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

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.

[1]  Alan Solon Ivor Zinober,et al.  Smooth adaptive sliding mode observers in uncertain chaotic communication , 2007, Int. J. Syst. Sci..

[2]  E. Ruiz,et al.  Bootstrapping Financial Time Series , 2002 .

[3]  J..  Estimating the Fractal Dimension of Chaotic Time Series , 1990 .

[4]  James P. Crutchfield,et al.  Geometry from a Time Series , 1980 .

[5]  Farmer,et al.  Predicting chaotic time series. , 1987, Physical review letters.

[6]  George Sugihara,et al.  Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series , 1990, Nature.

[7]  Fernando de Oliveira Souza,et al.  Synchronisation of chaotic delayed artificial neural networks: an ℍ ∞ control approach , 2009, Int. J. Syst. Sci..

[8]  J. Yorke,et al.  Period Three Implies Chaos , 1975 .

[9]  F. Takens.  Detecting strange attractors in turbulence , 1981 .

[10]  P. Grassberger,et al.  Measuring the Strangeness of Strange Attractors , 1983 .

[11]  Ioannis Andreadis,et al.  Chaotic analysis of US money and velocity measures , 2000, Int. J. Syst. Sci..

[12]  Upmanu Lall,et al.  Non‐parametric short‐term forecasts of the Great Salt Lake using atmospheric indices , 2007 .

[13]  Hsin-Chia Fu,et al.  Weighted bootstrap for neural model selection , 2008, Int. J. Syst. Sci..

[14]  James Theiler,et al.  Estimating fractal dimension , 1990 .

[15]  Wenlei Li.  Tracking control of chaotic coronary artery system , 2012, Int. J. Syst. Sci..

[16]  A. Wolf,et al.  Determining Lyapunov exponents from a time series , 1985 .

[17]  Martin Casdagli,et al.  Nonlinear prediction of chaotic time series , 1989 .