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A Generalized BDS Statistic

Author

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  • M. Matilla-GarcÍa
  • R. Queralt
  • P. Sanz
  • F. VÁzquez

Abstract

The BDS statistic, rooted on the correlation integral, has been proven to be useful for different problems. But although the correlation integral is defined for any choice of delay time, the BDS statistic assumes delay time is one. As different studies have shown, an adequate choice of delay time is important in order to determine the dynamical properties of a system from an observed time series, specially when the data sets are small and there is some noise. This paper introduces a new statistic that generalizes BDS by allowing the choice of any delay time. Copyright Kluwer Academic Publishers 2004

Suggested Citation

  • M. Matilla-GarcÍa & R. Queralt & P. Sanz & F. VÁzquez, 2004. "A Generalized BDS Statistic," Computational Economics, Springer;Society for Computational Economics, vol. 24(3), pages 277-300, September.
    • Handle: RePEc:kap:compec:v:24:y:2004:i:3:p:277-300
    DOI: 10.1007/s10614-004-4657-y
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    References listed on IDEAS

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    1. M. Matilla-Garcia & P. Sanz & F. J. Vazquez, 2004. "Dimension estimation with the BDS-G statistic," Applied Economics, Taylor & Francis Journals, vol. 36(11), pages 1219-1223.
    2. William A. Barnett & A. Ronald Gallant & Melvin J. Hinich & Jochen A. Jungeilges & Daniel T. Kaplan, 2004. "A Single-Blind Controlled Competition Among Tests for Nonlinearity and Chaos," Contributions to Economic Analysis, in: Functional Structure and Approximation in Econometrics, pages 581-615, Emerald Group Publishing Limited.
    3. Ramsey, James B & Sayers, Chera L & Rothman, Philip, 1990. "The Statistical Properties of Dimension Calculations Using Small Data Sets: Some Economic Applications," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 31(4), pages 991-1020, November.
    4. LeBaron Blake, 1997. "A Fast Algorithm for the BDS Statistic," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 2(2), pages 1-9, July.
    5. Brock, W.A. & Dechert, W.D. & LeBaron, B. & Scheinkman, J.A., 1995. "A Test for Independence Based on the Correlation Dimension," Working papers 9520, Wisconsin Madison - Social Systems.
    6. William Barnett, 2005. "Monetary Aggregation," Macroeconomics 0503017, University Library of Munich, Germany.
    7. Unknown, 1986. "Letters," Choices: The Magazine of Food, Farm, and Resource Issues, Agricultural and Applied Economics Association, vol. 1(4), pages 1-9.
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    Cited by:

    1. Mariano Matilla-García & Manuel Ruiz Marín & Mohammed Dore & Rina Ojeda, 2014. "Nonparametric correlation integral–based tests for linear and nonlinear stochastic processes," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 37(1), pages 181-193, April.
    2. Matilla-García, Mariano & Marín, Manuel Ruiz, 2010. "A new test for chaos and determinism based on symbolic dynamics," Journal of Economic Behavior & Organization, Elsevier, vol. 76(3), pages 600-614, December.
    3. Marisa Faggini, 2011. "Chaotic Time Series Analysis in Economics: Balance and Perspectives," Working papers 25, Former Department of Economics and Public Finance "G. Prato", University of Torino.
    4. Matilla-Garcia, Mariano, 2007. "A non-parametric test for independence based on symbolic dynamics," Journal of Economic Dynamics and Control, Elsevier, vol. 31(12), pages 3889-3903, December.

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