Skip to main content

Nonlinear time series analysis — Potentials and limitations

  • Conference paper
  • First Online:
Nonlinear Physics of Complex Systems

Part of the book series: Lecture Notes in Physics ((LNP,volume 476))

  • 181 Accesses

Abstract

Nonlinear time series analysis offers an approach to the understanding of complex systems on the basis of observed data, if the dynamics is effectively lowdimensional deterministic. Since only a small subset out of all interesting signals with irregular time dependence falls into this class, extensions of the methods towards deterministic systems coupled to random noises and towards systems with more than a few active degrees of freedom are required.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Eckmann, J. P., Oliffson Kamphorst, S., Ruelle, D., & Ciliberto, S. (1986): Lyapunov exponents from a time series. Phys. Rev. A34, 4971–4979

    ADS  Google Scholar 

  • Flepp, L., Holzner, R., Brun, E., Finardi, M., & Badii, R. (1991): Model identification by periodic-orbit analysis for NMR-laser chaos. Phys. Rev. Lett. 67, 2244–2247

    Article  ADS  Google Scholar 

  • Grassberger, P. & Procaccia, I. (1983): Characterization of strange attractors Phys. Rev. Lett. 50, 346–349

    Article  ADS  MathSciNet  Google Scholar 

  • Grassberger, P. & Procaccia, I. (1983): Measuring the strangeness of strange attractors Physica 9D, 189–208

    ADS  MathSciNet  Google Scholar 

  • Grassberger, P., Schreiber, T., & Schaffrath, C. (1991): Nonlinear time sequence analysis., Intl. J. Bifurcation and Chaos 1, 521–547

    Article  MATH  MathSciNet  Google Scholar 

  • Haken, H. (1975): Analogy between higher instabilities in fluids and lasers. Phys. Lett. A 53, 77–88

    ADS  Google Scholar 

  • Haken, H. and Borland, L. (1992): Unbiased determination of forces causing observed processes. Z. Phys. B — Condensed Matter 88, 95–103

    Article  ADS  Google Scholar 

  • Jaeger, L. and Kantz, H. (1996): Unbiased estimation underlying the dynamics of a noisy chaotic time series. unpublished

    Google Scholar 

  • Kantz, H. (1994): A robust method to estimate the maximal Lyapunov exponent of a time series. Phys. Lett. A 185, 77–87

    ADS  Google Scholar 

  • Kantz, H., Schreiber, T., Hoffmann, I., Buzug, T., Pfister, G., Flepp, L. G., Simonet, J., Badii, R., & Brun, E. (1993): H. Kantz, T. Schreiber, I. Hoffmann, T. Buzug, Nonlinear noise reduction: A case study on experimantal data. Phys. Rev. E 48, 1529–1538

    ADS  Google Scholar 

  • Kantz, H. and Schreiber, T. (1996): Nonlinear Time Series Analysis. Cambridge University Press, in press

    Google Scholar 

  • Packard, N. H., Crutchfield, J. P., Farmer, J. D., & Shaw, R. S. (1980): Geometry from a time series. Phys. Rev. Lett. 45, 712–716

    Article  ADS  Google Scholar 

  • Rosenstein, M. T., Collins, J. J., & De Luca, C. J. (1994): Reconstruction expansion as a geometry-based framework for choosing proper delay times. Physica D 65, 117–134

    ADS  Google Scholar 

  • Sano, M. & Sawada, Y. (1985): Measurement of the Lyapunow spectrum from a chaotic time series. Phys. Rev. Lett. 55, 1082–1085

    Article  ADS  MathSciNet  Google Scholar 

  • Sauer, T., Yorke, J., & Casdagli, M. (1991): Embedology. J. Stat. Phys. 65, 579–616

    Article  MATH  MathSciNet  ADS  Google Scholar 

  • Takens, F. (1981): Detecting strange attractors in turbulence. Lecture Notes in Math. Vol. 898, Springer, New York.

    Google Scholar 

  • Theiler, J. (1986): Spurious dimension from correlation algorithms applied to limited time series data. Phys. Rev. A34, 2427–2432

    ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Jürgen Parisi Stefan C. Müller Walter Zimmermann

Rights and permissions

Reprints and permissions

Copyright information

© 1996 Springer-Verlag

About this paper

Cite this paper

Kantz, H. (1996). Nonlinear time series analysis — Potentials and limitations. In: Parisi, J., Müller, S.C., Zimmermann, W. (eds) Nonlinear Physics of Complex Systems. Lecture Notes in Physics, vol 476. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0105440

Download citation

  • DOI: https://doi.org/10.1007/BFb0105440

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61734-1

  • Online ISBN: 978-3-540-70699-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics