高阶常微分方程的动态演化建模

提出了采用高阶常微分方程模型代替传统时序分析中所用的ARMA模型来实现一维时间序列的建模和预报．设计的将遗传程序设计与遗传算法相嵌套的动态演化建模算法，用遗传程序设计优化模型结构，以遗传算法优化模型参数，边收集数据边建模边预报，首次成功地实现了时间序列实时预报的程序自动化．两个时间序列的应用实例表明采用此算法可获得较好的实时预报效果．

The Dynamic Evolutionary Modeling of Higher-Order Ordinary Differential Equations

A new idea of modeling and predicting one - dimensional time series by high - order ordinary differential equations (HODEs) instead of by the ARMA models used in traditional time series analysis is presented. Accordingly, a dynamic evolutionary modeling algorithm is proposed to approach this task whose main idea is to embed a genetic algorithm (GA) in genetic programming (GP) where GP is employed to optimize the structure of a model, while a GA is employed to optimize its parameters. It has succeeded in implementing the dynamic modeling of time series which enables the modeling and prediction to be carried on concurrently with the renewing of observed data and has taken a first step toward the automatic programming of time series real-time prediction. Two practical examples of time series show that the algorithm works well in modeling and prediction for one-dimensional time series analysis.