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Non-linear noise reduction and detecting chaos: some evidence from the S&P Composite Price Index

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  • Harrison, Robert G.
  • Yu, Dejin
  • Oxley, Les
  • Lu, Weiping
  • George, Donald

Abstract

Academic and applied researchers in economics have, in the last 10 years, become increasingly interested in the topic of chaotic dynamics. In this paper we undertake non-linear dynamical analysis of one representative time series taken from financial markets, namely the Standard and Poor's (S&P) Composite Price Index. The data is based upon (adjusted) daily data from 1928 to 1987 comprising 16 127 observations. The results in the paper, based on the Grassberger–Procaccia (GP) correlation dimension measurement in conjunction with non-linear noise filtering and the surrogate technique, show strong evidence of chaos in one of these series, the S&P 500. The analysis shows that the accuracy of results improves with the increase in the number of recording points and the length of the time series, 5000 data points being sufficient to identify deterministic dynamics.

Suggested Citation

  • Harrison, Robert G. & Yu, Dejin & Oxley, Les & Lu, Weiping & George, Donald, 1999. "Non-linear noise reduction and detecting chaos: some evidence from the S&P Composite Price Index," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 48(4), pages 497-502.
    • Handle: RePEc:eee:matcom:v:48:y:1999:i:4:p:497-502
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    References listed on IDEAS

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    1. Hodrick, Robert J & Prescott, Edward C, 1997. "Postwar U.S. Business Cycles: An Empirical Investigation," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 29(1), pages 1-16, February.
    2. Ramsey, James B & Sayers, Chera L & Rothman, Philip, 1990. "The Statistical Properties of Dimension Calculations Using Small Data Sets: Some Economic Applications," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 31(4), pages 991-1020, November.
    3. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
    4. Chen Ping, 1996. "A Random Walk or Color Chaos on the Stock Market? Time-Frequency Analysis of S&P Indexes," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 1(2), pages 1-19, July.
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    2. Small Michael & Tse Chi K., 2003. "Determinism in Financial Time Series," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 7(3), pages 1-31, October.
    3. Akbar, Muhammad & Ullah, Ihsan & Ali, Shahid & Rehman, Naser, 2024. "Adaptive market hypothesis: A comparison of Islamic and conventional stock indices," International Review of Economics & Finance, Elsevier, vol. 89(PA), pages 460-477.

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