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

The paper presents a new idea for modeling and predicting one dimensional time series using higher order ordinary differential equations (HODEs) models instead of the models as used in traditional time series analysis. Accordingly, based on the idea of two-level evolutionary modeling in the HEMA algorithm (H.Q. Cao et al., 1998), a dynamic hybrid evolutionary modeling algorithm called DHEMA is proposed to approach this task. By running the DHEMA, the modeling process and the predicting process can be carried on concurrently and dynamically with the renewing of observed data. Two practical examples are used to examine the effectiveness of the algorithm in performing the real time modeling and predicting tasks of time series