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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. 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.
    3. Marisa Faggini & Anna Parziale, 2016. "More than 20 years of chaos in economics," Mind & Society: Cognitive Studies in Economics and Social Sciences, Springer;Fondazione Rosselli, vol. 15(1), pages 53-69, June.
    4. 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.
    5. Nie, Chun-Xiao, 2017. "Correlation dimension of financial market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 632-639.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. Rohnn Sanderson, 2011. "Compartmentalising Gold Prices," International Journal of Business and Economic Sciences Applied Research (IJBESAR), Eastern Macedonia and Thrace Institute of Technology (EMATTECH), Kavala, Greece, vol. 4(2), pages 99-124, August.

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