Evaluation of deterministic property of time series by the method of surrogate data and the trajectory parallel measure method

IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

Volumn E82-A, Issue 2, 2000, Pages 343-349

  Fujimoto, Yasunari ^a   Iokibe, Tadashi ^a  

^a MEIDENSHA CORPORATION   (Japan)

Author keywords

Chaos; Surrogate data; Time series analysis; Trajectory parallel measure method

Indexed keywords

CHAOS THEORY; RANDOM PROCESSES;

TRAJECTORY PARALLEL MEASURE (TPM) METHODS;

TIME SERIES ANALYSIS;

EID: 0033871020     PISSN: 09168508     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (15)

1. F. Takens, Dynamical systems and turbulence, pp.366-381, Springer-Verlag, Berlin, 1981.
2. P. Grassberger and I. Procaccia, "Characterization of strange attractors," Phys. Rev. Lett, vol.50, pp.346-349, 1983.
3. P. Grassberger and I. Procaccia, "Measuring the strangeness of strange attractor," Physica 9D, pp. 189-208, 1983.
4. A. Wolf, J.B. Swift, H.L. Swinney, and J.A. Vastano, "Determining lyapunov exponents from a time series," Physica D 16, pp.285-317, 1985.
5. N. Tanaka, H. Okamato, and M. Naito, "A way of distinguishing chaos from random fractal sequences based on the difference in time reversal symmetry," Jpn. J. Appl. Phys. vol.34, pp.863-865, 1995.
6. D. T.Kaplan and L. Glass, "Coarse-grained embeddings of time series: random walks, Gaussian random processes, and deterministic chaos," Physica D 64, pp.431-454, 1993.
7. Y. Fujimoto and T. Iokibe, "Measurement of determinism in time series by chaotic approach and its applications," International Journal of Advanced Computational Intelligence, vol.3, no.1, pp.50-55, 1999.
8. A.R. Osborne and A. Provenzale, "Finite correlation dimension for stochastic systems with power-low," Physica D, vol.35, pp.357-381, 1989.
9. J. Theiler, "Some comments on the correlation dimension of 1/f α noise," Physics Letters A, vol.155, nos.8, 9, pp.480-493, May 1991.
10. J. Theiler, S. Eubank, A. Lonting, B. Galdrinkian, and J.D. Framer, "Testing for nonlinearity in time series: the method of surrogate data," Physica D, vol.58, pp.77-94, 1992.
11. J. Theiler and D. Prichard, "Constrained-realization monte-carlo method for hypothesis testing," Physica D, vol.94, pp.221-235, 1996.
12. J. Theiler, B. Galdrikian, A. Longtin, S. Eubank, and J.D. Farmer, "Using surrogate data to detect nonlinearity in time series," in eds. M. Casdagli and S. Eubank, Nonlinear Modelling and Forecasting, pp. 163-188, Addison Wesley, 1992.
13. T. Ikeguchi and K. Aihara, "On dimension estimates with surrogate data sets," IECE Trans. Fundamentals, vol.E80-A, no.5, pp.859-868, 1997.
14. E.N. Lorenz, "Deterministic nonperiodic flow," J. Atmos Sci. vol.20, pp.130-141, 1963.
15. T. Iokibe, M. Kanke, Y. Fujimoto, and S. Suzuki, "Short-term prediction of chaotic time series by local fuzzy reconstruction method," J. Intelligent & Fuzzy Systems, vol.5, pp.3-21, John Wiley & Sons, 1997.