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Dynamic relationship analysis between NAFTA stock markets using nonlinear, nonparametric, non-stationary methods

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Abstract

This paper seeks to investigate the dynamic relationship between daily stock market indices in NAFTA countries from 8 November 1991 to 16 March 2018, using for the first time nonlinear, nonparametric, non-stationary methods. We apply two novel nonlinear, nonparametric, non-stationary dynamic correlation techniques—rolling window Spearman correlation and wavelet coherence—to study the relationships between the three pairwise comparisons. We apply a nonlinear, nonparametric causality test to four specific sub-periods and to the full period of these indices to check the direction of causality. Our results show the following: (1) the correlation between the indices increases from 2000 to 2011, but that correlation increase is interrupted around 2011/2012 and then falls noticeably, picking up again from 2015 onwards. (2) The pairs that show the lowest correlation are those involving the IPC. (3) The causality test reveals nonlinear bidirectional causality for all three indices and all the intervals analysed, indicating that there is a strong interrelationship between NAFTA members. These results are relevant to obtain a better understanding of the complex dynamical system formed by NAFTA stock markets and have direct implications for hedging and portfolio diversification policies.

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Notes

  1. https://finance.yahoo.com/world-indices.

  2. https://cran.r-project.org/web/packages/zoo/index.html.

  3. https://cran.r-project.org/web/packages/gtools/index.html.

  4. A versatile R package to carry out this aim is bestNormalize (https://CRAN.R-project.org/package=bestNormalize).

  5. http://tocsy.pik-potsdam.de/wavelets/.

  6. Currently, some very interesting developments related to significance testing in wavelet analysis are being developed (Schulte: Statistical Hypothesis Testing in Wavelet Analysis: Theoretical Developments and Applications to India Rainfall, Nonlinear Processes Geophys. Discuss., https://doi.org/10.5194/npg-2018-55, in review, 2018).

  7. http://research.economics.unsw.edu.au/vpanchenko/software/2006_GC_JEDC_c_and_exe_code.zip.

  8. http://research.economics.unsw.edu.au/vpanchenko/software/2006_GC_JEDC_c_and_exe_code.zip.

  9. The theoretical value for a Gaussian probability distribution.

  10. We also applied WCO analysis to the returns, and the results are quite similar to the exception for the largest scales for the pair DJI–GSPTSE. These results are not shown but are available upon request.

  11. Note that labels A and B on the right Y-axis in Fig. 9 correspond to the same scales presented in Fig. 8a, b.

  12. Note that labels C and D on the right Y-axis in Fig. 9 correspond to the same scales presented in Fig. 8c, d.

  13. Note that labels E and F on the right Y-axis in Fig. 9 correspond to the same scales presented in Fig. 8c, d.

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Acknowledgements

JMPM was funded by a Basque Government post-doctoral fellowship. We greatly thank to the Editor JA Tenreiro Machado and anonymous reviewers for their helpful comments and suggestions.

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  1. Institute of Public Economics, University of the Basque Country, 48015, Bilbao, Spain

    Josué M. Polanco-Martínez

  2. Basque Centre for Climate Change – BC3, 48940, Leioa, Spain

    Josué M. Polanco-Martínez

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Polanco-Martínez, J.M. Dynamic relationship analysis between NAFTA stock markets using nonlinear, nonparametric, non-stationary methods . Nonlinear Dyn 97, 369–389 (2019). https://doi.org/10.1007/s11071-019-04974-y

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