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On Determining the Dimension of Real-Time Stock-Price Data

Author

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  • Mayfield, E Scott
  • Mizrach, Bruce

Abstract

The authors estimate the dimension of high-frequency stock-price data using the correlation integral of P. Grassberger and I. Procaccia. The data, even after filtering, appear to be of low dimension. To control for dependence in higher moments, the authors use a new technique known as the method of delays in their reconstruction. Delaying the data leads dimension estimates similar to random processes. They conclude that the data are either of low dimension with high entropy or nonlinear but of high dimension.

Suggested Citation

  • Mayfield, E Scott & Mizrach, Bruce, 1992. "On Determining the Dimension of Real-Time Stock-Price Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(3), pages 367-374, July.
    • Handle: RePEc:bes:jnlbes:v:10:y:1992:i:3:p:367-74
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    Citations

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    Cited by:

    1. M. Matilla-Garcia & P. Sanz & F. J. Vazquez, 2004. "Dimension estimation with the BDS-G statistic," Applied Economics, Taylor & Francis Journals, vol. 36(11), pages 1219-1223.
    2. Eduardo Pozo & Lucia Amboj, 2001. "Noise reduction methods and the Grassberger-Procaccia algorithm. A simulation study," Applied Economics Letters, Taylor & Francis Journals, vol. 8(2), pages 71-75.
    3. Samir Saadi & Devinder Gandhi & Khaled Elmawazini, 2006. "On the validity of conventional statistical tests given evidence of non-synchronous trading and non-linear dynamics in returns generating process," Applied Economics Letters, Taylor & Francis Journals, vol. 13(5), pages 301-305.
    4. Ayşe İşi & Fatih Çemrek, 2019. "Comparison of the Global, Local and Semi-Local Chaotic Prediction Methods for Stock Markets: The Case of FTSE-100 Index," Alphanumeric Journal, Bahadir Fatih Yildirim, vol. 7(2), pages 289-300, December.
    5. Aparicio, Teresa & Pozo, Eduardo F. & Saura, Dulce, 2008. "Detecting determinism using recurrence quantification analysis: Three test procedures," Journal of Economic Behavior & Organization, Elsevier, vol. 65(3-4), pages 768-787, March.
    6. Rohnn Sanderson, 2011. "Compartmentalising Gold Prices," International Journal of Business and Economic Sciences Applied Research (IJBESAR), International Hellenic University (IHU), Kavala Campus, Greece (formerly Eastern Macedonia and Thrace Institute of Technology - EMaTTech), vol. 4(2), pages 99-124, August.
    7. Mastroeni, Loretta & Vellucci, Pierluigi & Naldi, Maurizio, 2019. "A reappraisal of the chaotic paradigm for energy commodity prices," Energy Economics, Elsevier, vol. 82(C), pages 167-178.
    8. Costas Siriopoulos & Alexandros Leontitsis, 2002. "Nonlinear Noise Estimation in International Capital Markets," Multinational Finance Journal, Multinational Finance Journal, vol. 6(1), pages 43-63, March.
    9. Simón Sosvilla-Rivero & Fernando Fernández-Rodriguez & Julián Andrada-Félix, 2005. "Testing chaotic dynamics via Lyapunov exponents," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(7), pages 911-930.
    10. McKenzie, Michael D., 2001. "Chaotic behavior in national stock market indices: New evidence from the close returns test," Global Finance Journal, Elsevier, vol. 12(1), pages 35-53.
    11. Mizrach, Bruce, 1996. "Determining delay times for phase space reconstruction with application to the FF/DM exchange rate," Journal of Economic Behavior & Organization, Elsevier, vol. 30(3), pages 369-381, September.
    12. Nie, Chun-Xiao, 2017. "Correlation dimension of financial market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 632-639.
    13. 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.
    14. Leontitsis, Alexandros & Vorlow, Constantinos E., 2006. "Accounting for outliers and calendar effects in surrogate simulations of stock return sequences," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 368(2), pages 522-530.
    15. Cheung, Yin-Wong & Lai, Kon S., 1995. "A search for long memory in international stock market returns," Journal of International Money and Finance, Elsevier, vol. 14(4), pages 597-615, August.
    16. Nie, Chun-Xiao, 2019. "Applying correlation dimension to the analysis of the evolution of network structure," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 294-303.
    17. Orzeszko, Witold, 2008. "The new method of measuring the effects of noise reduction in chaotic data," Chaos, Solitons & Fractals, Elsevier, vol. 38(5), pages 1355-1368.
    18. Barkoulas, John T. & Chakraborty, Atreya & Ouandlous, Arav, 2012. "A metric and topological analysis of determinism in the crude oil spot market," Energy Economics, Elsevier, vol. 34(2), pages 584-591.
    19. Anagnostidis, Panagiotis & Emmanouilides, Christos J., 2015. "Nonlinearity in high-frequency stock returns: Evidence from the Athens Stock Exchange," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 421(C), pages 473-487.
    20. Adrangi, Bahram & Chatrath, Arjun & Dhanda, Kanwalroop Kathy & Raffiee, Kambiz, 2001. "Chaos in oil prices? Evidence from futures markets," Energy Economics, Elsevier, vol. 23(4), pages 405-425, July.
    21. Marisa Faggini & Bruna Bruno & Anna Parziale, 2019. "Does Chaos Matter in Financial Time Series Analysis?," International Journal of Economics and Financial Issues, Econjournals, vol. 9(4), pages 18-24.
    22. Barkoulas, John T., 2008. "Testing for deterministic monetary chaos: Metric and topological diagnostics," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 1013-1024.

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