 Takens理论为基础 ,将小波和时间序列分析相结合 ,对时间序列进行非线性预测 .首先 ,对混沌吸引子做非线性长期预测 ;其次 ,对经济时间序列做非线性短期预测 ;另外 ,指出对于用充分多个小波基函数 φmn来逼近原时间序列的预测误差可以任意小的性质 .

As a new kind of tool, wavelet plays a more and more important role in all kinds of fields; time series analysis is the basis of prediction, in which a lot of current methods are still used in many ways. Wavelet is combined with time series analysis on the basis of Takens theory in order to realize nonlinear prediction of time series. Firstly, we have made long term nonlinear prediction of a chaos attractor and short term nonlinear prediction for economic time series; Furthermore, we have suggested that we could make the error small enough to be omitted if we use sufficient wavelet basis functions φ mn to approximate to original time series.