Nonparametric interval prediction of chaotic time series and its application to climatic system

Abstract

This article is concerned with nonlinear time series analysis and it proposes an interval prediction method for chaotic time series. The selection algorithm for the number of neighbour points is introduced based on the local approximation technique of the classic chaotic time series model. The nonparametric statistics method is considered here, and we obtain an interval prediction for one or more steps under a certain confidence level assumption with the help of order statistics distribution. We also find a sufficient condition for the existence of such interval prediction, and a sufficient condition for the relationship between the number of neighbour points and the interval confidence level. In addition to the bootstrap multiple sample based on the selected neighbour points implemented on the computer, another interval prediction method is described too. We focus on the air pressure difference data from a climatic system and find that the series data has a positive Lyapunov exponent, which shows that it contains chaos. The application of the techniques on the data shows that both the interval predictions are reasonable in this data sample.

Keywords:

• interval prediction
• chaotic time series
• nonparametric
• neighbour point

Acknowledgements

The authors thank the reviewers for their constructive comments, which helped improve the quality of this article. This research was supported by the Natural Science Foundation of China under Grant No. 71171209.