Analysis and Application of Step Size of RK4 for Performance Measure of Predictability Horizon of Chaotic Time Series
So far, we have presented several methods for chaotic time series prediction, and shown performance improvement on predictability horizon. However, we could not have shown the comparison of the performance with other methods. In order to obtain general and absolute performance measure of predictability horizon, this paper analyzes to formulate the relationship between the mean predictability horizon and the step size of the fourth-order Runge-Kutta method, or RK4. By means of using the formula which we have obtained in this article, the step size of RK4 corresponding to the mean predictability horizon achieved by a learning machine can be obtained without executing RK4. We execute numerical experiment of the prediction by several learning machines, and compare the performance by means of the step size of RK4 corresponding to the mean horizon achieved by the learning machines, and we show the effectiveness of the present method.
KeywordsChaotic time series prediction Analysis and application of step size of RK4 Performance measure of predictability horizon
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