Method to Discriminate Against Determinism in Time Series Data

  • Robert Cawley
  • Guan-Hsong Hsu
  • Liming W. Salvino
Part of the Springer Series in Synergetics book series (SSSYN, volume 69)


We describe a general, systematic method for assessing the presence or absence of determinism in time series. Our method is rooted in the standard engineering paradigm of hypothesis testing. Our application of this procedure is novel, however, for we test given data sets against the class of data sets that produce smoothness. That is, our null hypothesis is that of determinism. We highlight two inherently interactive key features of our approach which conspire to make this treatment promising, the use of a smoothness detector and of chaotic noise reduction.


Time Series Vector Field Fractal Dimension Phase Portrait Noise Reduction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Cawley, R. and Hsu, G.-H. (1992a): Phys. Rev. A 46, 3057.CrossRefADSMathSciNetGoogle Scholar
  2. Cawley, R., and Hsu, G.-H. (1992b): Another new chaotic noise reduction algorithm, in Proc. of the First experimental chaos conference, Arlington, VA, October 1–3, 1991 (ed. by S. Vohra, M. Spano, M. Shlesinger, L. Pecora and W. Ditto). World Scientific Press, Singapore, 38–46.Google Scholar
  3. Cawley, R., Hsu, G.-H. and Salvino, L.W. (1994): Detection and diagnosis of dynamics in time series data: theory of noise reduction, in The chaos paradigm: developments and applications in engineering science, AIP Conference Proceedings Vol. 296, American Institute of Physics, New York, pp. 182–192.ADSGoogle Scholar
  4. Cawley, R., Hsu, G.-H., and Salvino, L.W. (1995) (in preparation).Google Scholar
  5. Ditto, W.L., Rauseo, S.N., Cawley, R., Grebogi, C., Hsu, G.-H., Kostelich, E., Ott, E., Savage, H.T., Segnan, R., Spano M.L., and Yorke, J.A. (1989): Phys. Rev. Lett., 63, 923.CrossRefADSGoogle Scholar
  6. Grasssberger, P. and Procaccia, I. (1983): Phys. Rev. Lett. 50, 346 (1983); and Physica D 9, 189 (1983).CrossRefADSMathSciNetGoogle Scholar
  7. Grassberger, P., Hegger, R., Kantz, H., Schaffrath, C., and Schreiber, T. (1993): Chaos 2, 127.CrossRefADSMathSciNetGoogle Scholar
  8. Greenside, H., Wolf, A., Swift, J., and Pignataro, T. (1982): Phys. Rev. A 25, 3453.CrossRefADSMathSciNetGoogle Scholar
  9. Hammel, S.M., Jones, C.K.R.T., and Moloney, J.V. (1985): J. Opt. Soc. America, B2, 552.CrossRefADSGoogle Scholar
  10. Hübner, U., Weiss, C.-O., Abraham, N.B., and Tang, D. (1993): in Time Series Prediction: Forecasting the Future and Understanding the Past(ed. by A.S. Weigend and N.A. Gershenfeld). Addison-Wesley, Reading, Mass. 73.Google Scholar
  11. Kaplan, D.T., and Glass, L. (1992): Phys. Rev. Lett. 68, 427); and Physica D 64, 431.CrossRefADSGoogle Scholar
  12. Kennel, M.B., Brown, R., and Abarbanel, H.D.I. (1992): Phys. Rev. A 45, 3403.CrossRefADSGoogle Scholar
  13. Kostelich, E. and Yorke, J.A. (1988): Phys. Rev. A 38, 1649.CrossRefADSMathSciNetGoogle Scholar
  14. Kostelich, E.J. and Schreiber, T. (1993): Phys. Rev. E 48, 1752.CrossRefADSMathSciNetGoogle Scholar
  15. Mandelbrot, B.B. (1974): The Fractal Geometry of Nature, W.H. Freeman.Google Scholar
  16. Osborne, A.R., and Provenzale, A. (1989): Physica D 35, 357.CrossRefMATHADSMathSciNetGoogle Scholar
  17. Packard, N.H., Crutchfield, J.P., Farmer, J.D., and Shaw, R.S. (1980): Phys. Rev. Lett. 45, 712.CrossRefADSGoogle Scholar
  18. Parlitz, U. (1992): Int. J. Bif. Chaos 2, 155.CrossRefMATHMathSciNetGoogle Scholar
  19. Rapp, P.E. (1993): Biologist 40, 89.Google Scholar
  20. Salvino, L.W. and Cawley, R. (1994): Phys. Rev. Letters 73, 1091.CrossRefADSGoogle Scholar
  21. Takens, F. (1981): in Lecture Notes in Mathematics(ed. by D.A. Rand and L.-S. Young). Vol. 898, p. 366. Springer-Verlag, Berlin.CrossRefMathSciNetGoogle Scholar
  22. Theiler, J. (1991): Phys. Lett. A 155, 480.CrossRefADSMathSciNetGoogle Scholar
  23. Theiler, J. (1995): Phys. Lett. A 196, 335, 1995.CrossRefADSGoogle Scholar
  24. Theiler, J., Eubank, S., Longtin, A., Galdrikian, B., and Farmer, J.D. (1992): Physica D 58, 77.CrossRefMATHADSGoogle Scholar
  25. Tufillaro, N.B., Wyckoff, P., Brown, R., Schreiber, T., and Molteno, T. (1995): Phys. Rev. E 50, 164.CrossRefADSGoogle Scholar
  26. Wayland, R., Bromley, D., Pickett, D., and Passamante, A. (1993): Phys. Rev. Lett. 70, 580.CrossRefADSGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Robert Cawley
  • Guan-Hsong Hsu
  • Liming W. Salvino

There are no affiliations available

Personalised recommendations