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Dimension estimation with the BDS-G statistic

  • M. Matilla-Garcia
  • P. Sanz
  • F. J. Vazquez

The issue of time delay has been controversial among the specialized literature. In fact, there exist some contrasted methods to choose it. It is the case that even though they are investigated for chaotic series, they fail to detect which series come from a deterministic and chaotic system. In this study a new procedure for selecting the delay time which produces good results about the estimation of the correlation dimension in chaotic series is introduced. The method is based upon a statistic (BDS-G), rooted on the integral correlation function, that takes advantage of the information contained in the data in terms of dependence, and it uses it to choose proper delay times and embedding dimensions. The results for the studied series, even for small data sets, are satisfactory.

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File URL: http://www.tandfonline.com/doi/abs/10.1080/0003684042000247398
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Article provided by Taylor & Francis Journals in its journal Applied Economics.

Volume (Year): 36 (2004)
Issue (Month): 11 ()
Pages: 1219-1223

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Handle: RePEc:taf:applec:v:36:y:2004:i:11:p:1219-1223
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  1. Brock,W.A., 2000. "Chaos theory," Working papers 8, Wisconsin Madison - Social Systems.
  2. Ramsey, J.B. & Sayers, C.L. & Rothman, P., 1988. "The Statistical Properties Of Dimension Calculations Using Small Data Sets: Some Economic Applications," Papers 15, Houston - Department of Economics.
  3. Panas, Epaminondas & Ninni, Vassilia, 2000. "Are oil markets chaotic? A non-linear dynamic analysis," Energy Economics, Elsevier, vol. 22(5), pages 549-568, October.
  4. Frank, Murray & Stengos, Thanasis, 1989. "Measuring the Strangeness of Gold and Silver Rates of Return," Review of Economic Studies, Wiley Blackwell, vol. 56(4), pages 553-67, October.
  5. repec:att:wimass:9520 is not listed on IDEAS
  6. Mariano Matilla-Garcia & Paloma Sanz & Francisco Vazquez, 2005. "The BDS test and delay time," Applied Economics Letters, Taylor & Francis Journals, vol. 12(2), pages 109-113.
  7. William Barnett, 2005. "Monetary Aggregation," Macroeconomics 0503017, EconWPA.
  8. Brock, William A. & Sayers, Chera L., 1988. "Is the business cycle characterized by deterministic chaos?," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 71-90, July.
  9. Scheinkman, Jose A & LeBaron, Blake, 1989. "Nonlinear Dynamics and Stock Returns," The Journal of Business, University of Chicago Press, vol. 62(3), pages 311-37, July.
  10. Mayfield, E Scott & Mizrach, Bruce, 1992. "On Determining the Dimension of Real-Time Stock-Price Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(3), pages 367-74, July.
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