Skip to main content

Determining Minimum Embedding Dimension from Scalar Time Series

  • Chapter
Modelling and Forecasting Financial Data

Part of the book series: Studies in Computational Finance ((SICF,volume 2))

Abstract

Determining embedding dimension is considered as one of the most important steps in nonlinear time series modelling and prediction. A number of methods have been developed in determining the minimum embedding dimension since the early study of nonlinear time series analysis. Some of the methods are briefly reviewed in this chapter. The false nearest neighbor and the averaged false nearest neighbor methods are described in details, given the methods have been widely used in the literature. Several real economic time series are tested to demonstrate applications of the methods.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 329.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • H.D. Abarbanel, R. Brown, J. Sidorowich and L. Tsimring, The analysis of observed chaotic data in physical systems, Rev. Mod. Phys., Vol.65(1993), 1331.

    Article  Google Scholar 

  • A.M. Albano, J. Muench, C. Schwartz, A.I. Mees and P.E. Rapp, Singular-value decomposition and the Grassberger-Procaccia algorithm, Phys. Rev. A, Vol.38(1988), 3017.

    Article  Google Scholar 

  • D.S. Broomhead and G.P. King, Extracting qualitative dynamics from experimental data, Physica D, Vol.20(1986), 217–236.

    Article  Google Scholar 

  • L.Y. Cao, Practical method for determining the minimum embedding dimension of a scalar time series, Physica D, Vol.110(1997), 43–50.

    Article  Google Scholar 

  •  L.Y. Cao, Y.G. Hong, H.Z. Zhao and S.H. Deng, Predicting economic time series using a nonlinear deterministic technique, Computational Economics, Vol.9(1996), 149–178.

    Article  Google Scholar 

  • J.P. Eckmann and D. Ruelle, Ergodic theory of chaos and strange attractors, Rev. Mod. Phys., Vol.57(1985), 617.

    Article  Google Scholar 

  • J.D. Farmer, Chaotic attractors of an infinite dimensional system, Physica D, Vol.4(1982), 366.

    Article  Google Scholar 

  • A.M. Fraser and H.L. Swinney, Independent coordinates for strange attractors from mutual information, Phys. Rev. A, Vol.33(1986), 1134–1140.

    Article  Google Scholar 

  • P. Grassberger and I. Procaccia, Characterization of strange attractors, Phys. Rev. Lett., Vol.50(1983), 346.

    Article  Google Scholar 

  • D. Kaplan and L. Glass, Direct test for determinism in a time series, Phys. Rev. Lett., Vol.68(1992), 427–430.

    Article  Google Scholar 

  • M. Kennel, R. Brown and H. Abarbanel, Determining embedding dimension for phase-space reconstruction using a geometrical construction, Phys. Rev. A, Vol.45(1992), 3403–3411.

    Article  Google Scholar 

  • W. Liebert and H.G. Schuster, Proper choice of time-delay for the analysis of chaotic time series, Phys. Lett. A, Vol.l42(1989), 107.

    Article  Google Scholar 

  • M.C. Mackey and L. Glass, Oscillation and chaos in physiological control systems, Science, Vol.197(1977), 287.

    Article  Google Scholar 

  • A.I. Mees, P.E. Rapp and L.S. Jennings, Singular-value decomposition and embedding dimension, Phys. Rev. A, Vol.36(1987), 340.

    Article  Google Scholar 

  • E. Ott, T. Sauer and J.A. Yorke, Coping with chaos: Analysis of chaotic data and the exploitation of chaotic systems, John Wiley & Sons, Inc. (1994).

    Google Scholar 

  • T. Sauer, J.A. Yorke and M. Casdagli, Embedology, Journal of Statistical Physics, Vol.65(1991), 579–616.

    Article  Google Scholar 

  • F. Takens, in Dynamical Systems and Turbulence, Warwick, edited by D. Rand and L.S. Young, Lecture Notes in Mathematics, Vol.898(1980), 366–381.

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer Science+Business Media New York

About this chapter

Cite this chapter

Cao, L. (2002). Determining Minimum Embedding Dimension from Scalar Time Series. In: Soofi, A.S., Cao, L. (eds) Modelling and Forecasting Financial Data. Studies in Computational Finance, vol 2. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-0931-8_3

Download citation

  • DOI: https://doi.org/10.1007/978-1-4615-0931-8_3

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-5310-2

  • Online ISBN: 978-1-4615-0931-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics