Abstract
To solve chaotic time series prediction problem, a novel Prediction approach for chaotic time series based on Immune Optimization Theory (PIOT) is proposed. In PIOT, the concepts and formal definitions of antigen, antibody and affinity being used for time series prediction are given, and the mathematical models of immune optimization operators being used for establishing time series prediction model are exhibited. Chaotic time series is analyzed and corresponding sample space is reconstructed by phase space reconstruction method; then, the prediction model of chaotic time series is constructed by immune optimization theory; finally, using this prediction model to forecast chaotic time series. To demonstrate the effectiveness of PIOT, the three typical chaotic nonlinear time series are generated by nonlinear dynamics systems that are Lorenz, Mackey–Glass and Henon, respectively, and are used for simulating prediction. The simulation results show that PIOT is a feasible and effective prediction method, and ...
Highlights
Time series is a set of data constructed by chronological T observed data
To demonstrate the accuracy of PIOT, we introduce three prediction evaluation criterions: the absolute error (AE), the root mean square error (RMSE) and the mean absolute error (MAE)
In the process of time series experiments, we select respectively 100, 100 and 50 last sample points from three sample spaces as a prediction sample subset to demonstrate the effectiveness of PIOT, and the rest of sample spaces are considered as a training sample subset, namely selecting a part of training samples being close to a prediction point to build time series prediction model according to sample window w given by Table 1
Summary
Time series is a set of data constructed by chronological T observed data. Generally speaking, time series prediction mainly includes three operation steps, namely analyzing the past and current data of time series, establishing the corresponding time series prediction model, and predicting the future data of time series. The mainly contributions of this paper are: 1) Propose a novel prediction modelling method for chaotic time series based on phase space reconstruction method and immune optimization theory; 2) Introduce a new antibody encoding form corresponding with time series prediction problem that inspired by the antibody characteristics of BIS; 3) Give a new immune selection operator in terms of artificial immune network, the new operator introduces affinity between antibody and antigen but between antibody and antibody in order to enhance the diversity of population; 4) Give a new antibody mutation operator according to the new antibody encoding form, the new operator utilizes affinity between antibody and antigen to determine antibody mutation strategy so as to improve the capabilities of the global search and local optimization for population.
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