非线性时间序列的投影寻踪学习网络逼近

摘要

The convergence property of the projection pursuit learning network (PPLN) that is used to approximate to non-linear autoregrcssion is studied in this paper. The authros prove that PPLN can approximate to non-linear autoregression at any given precision in Lk space, where k is integer. The learning strategy and calculative procedures of PPLN's, which are used to establishthe models of non-linear time series {Xt } and forecast the subsequent behavior of {Xt}, are also presented. Using PPLN, the Wolfer sunspont number(1749-1894), Canada lvnx data(1821-1924) and Xi'an data(0-360) are fitted. Furthermore, the predictors for the above three kinds of data are also pre sented, respectively. Finally, we compare the performance the projection pursuit learning network not only with that of backpropagation learning (BPLN) but also with that of the threshold model. It is shown that the projection pursuit learning networks perform well and compare favorably to BPLN and the threshold model.%本文研究非线性自回归模型投影寻踪学习网络逼近的收敛性，证明了在Lk(k为正整数)空间上，投影寻踪学习网络可以以任意精度逼近非线性自回归模型，给出基于投影寻踪学习网络的非线性时间序列模型建模和预报的计算方法和应用实例，对太阳黑子数据、山猫数据及西安数据进行了拟合和预报，将其结果与改进的BP网和门限自回归模型相应的结果进行比较，结果表明基于投影寻踪学习网络的非线性时间序列的建模和预报方法是一类行之有效的方法。