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Nonparametric correlation integral–based tests for linear and nonlinear stochastic processes

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Listed:
  • Mariano Matilla-García
  • Manuel Ruiz Marín
  • Mohammed Dore
  • Rina Ojeda

Abstract

The BDS test is the best-known correlation integral–based test, and it is now an important part of most standard econometric data analysis software packages. This test depends on the proximity ( $$\varepsilon )$$ and the embedding dimension ( $$m)$$ parameters both of which are chosen by the researcher. Although different studies (e.g., Kanzler in Very fast and correctly sized estimation of the BDS statistic. Department of Economics, Oxford University, Oxford, 1999 ) have been carried out to provide an adequate selection of the proximity parameter, no relevant research has yet been done on $$m$$ . In practice, researchers usually compute the BDS statistic for different values of $$m$$ , but sometimes these results are contradictory because some of them accept the null and others reject it. This paper aims to fill this gap. To that end, we propose a new simple, yet powerful, aggregate test for independence, based on BDS outputs from a given data set, that allows the consideration of all of the information contained in several embedding dimensions without the ambiguity of the well-known BDS tests. Copyright Springer-Verlag Italia 2014

Suggested Citation

  • 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.
    • Handle: RePEc:spr:decfin:v:37:y:2014:i:1:p:181-193
    DOI: 10.1007/s10203-013-0143-0
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    References listed on IDEAS

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    1. 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.
    2. Simón Sosvilla-Rivero & Fernando Fernández-Rodriguez & Julián Andrada-Félix, 2005. "Testing chaotic dynamics via Lyapunov exponents," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(7), pages 911-930.
    3. 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.
    4. David G. McMillan, 2003. "Non‐linear Predictability of UK Stock Market Returns," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 65(5), pages 557-573, December.
    5. Matilla-Garci­a, Mariano & Ruiz Mari­n, Manuel, 2008. "A non-parametric independence test using permutation entropy," Journal of Econometrics, Elsevier, vol. 144(1), pages 139-155, May.
    6. Brooks, Chris, 1999. "Portmanteau Model Diagnostics and Tests for Nonlinearity: A Comparative Monte Carlo Study of Two Alternative Methods," Computational Economics, Springer;Society for Computational Economics, vol. 13(3), pages 249-263, June.
    7. Mariano Matilla-García, 2007. "Nonlinear Dynamics in Energy Futures," The Energy Journal, International Association for Energy Economics, vol. 0(Number 3), pages 7-30.
    8. 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.
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    More about this item

    Keywords

    Independence test; BDS; Nonlinearity; C12; C14; C15;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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