Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Cawley, R. and Hsu, G.-H. (1992a): Phys. Rev. A 46, 3057.
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.
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.
Cawley, R., Hsu, G.-H., and Salvino, L.W. (1995) (in preparation).
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.
Grasssberger, P. and Procaccia, I. (1983): Phys. Rev. Lett. 50, 346 (1983); and Physica D 9, 189 (1983).
Grassberger, P., Hegger, R., Kantz, H., Schaffrath, C., and Schreiber, T. (1993): Chaos 2, 127.
Greenside, H., Wolf, A., Swift, J., and Pignataro, T. (1982): Phys. Rev. A 25, 3453.
Hammel, S.M., Jones, C.K.R.T., and Moloney, J.V. (1985): J. Opt. Soc. America, B2, 552.
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.
Kaplan, D.T., and Glass, L. (1992): Phys. Rev. Lett. 68, 427); and Physica D 64, 431.
Kennel, M.B., Brown, R., and Abarbanel, H.D.I. (1992): Phys. Rev. A 45, 3403.
Kostelich, E. and Yorke, J.A. (1988): Phys. Rev. A 38, 1649.
Kostelich, E.J. and Schreiber, T. (1993): Phys. Rev. E 48, 1752.
Mandelbrot, B.B. (1974): The Fractal Geometry of Nature, W.H. Freeman.
Osborne, A.R., and Provenzale, A. (1989): Physica D 35, 357.
Packard, N.H., Crutchfield, J.P., Farmer, J.D., and Shaw, R.S. (1980): Phys. Rev. Lett. 45, 712.
Parlitz, U. (1992): Int. J. Bif. Chaos 2, 155.
Rapp, P.E. (1993): Biologist 40, 89.
Salvino, L.W. and Cawley, R. (1994): Phys. Rev. Letters 73, 1091.
Takens, F. (1981): in Lecture Notes in Mathematics(ed. by D.A. Rand and L.-S. Young). Vol. 898, p. 366. Springer-Verlag, Berlin.
Theiler, J. (1991): Phys. Lett. A 155, 480.
Theiler, J. (1995): Phys. Lett. A 196, 335, 1995.
Theiler, J., Eubank, S., Longtin, A., Galdrikian, B., and Farmer, J.D. (1992): Physica D 58, 77.
Tufillaro, N.B., Wyckoff, P., Brown, R., Schreiber, T., and Molteno, T. (1995): Phys. Rev. E 50, 164.
Wayland, R., Bromley, D., Pickett, D., and Passamante, A. (1993): Phys. Rev. Lett. 70, 580.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Cawley, R., Hsu, GH., Salvino, L.W. (1996). Method to Discriminate Against Determinism in Time Series Data. In: Kravtsov, Y.A., Kadtke, J.B. (eds) Predictability of Complex Dynamical Systems. Springer Series in Synergetics, vol 69. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-80254-6_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-80254-6_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-80256-0
Online ISBN: 978-3-642-80254-6
eBook Packages: Springer Book Archive