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Evaluating measures of dependence for linearly generated nonlinear time series along with spurious correlation

Author

Listed:
  • Christos Agiakloglou

    (University of Piraeus
    University of Illinois at Urbana-Champaign)

  • Anil Bera

    (University of Illinois at Urbana-Champaign)

  • Emmanouil Deligiannakis

    (University of Piraeus)

Abstract

The issue of determining dependence between two series is typically one of the most important aspects in any quantitative analysis. This study, using a Monte Carlo analysis, investigates the performance of several dependence measures for linearly generated nonlinear time series based on the family of AR(1) – ARCH(1) in variable models presented by Bera et al. (1992 and 1996) and it finds that copulas capture the concept of dependence better than the correlation coefficient. In addition, this study examines the performance of the test for zero association and it discovers that the spurious behavior can be eliminated asymptotically for this type on nonlinear processes, although the power of the test remains relatively low.

Suggested Citation

  • Christos Agiakloglou & Anil Bera & Emmanouil Deligiannakis, 2022. "Evaluating measures of dependence for linearly generated nonlinear time series along with spurious correlation," Journal of Economics and Finance, Springer;Academy of Economics and Finance, vol. 46(3), pages 535-552, July.
    • Handle: RePEc:spr:jecfin:v:46:y:2022:i:3:d:10.1007_s12197-022-09579-7
    DOI: 10.1007/s12197-022-09579-7
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    References listed on IDEAS

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    1. Bera, Anil K & Higgins, Matthew L & Lee, Sangkyu, 1992. "Interaction between Autocorrelation and Conditional Heteroscedasticity: A Random-Coefficient Approach," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(2), pages 133-142, April.
    2. Christos Agiakloglou & Charalampos Agiropoulos, 2016. "The balance between size and power in testing for linear association for two stationary AR(1) processes," Applied Economics Letters, Taylor & Francis Journals, vol. 23(4), pages 230-234, March.
    3. Janus, Paweł & Koopman, Siem Jan & Lucas, André, 2014. "Long memory dynamics for multivariate dependence under heavy tails," Journal of Empirical Finance, Elsevier, vol. 29(C), pages 187-206.
    4. Clive Granger & Namwon Hyung & Yongil Jeon, 2001. "Spurious regressions with stationary series," Applied Economics, Taylor & Francis Journals, vol. 33(7), pages 899-904.
    5. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
    6. Ning, Cathy, 2010. "Dependence structure between the equity market and the foreign exchange market-A copula approach," Journal of International Money and Finance, Elsevier, vol. 29(5), pages 743-759, September.
    7. Banerjee, Anindya & Dolado, Juan J. & Galbraith, John W. & Hendry, David, 1993. "Co-integration, Error Correction, and the Econometric Analysis of Non-Stationary Data," OUP Catalogue, Oxford University Press, number 9780198288107, Decembrie.
    8. Granger Clive W.J., 2008. "Non-Linear Models: Where Do We Go Next - Time Varying Parameter Models?," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 12(3), pages 1-11, September.
    9. Jondeau, Eric & Rockinger, Michael, 2006. "The Copula-GARCH model of conditional dependencies: An international stock market application," Journal of International Money and Finance, Elsevier, vol. 25(5), pages 827-853, August.
    10. 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.
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    More about this item

    Keywords

    Correlation coefficient; Copulas; Non-linear time series; Spurious correlation; Monte Carlo Analysis;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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