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Generalized Measures of Correlation for Asymmetry, Nonlinearity, and Beyond

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  • Shurong Zheng
  • Ning-Zhong Shi
  • Zhengjun Zhang

Abstract

Applicability of Pearson's correlation as a measure of explained variance is by now well understood. One of its limitations is that it does not account for asymmetry in explained variance. Aiming to develop broad applicable correlation measures, we study a pair of generalized measures of correlation (GMC) that deals with asymmetries in explained variances, and linear or nonlinear relations between random variables. We present examples under which the paired measures are identical, and they become a symmetric correlation measure that is the same as the squared Pearson's correlation coefficient. As a result, Pearson's correlation is a special case of GMC. Theoretical properties of GMC show that GMC can be applicable in numerous applications and can lead to more meaningful conclusions and improved decision making. In statistical inference, the joint asymptotics of the kernel-based estimators for GMC are derived and are used to test whether or not two random variables are symmetric in explaining variances. The testing results give important guidance in practical model selection problems. The efficiency of the test statistics is illustrated in simulation examples. In real-data analysis, we present an important application of GMC in explained variances and market movements among three important economic and financial monetary indicators. This article has online supplementary materials.

Suggested Citation

  • Shurong Zheng & Ning-Zhong Shi & Zhengjun Zhang, 2012. "Generalized Measures of Correlation for Asymmetry, Nonlinearity, and Beyond," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(499), pages 1239-1252, September.
    • Handle: RePEc:taf:jnlasa:v:107:y:2012:i:499:p:1239-1252
    DOI: 10.1080/01621459.2012.710509
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    Cited by:

    1. Taamouti, Abderrahim & Bouezmarni, Taoufik & El Ghouch, Anouar, 2014. "Nonparametric estimation and inference for conditional density based Granger causality measures," Journal of Econometrics, Elsevier, vol. 180(2), pages 251-264.
    2. Polanski, Arnold & Stoja, Evarist, 2017. "Forecasting multidimensional tail risk at short and long horizons," International Journal of Forecasting, Elsevier, vol. 33(4), pages 958-969.
    3. Polanski, Arnold & Stoja, Evarist, 2017. "Forecasting multidimensional tail risk at short and long horizons," Bank of England working papers 660, Bank of England.
    4. Wang, Christina Dan & Chen, Zhao & Lian, Yimin & Chen, Min, 2022. "Asset selection based on high frequency Sharpe ratio," Journal of Econometrics, Elsevier, vol. 227(1), pages 168-188.
    5. David E Allen & Vince Hooper, 2018. "Generalized Correlation Measures of Causality and Forecasts of the VIX Using Non-Linear Models," Sustainability, MDPI, vol. 10(8), pages 1-15, August.
    6. Ćmiel, Bogdan & Ledwina, Teresa, 2020. "Validation of association," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 55-67.
    7. De Mier Manuel & Delbianco Fernando & Tohmé Fernando & Patrizio Luisina & Rodriguez Facundo & Stéfani Mauro, 2023. "Causality by Vote: Aggregating Evidence on Causal Relations in Economic Growth Processes," Asociación Argentina de Economía Política: Working Papers 4641, Asociación Argentina de Economía Política.
    8. Han Lin Shang & Kaiying Ji & Ufuk Beyaztas, 2021. "Granger causality of bivariate stationary curve time series," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(4), pages 626-635, July.
    9. Hrishikesh D. Vinod & P. M. Rao, 2019. "Externalities from Intra-Firm Trade by U.S. Multinationals," International Advances in Economic Research, Springer;International Atlantic Economic Society, vol. 25(4), pages 389-397, November.
    10. H. D. Vinod, 2022. "Generalized, Partial and Canonical Correlation Coefficients," Computational Economics, Springer;Society for Computational Economics, vol. 60(4), pages 1479-1506, December.
    11. David E. Allen, 2022. "Cryptocurrencies, Diversification and the COVID-19 Pandemic," JRFM, MDPI, vol. 15(3), pages 1-25, February.
    12. Lyu, Yongjian & Yi, Heling & Wei, Yu & Yang, Mo, 2021. "Revisiting the role of economic uncertainty in oil price fluctuations: Evidence from a new time-varying oil market model," Economic Modelling, Elsevier, vol. 103(C).
    13. Min Chen & Yimin Lian & Zhao Chen & Zhengjun Zhang, 2017. "Sure explained variability and independence screening," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(4), pages 849-883, October.
    14. Jiang, Zhenzhen & Guo, Hongping & Wang, Jinjuan, 2023. "Feature screening for multiple responses," Journal of Multivariate Analysis, Elsevier, vol. 198(C).
    15. Maneejuk, Paravee & Yamaka, Woraphon, 2020. "An analysis of the impacts of telecommunications technology and innovation on economic growth," Telecommunications Policy, Elsevier, vol. 44(10).

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