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The finite sample behavior of the 0–1 test for chaos

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  • Belaire-Franch, Jorge

Abstract

In a recent paper, Webel (2012) provides evidence of chaotic structures in the stock returns of all DAX members, by using the so-called 0–1 test developed by Gottwald and Melbourne (2004). The main aim of this paper is to show, through a Monte Carlo experiment, that the 0–1 test is severely oversized against leptokurtic random processes, hence Webel (2012) conclusions may not be reliable. Moreover, noise filtering may affect the power of the test against noisy discrete chaotic systems. Therefore, the application of this procedure on high frequency financial data, and in general on noise-filtered data, should be performed with caution.

Suggested Citation

  • Belaire-Franch, Jorge, 2020. "The finite sample behavior of the 0–1 test for chaos," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).
    • Handle: RePEc:eee:phsmap:v:555:y:2020:i:c:s0378437120303666
    DOI: 10.1016/j.physa.2020.124733
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    1. Litak, G. & Syta, A. & Budhraja, M. & Saha, L.M., 2009. "Detection of the chaotic behaviour of a bouncing ball by the 0–1 test," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1511-1517.
    2. Loukas Zachilas & Iacovos N. Psarianos, 2012. "Examining the Chaotic Behavior in Dynamical Systems by Means of the 0-1 Test," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-14, May.
    3. M. Angeles Carnero, 2004. "Persistence and Kurtosis in GARCH and Stochastic Volatility Models," Journal of Financial Econometrics, Oxford University Press, vol. 2(2), pages 319-342.
    4. Litak, Grzegorz & Syta, Arkadiusz & Wiercigroch, Marian, 2009. "Identification of chaos in a cutting process by the 0–1 test," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2095-2101.
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