IDEAS home Printed from https://ideas.repec.org/a/spr/decfin/v37y2014i1p181-193.html
   My bibliography  Save this article

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

Author

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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10203-013-0143-0
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10203-013-0143-0?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. Mariano Matilla-García, 2007. "Nonlinear Dynamics in Energy Futures," The Energy Journal, International Association for Energy Economics, vol. 0(Number 3), pages 7-30.
    4. 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.
    5. 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.
    6. Hsieh, David A, 1989. "Testing for Nonlinear Dependence in Daily Foreign Exchange Rates," The Journal of Business, University of Chicago Press, vol. 62(3), pages 339-368, July.
    7. 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.
    8. 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.
    9. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Olmedo,E. & Velasco, F. & Valderas, J.M., 2007. "Caracterización no lineal y predicción no paramétrica en el IBEX35/Nonlinear Characterization and Predictions of IBEX 35," Estudios de Economia Aplicada, Estudios de Economia Aplicada, vol. 25, pages 815-842, Diciembre.
    3. 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.
    4. Evzen Kocenda & Lubos Briatka, 2005. "Optimal Range for the iid Test Based on Integration Across the Correlation Integral," Econometric Reviews, Taylor & Francis Journals, vol. 24(3), pages 265-296.
    5. 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, Springer;Society for Computational Economics, vol. 21(3), pages 257-276, June.
    6. 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.
    7. Manfred M. Fischer & Wolfgang Koller, 2001. "Testing for Non-Linear Dependence in Univariate Time Series: An Empirical Investigation of the Austrian Unemployment Rate," ERSA conference papers ersa01p233, European Regional Science Association.
    8. Reidar Hagtvedt, 2009. "Stock return dynamics and the CAPM anomalies," Applied Economics Letters, Taylor & Francis Journals, vol. 16(16), pages 1593-1596.
    9. Elsinger, Helmut, 2013. "Comment on: A new test for chaos and determinism based on symbolic dynamics," Journal of Economic Behavior & Organization, Elsevier, vol. 91(C), pages 131-138.
    10. Suresh K. G. & Aviral Kumar Tiwari & Anto Joseph, 2012. "Are the emerging bric stock markets efficient?," Economics Bulletin, AccessEcon, vol. 32(2), pages 1261-1271.
    11. Belaire-Franch, Jorge, 2004. "Testing for non-linearity in an artificial financial market: a recurrence quantification approach," Journal of Economic Behavior & Organization, Elsevier, vol. 54(4), pages 483-494, August.
    12. Loretta Mastroeni & Pierluigi Vellucci, 2016. "“Butterfly Effect" vs Chaos in Energy Futures Markets," Departmental Working Papers of Economics - University 'Roma Tre' 0209, Department of Economics - University Roma Tre.
    13. Chen, Shu-Heng & Yeh, Chia-Hsuan, 2002. "On the emergent properties of artificial stock markets: the efficient market hypothesis and the rational expectations hypothesis," Journal of Economic Behavior & Organization, Elsevier, vol. 49(2), pages 217-239, October.
    14. Loretta Mastroeni & Pierluigi Vellucci, 2016. ""Butterfly Effect" vs Chaos in Energy Futures Markets," Papers 1610.05697, arXiv.org.
    15. K.P. Lim & M.J. Hinich & K.S. Liew, 2003. "GARCH Diagnosis with Portmanteau Bicorrelation Test: An Application on the Malaysia's Stock Market," Finance 0307013, University Library of Munich, Germany.
    16. repec:wyi:journl:002062 is not listed on IDEAS
    17. Marcos Álvarez-Díaz & Alberto Álvarez, 2002. "Predicción No-Lineal De Tipos De Cambio: Algoritmos Genéticos, Redes Neuronales Y Fusión De Datos," Working Papers 0205, Universidade de Vigo, Departamento de Economía Aplicada.
    18. Kian-Ping Lim & Melvin J. Hinich & Venus Khim-Sen Liew, 2005. "Statistical Inadequacy of GARCH Models for Asian Stock Markets," Journal of Emerging Market Finance, Institute for Financial Management and Research, vol. 4(3), pages 263-279, December.
    19. repec:wyi:journl:002087 is not listed on IDEAS
    20. Park, Joon Y. & Whang, Yoon-Jae, 2012. "Random walk or chaos: A formal test on the Lyapunov exponent," Journal of Econometrics, Elsevier, vol. 169(1), pages 61-74.
    21. Herrera Gómez, Marcos & Ruiz Marín, Manuel & Mur Lacambra, Jesús, 2014. "Testing Spatial Causality in Cross-section Data," MPRA Paper 56678, University Library of Munich, Germany.
    22. Bask, Mikael, 2010. "Measuring potential market risk," Journal of Financial Stability, Elsevier, vol. 6(3), pages 180-186, September.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:decfin:v:37:y:2014:i:1:p:181-193. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.