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A Random Walk or Color Chaos on the Stock Market? Time-Frequency Analysis of S&P Indexes

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  • Chen Ping

    (The University of Texas Austin, Texas)

Abstract

The random-walk (white-noise) model and the harmonic model are two polar models in linear systems. A model in between is color chaos, which generates irregular oscillations with a narrow frequency (color) band. Time-frequency analysis is introduced for evolutionary time-series analysis. The deterministic component from noisy data can be recovered by a time-variant filter in Gabor space. The characteristic frequency is calculated from the Wigner decomposed distribution series. It is found that about 70 percent of fluctuations in Standard & Poor stock price indexes, such as the FSPCOM and FSDXP monthly series, detrended by the Hodrick-Prescott (HP) filter, can be explained by deterministic color chaos. The characteristic period of persistent cycles is around three to four years. Their correlation dimension is about 2.5. The existence of persistent chaotic cycles reveals a new perspective of market resilience and new sources of economic uncertainties. The nonlinear pattern in the stock market may not be wiped out by market competition under nonequilibrium situations with trend evolution and frequency shifts. The color-chaos model of stock-market movements may establish a potential link between business-cycle theory and asset-pricing theory.

Suggested Citation

  • 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.
    • Handle: RePEc:bpj:sndecm:v:1:y:1996:i:2:n:2
    DOI: 10.2202/1558-3708.1014
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    Cited by:

    1. Jason Angelopoulos, 2017. "Time–frequency analysis of the Baltic Dry Index," Maritime Economics & Logistics, Palgrave Macmillan;International Association of Maritime Economists (IAME), vol. 19(2), pages 211-233, June.
    2. Ping Chen, 2014. "Metabolic growth theory: market-share competition, learning uncertainty, and technology wavelets," Journal of Evolutionary Economics, Springer, vol. 24(2), pages 239-262, April.
    3. Tangian, Andranik, 2008. "Predicting DAX trends from Dow Jones data by methods of the mathematical theory of democracy," European Journal of Operational Research, Elsevier, vol. 185(3), pages 1632-1662, March.
    4. Ali Moeini & Mehdi Ahrari & Saeed Sadat Madarshahi3, 2007. "Investigating Chaos in Tehran Stock Exchange Index," Iranian Economic Review (IER), Faculty of Economics,University of Tehran.Tehran,Iran, vol. 12(1), pages 103-120, winter.
    5. Kapil Gupta & Balwinder Singh, 2009. "Information Memory and Pricing Efficiency of Futures Contracts," Journal of Emerging Market Finance, Institute for Financial Management and Research, vol. 8(2), pages 191-250, May.
    6. Antonios Antoniou & Constantinos E. Vorlow, 2004. "Price Clustering and Discreteness: Is there Chaos behind the Noise?," Papers cond-mat/0407471, arXiv.org.
    7. Carlos Pedro Gonc{c}alves, 2018. "Financial Risk and Returns Prediction with Modular Networked Learning," Papers 1806.05876, arXiv.org.
    8. Antoniou, Antonios & Vorlow, Constantinos E., 2005. "Price clustering and discreteness: is there chaos behind the noise?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 348(C), pages 389-403.
    9. Tan, Zhengxun & Liu, Juan & Chen, Juanjuan, 2021. "Detecting stock market turning points using wavelet leaders method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 565(C).
    10. 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.
    11. Greg Hannsgen & Tai Young-Taft, 2015. "Inside Money in a Kaldor-Kalecki-Steindl Fiscal Policy Model: The Unit of Account, Inflation, Leverage, and Financial Fragility," Economics Working Paper Archive wp_839, Levy Economics Institute.
    12. Antoniou, Antonios & Vorlow, Constantinos E., 2004. "Recurrence quantification analysis of wavelet pre-filtered index returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(1), pages 257-262.
    13. Ignacio Escanuela Romana & Clara Escanuela Nieves, 2023. "A spectral approach to stock market performance," Papers 2305.05762, arXiv.org.
    14. Yinghao LUO, 2016. "Nonlinear Trend and Purchasing Power Parity," Journal of Economics Bibliography, KSP Journals, vol. 3(3), pages 490-497, September.
    15. Tahsina Haque Simu, 2012. "Randomness in CASPI (CSE All Share Price Index): An Empirical Study," Indian Journal of Commerce and Management Studies, Educational Research Multimedia & Publications,India, vol. 3(2), pages 01-05, May.
    16. Tao You & Paweł Fiedor & Artur Hołda, 2015. "Network Analysis of the Shanghai Stock Exchange Based on Partial Mutual Information," JRFM, MDPI, vol. 8(2), pages 1-19, June.
    17. Scarlat, E.I. & Stan, Cristina & Cristescu, C.P., 2007. "Chaotic features in Romanian transition economy as reflected onto the currency exchange rate," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 396-404.
    18. Gurmeet Singh, 2017. "Estimating Optimal Hedge Ratio and Hedging Effectiveness in the NSE Index Futures," Jindal Journal of Business Research, , vol. 6(2), pages 108-131, December.
    19. Sharif Md. Raihan & Yi Wen & Bing Zeng, 2005. "Wavelet: a new tool for business cycle analysis," Working Papers 2005-050, Federal Reserve Bank of St. Louis.

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