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Advancing the iid Test Based on Integration across the Correlation Integral: Ranges, Competition, and Power

  • Evzen Kocenda

    (CERGE-EI)

  • Lubos Briatka

    (CERGE-EI)

This paper builds on Kočenda (2001) and extends it in two ways. First, two new intervals of the proximity parameter ε (over which the correlation integral is calculated) are specified. For these ε- ranges new critical values for various lengths of the data sets are introduced and through Monte Carlo studies it is shown that within new ε-ranges the test is even more powerful than within the original ε-range. A sensitivity analysis of the critical values with respect to ε-range choice is also given. Second, a comparison with existing results of the controlled competition of Barnett et al. (1997) as well as broad power tests on various nonlinear and chaotic data are provided. The results of the comparison strongly favor our robust procedure and confirm the ability of the test in finding nonlinear dependencies. An empirical comparison of the new ε-ranges with the original one shows that the test within the new ε-ranges is able to detect hidden patterns with much higher precision. Finally, new user-friendly and fast software is introduced.

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File URL: http://econwpa.repec.org/eps/em/papers/0409/0409001.pdf
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Paper provided by EconWPA in its series Econometrics with number 0409001.

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Length: 40 pages
Date of creation: 02 Sep 2004
Date of revision:
Handle: RePEc:wpa:wuwpem:0409001
Note: Type of Document - pdf; pages: 40. Paper has the link to a webpage to download the software.
Contact details of provider: Web page: http://econwpa.repec.org

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  1. Jorge Belaire-Franch, 2003. "A Note on Resampling the Integration Across the Correlation Integral with Alternative Ranges," Econometric Reviews, Taylor & Francis Journals, vol. 22(4), pages 337-349.
  2. Hsieh, David A., 1993. "Implications of Nonlinear Dynamics for Financial Risk Management," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 28(01), pages 41-64, March.
  3. Bollerslev, Tim & Ole Mikkelsen, Hans, 1999. "Long-term equity anticipation securities and stock market volatility dynamics," Journal of Econometrics, Elsevier, vol. 92(1), pages 75-99, September.
  4. 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.
  5. Kramer, Walter & Runde, Ralf, 1997. "Chaos and the compass rose," Economics Letters, Elsevier, vol. 54(2), pages 113-118, February.
  6. Diks, Cees, 2003. "Detecting serial dependence in tail events: a test dual to the BDS test," Economics Letters, Elsevier, vol. 79(3), pages 319-324, June.
  7. Brooks, C. & Henry, O.T., 1999. "Can Portemanteau Nonlinearity Tests Serve as General Mis-Specification Tests? Evidence from Symmetric and Asymmetric GARCH Models," Department of Economics - Working Papers Series 723, The University of Melbourne.
  8. Chappell, David & Padmore, Joanne & Ellis, Catherine, 1996. "A Note on the Distribution of BDS Statistics for a Real Exchange Rate Series," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 58(3), pages 561-65, August.
  9. de Lima, Pedro J F, 1998. "Nonlinearities and Nonstationarities in Stock Returns," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(2), pages 227-36, April.
  10. Barnett, William A. & Gallant, A. Ronald & Hinich, Melvin J. & Jungeilges, Jochen A. & Kaplan, Daniel T. & Jensen, Mark J., 1997. "A single-blind controlled competition among tests for nonlinearity and chaos," Journal of Econometrics, Elsevier, vol. 82(1), pages 157-192.
  11. Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Ebens, Heiko, 2001. "The distribution of realized stock return volatility," Journal of Financial Economics, Elsevier, vol. 61(1), pages 43-76, July.
  12. Yi-Ting Chen & Chung-Ming Kuan, 2002. "Time irreversibility and EGARCH effects in US stock index returns," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 565-578.
  13. Peter Kugler & Carlos Lenz, 1990. "Chaos, Arch and the Foreign Exchange Market: Empiri­cal Results from Weekly Data," Diskussionsschriften dp9005, Universitaet Bern, Departement Volkswirtschaft.
  14. Brooks, Chris & Heravi, Saeed M, 1999. "The Effect of (Mis-Specified) GARCH Filters on the Finite Sample Distribution of the BDS Test," Computational Economics, Society for Computational Economics, vol. 13(2), pages 147-62, April.
  15. Antonio Aguirre & Luis Antonio Aguirre, 2000. "Time series analysis of monthly beef cattle prices with nonlinear autoregressive models," Applied Economics, Taylor & Francis Journals, vol. 32(3), pages 265-275.
  16. Mahajan, Arvind & Wagner, Andrew J., 1999. "Nonlinear dynamics in foreign exchange rates," Global Finance Journal, Elsevier, vol. 10(1), pages 1-23.
  17. Dejian Lai & Guanrong Chen, 2003. "Distribution of the estimated lyapunov exponents from noisy chaotic time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(6), pages 705-720, November.
  18. Serletis, Apostolos & Gogas, Periklis, 1997. "Chaos in East European black market exchange rates," Research in Economics, Elsevier, vol. 51(4), pages 359-385, December.
  19. B. Wade Brorsen & Seung-Ryong Yang, 1994. "Nonlinear Dynamics And The Distribution Of Daily Stock Index Returns," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 17(2), pages 187-203, 06.
  20. Evžen Kočenda, 1996. "Volatility of a Seemingly Fixed Exchange Rate," Eastern European Economics, M.E. Sharpe, Inc., vol. 34(6), pages 37-67, December.
  21. Aydin Cecen, A. & Erkal, Cahit, 1996. "Distinguishing between stochastic and deterministic behavior in foreign exchange rate returns: Further evidence," Economics Letters, Elsevier, vol. 51(3), pages 323-329, June.
  22. Brooks, Chris, 1999. "Portmanteau Model Diagnostics and Tests for Nonlinearity: A Comparative Monte Carlo Study of Two Alternative Methods," Computational Economics, Society for Computational Economics, vol. 13(3), pages 249-63, June.
  23. Opong, Kwaku K. & Mulholland, Gwyneth & Fox, Alan F. & Farahmand, Kambiz, 1999. "The behaviour of some UK equity indices: An application of Hurst and BDS tests1," Journal of Empirical Finance, Elsevier, vol. 6(3), pages 267-282, September.
  24. David Johnson & Robert McClelland, 1998. "A general dependence test and applications," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 13(6), pages 627-644.
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