The dynamic evolutionary modeling of higher order ordinary differential equations for time series prediction

The prediction of future values of a time series generated by a chaotic dynamic system is an extremely challenging task. Besides some methods used in traditional time series analysis, a number of nonlinear prediction methods have been developed for time series prediction, especially the evolutionary algorithms. Many researchers have built various models by utilizing different evolutionary techniques. Different from those available models, this paper presents a new idea for modeling time series using higher-order ordinary differential equations (HODEs) models. Accordingly, a dynamic hybrid evolutional modeling algorithm called DHEMA is proposed to approach this task. Its main idea is to embed a genetic algorithm (GA) into genetic programming (GP) where GP is employed to optimize the structure of a model, while a GA is employed to optimize its parameters. By running the DHEMA, the modeling and predicting processes can be carried on successively and dynamically with the renewing of observed data. Two practical examples are used to examine the effectiveness of the algorithm in performing the prediction task of time series whose experimental results are compared with those of standard GP.