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A Fast Algorithm for the BDS Statistic

Author

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  • LeBaron Blake

    (University of Wisconsin, Madison)

Abstract

The BDS statistic has proved to be one of several useful nonlinear diagnostics. It has been shown to have good power against many nonlinear alternatives, and its asymptotic properties as a residual diagnostic are well understood. Furthermore, extensive Monte Carlo results have proved it useful in relatively small samples. However, the BDS test is not trivial to calculate, and is even more difficult to deal with if one wants the speed necessary to make bootstrap resampling feasible. This short paper presents a fast algorithm for the BDS statistic, and outlines how these speed improvements are achieved. Source code in the C programming language is included.

Suggested Citation

  • LeBaron Blake, 1997. "A Fast Algorithm for the BDS Statistic," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 2(2), pages 1-9, July.
    • Handle: RePEc:bpj:sndecm:v:2:y:1997:i:2:n:al1
    DOI: 10.2202/1558-3708.1029
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    Citations

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    Cited by:

    1. Belaire-Franch Jorge & Peiro Amado, 2003. "Conditional and Unconditional Asymmetry in U.S. Macroeconomic Time Series," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 7(1), pages 1-19, April.
    2. Musshoff, Oliver & Hirschauer, Norbert, 2004. "Die Berücksichtigung von Unsicherheit und Flexibilität in der Investitionsplanung – dargestellt am Beispiel einer Vertragsinvestition für Roggen," German Journal of Agricultural Economics, Humboldt-Universitaet zu Berlin, Department for Agricultural Economics, vol. 53(04), pages 1-12.
    3. Mayer-Foulkes David, 2000. "A Generalized Fast Algorithm for BDS-Type Statistics," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 4(1), pages 1-7, April.
    4. Scott C. Linn & Nicholas S. P. Tay, 2007. "Complexity and the Character of Stock Returns: Empirical Evidence and a Model of Asset Prices Based on Complex Investor Learning," Management Science, INFORMS, vol. 53(7), pages 1165-1180, July.
    5. Mikhail Stolbov, 2017. "Causality between credit depth and economic growth: evidence from 24 OECD countries," Empirical Economics, Springer, vol. 53(2), pages 493-524, September.
    6. Luo, Wenya & Bai, Zhidong & Zheng, Shurong & Hui, Yongchang, 2020. "A modified BDS test," Statistics & Probability Letters, Elsevier, vol. 164(C).
    7. Antonios Antoniou & Constantinos E. Vorlow, 2004. "Price Clustering and Discreteness: Is there Chaos behind the Noise?," Papers cond-mat/0407471, arXiv.org.
    8. Mußhoff, O. & Hirschauer, N., 2006. "Die Rehabilitation von Optimierungsverfahren? - Eine Analyse des Anbauverhaltens ausgewählter Brandenburger Marktfruchtbetriebe," Proceedings “Schriften der Gesellschaft für Wirtschafts- und Sozialwissenschaften des Landbaues e.V.”, German Association of Agricultural Economists (GEWISOLA), vol. 41, March.
    9. McKenzie, Michael D., 2001. "Chaotic behavior in national stock market indices: New evidence from the close returns test," Global Finance Journal, Elsevier, vol. 12(1), pages 35-53.
    10. Shamaila Butt & Suresh Ramakrishnan & Nanthakumar Loganathan & Muhammad Ali Chohan, 2020. "Evaluating the exchange rate and commodity price nexus in Malaysia: evidence from the threshold cointegration approach," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 6(1), pages 1-19, December.
    11. Chaudhry, Muhammad Imran & Miranda, Mario J., 2018. "Complex price dynamics in vertically linked cobweb markets," Economic Modelling, Elsevier, vol. 72(C), pages 363-378.
    12. 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.
    13. Antoniou, Antonios & Vorlow, Constantinos E., 2005. "Price clustering and discreteness: is there chaos behind the noise?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 348(C), pages 389-403.
    14. Ferreira, Fernando F & Francisco, Gerson & Machado, Birajara S & Muruganandam, Paulsamy, 2003. "Time series analysis for minority game simulations of financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 321(3), pages 619-632.

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