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Using the Correlation Exponent to Decide whether an Economic Series is Chaotic

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  • Liu, T
  • Granger, C W J
  • Heller, W P

Abstract

We consider two ways of distinguishing deterministic time-series from stochastic white noise; the Grassberger-Procaccia correlation exponent test and the Brock, Dechert, Scheinkman (or BDS) test. Using simulated data to test the power of these tests, the correlation exponent test can distinguish white noise from chaos. It cannot distinguish white noise from chaos mixed with a small amount of white noise. With i.i.d. as the null, the BDS correctly rejects the null when the data are deterministic chaos. Although the BDS test may also reject the null even when the data are stochastic, it may be useful in distinguishing between linear and nonlinear stochastic processes. Copyright 1992 by John Wiley & Sons, Ltd.

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  • Liu, T & Granger, C W J & Heller, W P, 1992. "Using the Correlation Exponent to Decide whether an Economic Series is Chaotic," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(S), pages 25-39, Suppl. De.
  • Handle: RePEc:jae:japmet:v:7:y:1992:i:s:p:s25-39
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    Cited by:

    1. Cheteni, Priviledge, 2013. "Non-linearity behaviour of the ALBI Index: A case of Johannesburg Stock Exchange in South Africa," MPRA Paper 56369, University Library of Munich, Germany.
    2. Jose-Manuel Rey & Manuel Morán, 1999. "A Formalism for the Dimensional Analysis of Time Series," Computing in Economics and Finance 1999 1331, Society for Computational Economics.
    3. Mattarocci, Gianluca, 2006. "Market characteristics and chaos dynamics in stock markets: an international comparison," MPRA Paper 4296, University Library of Munich, Germany, revised Jun 2006.
    4. Granger, Clive W J, 1995. "Modelling Nonlinear Relationships between Extended-Memory Variables," Econometrica, Econometric Society, vol. 63(2), pages 265-279, March.
    5. M. Shibley Sadique, 2011. "Testing for Neglected Nonlinearity in Weekly Foreign Exchange Rates," Review of Economics & Finance, Better Advances Press, Canada, vol. 1, pages 77-88, June.
    6. Juan Benjamín Duarte Duarte & Juan Manuel Mascare?nas Pérez-Iñigo, 2014. "Comprobación de la eficiencia débil en los principales mercados financieros latinoamericanos," ESTUDIOS GERENCIALES, UNIVERSIDAD ICESI, November.
    7. Pierdzioch, Christian & Stadtmann, Georg, 1999. "Komplexe Aktien- und Wechselkursdynamik in einem makroökonomischen Modell mit heterogener Erwartungsbildung," Kiel Working Papers 911, Kiel Institute for the World Economy (IfW).
    8. Domenico Mignacca & Mauro Gallegati, 1994. "Is US Real GNP Chaotic? On Using the BDS test to Decide Whether an ARMA Model forthe US GNP Genreates I.I.D. Residuals," International Finance 9410002, EconWPA, revised 09 Nov 1994.

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