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A suggested statistical test for measuring bivariate nonlinear dependence

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  • Matsushita, Raul
  • Figueiredo, Annibal
  • Da Silva, Sergio

Abstract

We devise a new asymptotic statistical test to assess independence in bivariate continuous distributions. Our approach is based on the Cramér–von Mises test, in which the empirical process is viewed as the Kullback–Leibler divergence, that is, as the distance between the data under the independence hypothesis and the data empirically observed. We derive the theoretical characteristic function of the limit distribution of the test statistic and find the critical values through computer simulation. A Monte Carlo experiment is considered as assessing the validation and power performance of the test by assuming a bivariate nonlinear dependence structure with fat tails. Two extra examples, respectively, consider stationary and conditionally nonstationary series. Results confirm that our suggested test is consistent and powerful in the presence of bivariate nonlinear dependence even if the environment is non-Gaussian. Our case is illustrated with high-frequency data from stocks listed on the NYSE that recently experienced so-called mini-flash crashes.

Suggested Citation

  • Matsushita, Raul & Figueiredo, Annibal & Da Silva, Sergio, 2012. "A suggested statistical test for measuring bivariate nonlinear dependence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(20), pages 4891-4898.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:20:p:4891-4898
    DOI: 10.1016/j.physa.2012.05.053
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    References listed on IDEAS

    as
    1. Matsushita, Raul & da Silva, Sergio & Figueiredo, Annibal & Gleria, Iram, 2006. "Log-periodic crashes revisited," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 364(C), pages 331-335.
    2. Nakamura, Tomomichi & Small, Michael, 2007. "Correlation structures in short-term variabilities of stock indices and exchange rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 383(1), pages 96-101.
    3. Cajueiro, Daniel O. & Tabak, Benjamin M., 2009. "Multifractality and herding behavior in the Japanese stock market," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 497-504.
    4. Figueiredo, Annibal & Gleria, Iram & Matsushita, Raul & Da Silva, Sergio, 2004. "Lévy flights, autocorrelation, and slow convergence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 337(3), pages 369-383.
    5. Bakirov, Nail K. & Rizzo, Maria L. & Szekely, Gábor J., 2006. "A multivariate nonparametric test of independence," Journal of Multivariate Analysis, Elsevier, vol. 97(8), pages 1742-1756, September.
    6. Ghoudi, Kilani & Kulperger, Reg J. & Rémillard, Bruno, 2001. "A Nonparametric Test of Serial Independence for Time Series and Residuals," Journal of Multivariate Analysis, Elsevier, vol. 79(2), pages 191-218, November.
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    8. Figueiredo, Annibal & Gleria, Iram & Matsushita, Raul & Da Silva, Sergio, 2006. "Nonidentically distributed variables and nonlinear autocorrelation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 363(2), pages 171-180.
    9. Liu, Li & Wan, Jieqiu, 2011. "A study of correlations between crude oil spot and futures markets: A rolling sample test," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(21), pages 3754-3766.
    10. Raul Matsushita & Sergio Da Silva, 2011. "A log-periodic fit for the flash crash of May 6, 2010," Economics Bulletin, AccessEcon, vol. 31(2), pages 1772-1779.
    11. Cajueiro, Daniel O. & Tabak, Benjamin M., 2006. "Testing for rational bubbles in banking indices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 366(C), pages 365-376.
    12. Cajueiro, Daniel O. & Tabak, Benjamin M. & Werneck, Filipe K., 2009. "Can we predict crashes? The case of the Brazilian stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(8), pages 1603-1609.
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