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Is it Possible to Study Chaotic and ARCH Behaviour Jointly? Application of a Noisy Mackey–Glass Equation with Heteroskedastic Errors to the Paris Stock Exchange Returns Series

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Author Info

  • Catherine Kyrtsou
  • Michel Terraza

Abstract

Most recent empirical works that apply sophisticated statistical proceduressuch as a correlation-dimension method have shown that stock returns arehighly complex. The estimated correlation dimension is high and there islittle evidence of low-dimensional deterministic chaos. Taking the complexbehaviour in stock markets into account, we think it is more robust than thetraditional stochastic approach to model the observed data by a nonlinearchaotic model disturbed by dynamic noise. In fact, we construct a model havingnegligible or even zero autocorrelations in the conditional mean, but a richstructure in the conditional variance. The model is a noisy Mackey–Glassequation with errors that follow a GARCH(p,q) process. This model permits usto capture volatility-clustering phenomena. Its characteristic is thatvolatility clustering is interpreted as an endogenous phenomenon. The mainobjective of this article is the identification of the underlying process ofthe Paris Stock Exchange returns series CAC40. To this end, we apply severaldifferent tests to detect longmemory components and chaotic structures.Forecasting results for the CAC40 returns series, will conclude this paper. Copyright Kluwer Academic Publishers 2003

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File URL: http://hdl.handle.net/10.1023/A:1023939610962
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Bibliographic Info

Article provided by Society for Computational Economics in its journal Computational Economics.

Volume (Year): 21 (2003)
Issue (Month): 3 (June)
Pages: 257-276

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Handle: RePEc:kap:compec:v:21:y:2003:i:3:p:257-276

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Web page: http://www.springerlink.com/link.asp?id=100248
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Related research

Keywords: Mackey–Glass equation; noisy chaos; volatility clustering; correlation dimension; Lyapunov exponents; GARCH effects; forecasting;

References

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  1. Hsieh, David A, 1991. " Chaos and Nonlinear Dynamics: Application to Financial Markets," Journal of Finance, American Finance Association, vol. 46(5), pages 1839-77, December.
  2. Gaunersdorfer, Andrea, 2000. "Endogenous fluctuations in a simple asset pricing model with heterogeneous agents," Journal of Economic Dynamics and Control, Elsevier, vol. 24(5-7), pages 799-831, June.
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  5. Xue-Zhong He & Carl Chiarella, 1999. "Heterogeneous Beliefs, Risk and Learning in a Simple Asset-Pricing Model," Computing in Economics and Finance 1999 223, Society for Computational Economics.
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  8. Malliaris, A. G. & Stein, Jerome L., 1999. "Methodological issues in asset pricing: Random walk or chaotic dynamics," Journal of Banking & Finance, Elsevier, vol. 23(11), pages 1605-1635, November.
  9. Chen, Shu-Heng & Lux, Thomas & Marchesi, Michele, 2001. "Testing for non-linear structure in an artificial financial market," Journal of Economic Behavior & Organization, Elsevier, vol. 46(3), pages 327-342, November.
  10. Giulia Iori, 1999. "A microsimulation of traders activity in the stock market: the role of heterogeneity, agents' interactions and trade frictions," Finance 9905005, EconWPA.
  11. Hsieh, David A, 1989. "Testing for Nonlinear Dependence in Daily Foreign Exchange Rates," The Journal of Business, University of Chicago Press, vol. 62(3), pages 339-68, July.
  12. Carl Chiarella & Roberto Dieci & Laura Gardini, 2001. "Speculative Behaviour and Complex Asset Price Dynamics," Research Paper Series 49, Quantitative Finance Research Centre, University of Technology, Sydney.
  13. Kyrtsou, Catherine & Terraza, Michel, 2002. "Stochastic chaos or ARCH effects in stock series?: A comparative study," International Review of Financial Analysis, Elsevier, vol. 11(4), pages 407-431.
  14. Bruce Mizrach, 1996. "Learning and Conditional Heteroscedasticity in Asset Returns," Departmental Working Papers 199526, Rutgers University, Department of Economics.
  15. Lux, Thomas, 1998. "The socio-economic dynamics of speculative markets: interacting agents, chaos, and the fat tails of return distributions," Journal of Economic Behavior & Organization, Elsevier, vol. 33(2), pages 143-165, January.
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Citations

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Cited by:
  1. Kyrtsou, Catherine & Malliaris, Anastasios G., 2009. "The impact of information signals on market prices when agents have non-linear trading rules," Economic Modelling, Elsevier, vol. 26(1), pages 167-176, January.
  2. Kyrtsou, Catherine, 2008. "Re-examining the sources of heteroskedasticity: The paradigm of noisy chaotic models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(27), pages 6785-6789.
  3. Constantinos E. Vorlow, 2004. "Stock Price Clustering and Discreteness: The "Compass Rose" and Predictability," Papers cond-mat/0408013, arXiv.org.
  4. Nguyen, Dung Tien, 2012. "Mackey–Glass equation driven by fractional Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(22), pages 5465-5472.
  5. Emmanuel Anoruo, 2011. "Testing for Linear and Nonlinear Causality between Crude Oil Price Changes and Stock Market Returns," International Journal of Economic Sciences and Applied Research (IJESAR), Technological Educational Institute (TEI) of Kavala, Greece, vol. 4(3), pages 75-92, December.
  6. Kyrtsou, Catherine & Labys, Walter C., 2006. "Evidence for chaotic dependence between US inflation and commodity prices," Journal of Macroeconomics, Elsevier, vol. 28(1), pages 256-266, March.
  7. Kyrtsou, Catherine & Labys, Walter C., 2007. "Detecting positive feedback in multivariate time series: The case of metal prices and US inflation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 377(1), pages 227-229.
  8. Catherine Kyrtsou & Michel Terraza, 2008. "Seasonal Mackey-Glass-GARCH process and short-term dynamics," Discussion Paper Series 2008_09, Department of Economics, University of Macedonia, revised Sep 2008.
  9. Malliaris, A.G. & Kyrtsou, C., 2009. "Editorial introduction of the special issue: "Energy sector pricing and macroeconomic dynamics"," Energy Economics, Elsevier, vol. 31(6), pages 825-826, November.
  10. Alexandros Leontitsis & Constantinos E. Vorlow, 2005. "Accounting for outliers and calendar effects in surrogate simulations of stock return sequences," Papers physics/0504187, arXiv.org.
  11. Kyrtsou, Catherine & Serletis, Apostolos, 2006. "Univariate tests for nonlinear structure," Journal of Macroeconomics, Elsevier, vol. 28(1), pages 154-168, March.
  12. Manish Kumar, 2009. "A Bivariate Linear and Nonlinear Causality between Stock Prices and Exchange Rates," Economics Bulletin, AccessEcon, vol. 29(4), pages 2884-2895.
  13. Constantinos VORLOW & Antonios ANTONIOU & Catherine KYRTSOU, 2004. "Surrogate Data Analysis and Stochastic Chaotic Modelling: Application to Stock Exchange Returns Series," Computing in Economics and Finance 2004 27, Society for Computational Economics.
  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.

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