Stochastically equivalent dynamical system approach to nonlinear deterministic prediction

  • Authors:

  • Ikuo Matsuba;Hiroshi Takahashi;Shinya Wakasa

  • Affiliations:

  • Department of Information and Image Sciences, Faculty of Engineering, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba-shi, 263-8522 Japan;Department of Information and Image Sciences, Faculty of Engineering, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba-shi, 263-8522 Japan;Department of Information and Image Sciences, Faculty of Engineering, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba-shi, 263-8522 Japan

  • Venue:
  • Design and application of hybrid intelligent systems
  • Year:
  • 2003

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Abstract

We propose a new prediction method for the nonlinear time series based on the paradigm of deterministic chaos. Introducing the stochastically equivalent dynamical system to the original map, a prediction system is derived by minimizing the random term that defines intervals in which a good prediction performance is obtained. The use of the present method is illustrated for some chaotic systems with particular emphasis on issues of choices of variable time steps that are necessary when discretizing the stochastic differential equation. Applying to some systems, it is found that the present method works well.