Determination of optimal and stable prediction parameters values in chaotic time series

Abstract

The parameters values used in the prediction method for chaotic time series play a significant role in achieving high prediction accuracy. The conventional approach derives these values using, for example, Correlation Dimension, Lyapunov Exponent or Kolmogorov Entropy methods. In the present study, a search engine based on the Genetic Algorithm (GA), is coupled with an Inverse approach to arrive at the optimal values of these parameters. An artificial chaotic Mackey-Glass time series is considered in this study to test the performance of the coupled model, GA and Inverse approach. The study shows that the coupled model yields a prediction error measure, RMSE, of 0.068 which is much more accurate than that of the conventional approach. In addition, the resulting optimal values of the state space parameters are more stable with respect to different data record lengths used in optimization and a change in forecasting lead-time. Copyright ASCE 2004.