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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.

Suggested Citation

  • 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. 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. Gianluca Mattarocci, 2009. "Market Characteristics and Chaos Dynamics in Stock Markets: an International Comparison," Palgrave Macmillan Studies in Banking and Financial Institutions, in: Alessandro Carretta & Franco Fiordelisi & Gianluca Mattarocci (ed.), New Drivers of Performance in a Changing Financial World, chapter 6, pages 89-106, Palgrave Macmillan.
    4. 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.
    5. 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 Kiel).
    6. 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, University Library of Munich, Germany, revised 09 Nov 1994.
    7. 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.
    8. Granger, Clive W J, 1995. "Modelling Nonlinear Relationships between Extended-Memory Variables," Econometrica, Econometric Society, vol. 63(2), pages 265-279, March.
    9. Kaboudan, M. A., 2001. "Genetically evolved models and normality of their fitted residuals," Journal of Economic Dynamics and Control, Elsevier, vol. 25(11), pages 1719-1749, November.
    10. 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.
    11. Richard T. Baillie & Aydin A. Cecen & Young-Wook Han, 2000. "High Frequency Deutsche Mark-US Dollar Returns: FIGARCH Representations and Non Linearities," Multinational Finance Journal, Multinational Finance Journal, vol. 4(3-4), pages 247-267, September.
    12. Letícia P D Mortoza & José R C Piqueira, 2017. "Measuring complexity in Brazilian economic crises," PLOS ONE, Public Library of Science, vol. 12(3), pages 1-12, March.

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