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An Alternative to the BDS Test: Integration Across the Correlation Integral

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  • Kocenda, Evzen
Abstract
This paper extends and generalizes the BDS test presented by Brock, Dechert, Scheinkman, and LeBaron (1996). In doing so it aims to remove the limitation of having to arbitrarily select a proximity parameter by integrating across the correlation integral. The Monte Carlo simulation is used to tabulate critical values of the alternative statistic. Previously published empirical studies are replicated as well as power tests executed in order to evaluate the relative performance of the suggested alternative to the BDS test. The results are favorable for the suggested alternative.

Suggested Citation

  • Kocenda, Evzen, 1996. "An Alternative to the BDS Test: Integration Across the Correlation Integral," MPRA Paper 70510, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:70510
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    References listed on IDEAS

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    1. Brock, W. A., 1986. "Distinguishing random and deterministic systems: Abridged version," Journal of Economic Theory, Elsevier, vol. 40(1), pages 168-195, October.
    2. Serletis, Apostolos & Gogas, Periklis, 1997. "Chaos in East European black market exchange rates," Research in Economics, Elsevier, vol. 51(4), pages 359-385, December.
    3. 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.
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    6. Victor Chwee, 1998. "Chaos in Natural Gas Futures?," The Energy Journal, International Association for Energy Economics, vol. 0(Number 2), pages 149-164.
    7. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    8. Peter Kugler & Carlos Lenz, 1990. "Chaos, Arch and the Foreign Exchange Market: Empiri cal Results from Weekly Data," Diskussionsschriften dp9005, Universitaet Bern, Departement Volkswirtschaft.
    9. Ignacio Olmeda & Joaquin Pérez, 1995. "Non-linear dynamics and chaos in the Spanish stock market," Investigaciones Economicas, Fundación SEPI, vol. 19(2), pages 217-248, May.
    10. de Lima, Pedro J F, 1998. "Nonlinearities and Nonstationarities in Stock Returns," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(2), pages 227-236, April.
    11. Aydin Cecen, A. & Erkal, Cahit, 1996. "Distinguishing between stochastic and deterministic behavior in foreign exchange rate returns: Further evidence," Economics Letters, Elsevier, vol. 51(3), pages 323-329, June.
    12. Hsieh, David A., 1993. "Implications of Nonlinear Dynamics for Financial Risk Management," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 28(1), pages 41-64, March.
    13. Brock, W.A., 1988. "Nonlinearity And Complex Dynamics In Economics And Finance," Working papers 360, Wisconsin Madison - Social Systems.
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    Cited by:

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    2. Albulescu, C.T. & Bouri, E. & Tiwari, A.K. & Roubaud, D., 2020. "Quantile causality between banking stock and real estate securities returns in the US," The Quarterly Review of Economics and Finance, Elsevier, vol. 78(C), pages 251-260.
    3. Manigandan, Palanisamy & Alam, Md Shabbir & Murshed, Muntasir & Ozturk, Ilhan & Altuntas, Sumeyya & Alam, Mohammad Mahtab, 2024. "Promoting sustainable economic growth through natural resources management, green innovations, environmental policy deployment, and financial development: Fresh evidence from India," Resources Policy, Elsevier, vol. 90(C).
    4. Luo, Wenya & Bai, Zhidong & Zheng, Shurong & Hui, Yongchang, 2020. "A modified BDS test," Statistics & Probability Letters, Elsevier, vol. 164(C).
    5. Marcos Álvarez-Díaz & Rangan Gupta, 2015. "Forecasting the US CPI: Does Nonlinearity Matter?," Working Papers 201512, University of Pretoria, Department of Economics.
    6. Álvarez-Díaz, Marcos & Hammoudeh, Shawkat & Gupta, Rangan, 2014. "Detecting predictable non-linear dynamics in Dow Jones Islamic Market and Dow Jones Industrial Average indices using nonparametric regressions," The North American Journal of Economics and Finance, Elsevier, vol. 29(C), pages 22-35.
    7. Wali, Muammer & Chan, Felix & Manzur, Meher, 2017. "Nonlinear dependence in exchange rate returns: How do emerging Asian currencies compare with major currencies?," Journal of Asian Economics, Elsevier, vol. 50(C), pages 62-72.
    8. Marcos Álvarez-Díaz & Shawkat Hammoudeh & Rangan Gupta, 2013. "Detecting Predictable Non-linear Dynamics in Dow Jones Industrial Average and Dow Jones Islamic Market Indices using Nonparametric Regressions," Working Papers 201385, University of Pretoria, Department of Economics.

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    More about this item

    Keywords

    chaos; nonlinear dynamics; correlation integral; Monte Carlo; exchange rates;
    All these keywords.

    JEL classification:

    • 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
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • F31 - International Economics - - International Finance - - - Foreign Exchange

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