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Re-examining the sources of heteroskedasticity: The paradigm of noisy chaotic models

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  • Kyrtsou, Catherine

Abstract

In this paper, we analyze the rich dynamic properties of the noisy chaotic model developed by Kyrtsou [C. Kyrtsou, Evidence for neglected linearity in noisy chaotic models, International Journal of Bifurcation and Chaos 15 (10) (2005)] considering homoskedastic errors, with the aim of deriving information about possible links between noisy chaotic dynamics and ARCH effects. With the joint application of the Engle [R.F. Engle, Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation, Econometrica 50 (1982) 987–1007] and McLeod–Li [A.I. McLeod, W.K. Li, Diagnostic checking ARMA time series models using squared-residuals autocorrelations, Journal of Time Series Analysis 4 (1983) 269–273] tests for non-linearity in the second moment, we attempt to show how highly non-linear models can exhibit heteroskedasticity when no heteroskedastic structure is assumed by construction.

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Bibliographic Info

Article provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.

Volume (Year): 387 (2008)
Issue (Month): 27 ()
Pages: 6785-6789

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Handle: RePEc:eee:phsmap:v:387:y:2008:i:27:p:6785-6789

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Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/

Related research

Keywords: Heteroskedasticity; Noisy chaos; Endogenous dynamics; Econophysicss;

References

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  1. Diks, Cees, 2006. "Comments on "Global sunspots in OLG models"," Journal of Macroeconomics, Elsevier, vol. 28(1), pages 46-50, March.
  2. Blake, Andrew P. & Kapetanios, George, 2007. "Testing for ARCH in the presence of nonlinearity of unknown form in the conditional mean," Journal of Econometrics, Elsevier, vol. 137(2), pages 472-488, April.
  3. Cars H. Hommes, 2005. "Heterogeneous Agent Models in Economics and Finance," Tinbergen Institute Discussion Papers 05-056/1, Tinbergen Institute.
  4. Xavier Gabaix & Parameswaran Gopikrishnan & Vasiliki Plerou & H. Eugene Stanley, 2005. "Institutional Investors and Stock Market Volatility," NBER Working Papers 11722, National Bureau of Economic Research, Inc.
  5. repec:dgr:uvatin:2001014 is not listed on IDEAS
  6. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
  7. Hommes, C.H., 2000. "Financial Markets as Nonlinear Adaptive Evolutionary Systems," CeNDEF Working Papers 00-03, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
  8. Friedrich Wagner & Thomas Lux & Simone Alfarano, 2005. "Time-Variation of Higher Moments in a Financial Market with Heterogeneous Agents: An Analytical Approach," Working Papers wp05-02, Warwick Business School, Finance Group.
  9. Gabaix, Xavier & Gopikrishnan, Parameswaran & Plerou, Vasiliki & Eugene Stanley, H., 2008. "Quantifying and understanding the economics of large financial movements," Journal of Economic Dynamics and Control, Elsevier, vol. 32(1), pages 303-319, January.
  10. Stanley, H. Eugene & Plerou, Vasiliki & Gabaix, Xavier, 2008. "A statistical physics view of financial fluctuations: Evidence for scaling and universality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(15), pages 3967-3981.
  11. Catherine Kyrtsou & Michel Terraza, 2003. "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," Computational Economics, Society for Computational Economics, vol. 21(3), pages 257-276, June.
  12. Robert F. Engle & David F. Hendry & David Trumble, 1985. "Small-Sample Properties of ARCH Estimators and Tests," Canadian Journal of Economics, Canadian Economics Association, vol. 18(1), pages 66-93, February.
  13. Robin L. Lumsdaine & Serena Ng, 1998. "Testing for ARCH in the Presence of a Possibly Misspecified Conditional Mean," Boston College Working Papers in Economics 370, Boston College Department of Economics.
  14. 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.
  15. 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.
  16. James Theiler & Stephen Eubank, 1993. "Don't Bleach Chaotic Data," Working Papers 93-05-026, Santa Fe Institute.
  17. Hommes, Cars H. & Manzan, Sebastiano, 2006. "Comments on "Testing for nonlinear structure and chaos in economic time series"," Journal of Macroeconomics, Elsevier, vol. 28(1), pages 169-174, March.
  18. Chiarella, Carl & He, Xue-Zhong & Hommes, Cars, 2006. "Moving average rules as a source of market instability," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(1), pages 12-17.
  19. Bera, Anil K & Higgins, Matthew L & Lee, Sangkyu, 1992. "Interaction between Autocorrelation and Conditional Heteroscedasticity: A Random-Coefficient Approach," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(2), pages 133-42, April.
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Citations

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Cited by:
  1. Sadeck Melhem & Mahmoud Melhem, 2012. "Comments on “Re-examining the source of Heteroskedasticity: The paradigm of noisy chaotic models”," Working Papers 12-13, LAMETA, Universtiy of Montpellier, revised Apr 2012.
  2. Maria Grydaki & Stilianos Fountas, 2010. "What Explains Nominal Exchange Rate Volatility? Evidence from the Latin American Countries," Discussion Paper Series 2010_10, Department of Economics, University of Macedonia, revised Jul 2010.
  3. 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.
  4. Maria Grydaki & Stilianos Fountas, 2010. "What Explains Output Volatility? Evidence from the G3," Discussion Paper Series 2010_09, Department of Economics, University of Macedonia, revised Jul 2010.

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