IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v63y2022i4d10.1007_s00362-021-01268-7.html
   My bibliography  Save this article

Quantile correlation coefficient: a new tail dependence measure

Author

Listed:
  • Ji-Eun Choi

    (Pukyong National University)

  • Dong Wan Shin

    (Ewha University)

Abstract

A quantile correlation coefficient is newly defined as the geometric mean of two quantile regression slopes—that of X on Y and that of Y on X—in the same way that the Pearson correlation coefficient is related to regression coefficients. The quantile correlation is a measure of overall sensitivity of a conditional quantile of a random variable to changes in the other variable. The proposed quantile correlation can be compared across different tails within a given distribution to provide meaningful interpretations, for example, that there is stronger dependence in the left tail than overall. It can also be compared with the Pearson correlation. Neither of these two comparability within a given distribution is enabled by the existing tail-dependence correlation measures. Moreover a test for differences in the quantile correlations at different tails is proposed. The asymptotic normality of the estimated quantile correlation and the null distribution of the proposed test are established and are well supported by a Monte-Carlo study. The proposed quantile correlation methods are illustrated well by an analysis of stock return price data sets, yielding a clear indication of stronger left-tail dependence than overall dependence and stronger overall dependence than right-tail dependence.

Suggested Citation

  • Ji-Eun Choi & Dong Wan Shin, 2022. "Quantile correlation coefficient: a new tail dependence measure," Statistical Papers, Springer, vol. 63(4), pages 1075-1104, August.
    • Handle: RePEc:spr:stpapr:v:63:y:2022:i:4:d:10.1007_s00362-021-01268-7
    DOI: 10.1007/s00362-021-01268-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-021-01268-7
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00362-021-01268-7?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Giovanni De Luca & Paola Zuccolotto, 2017. "Dynamic tail dependence clustering of financial time series," Statistical Papers, Springer, vol. 58(3), pages 641-657, September.
    2. Hill, Jonathan B., 2011. "Tail And Nontail Memory With Applications To Extreme Value And Robust Statistics," Econometric Theory, Cambridge University Press, vol. 27(4), pages 844-884, August.
    3. Nikoloulopoulos, Aristidis K. & Joe, Harry & Li, Haijun, 2012. "Vine copulas with asymmetric tail dependence and applications to financial return data," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3659-3673.
    4. Y Hoga, 2018. "A structural break test for extremal dependence in β-mixing random vectors," Biometrika, Biometrika Trust, vol. 105(3), pages 627-643.
    5. Joe, Harry & Li, Haijun & Nikoloulopoulos, Aristidis K., 2010. "Tail dependence functions and vine copulas," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 252-270, January.
    6. Koenker, Roger & Bassett, Gilbert, Jr, 1982. "Robust Tests for Heteroscedasticity Based on Regression Quantiles," Econometrica, Econometric Society, vol. 50(1), pages 43-61, January.
    7. Guodong Li & Yang Li & Chih-Ling Tsai, 2015. "Quantile Correlations and Quantile Autoregressive Modeling," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 246-261, March.
    8. Jennifer L. Wadsworth & Jonathan A. Tawn, 2012. "Dependence modelling for spatial extremes," Biometrika, Biometrika Trust, vol. 99(2), pages 253-272.
    9. Joshua Angrist & Victor Chernozhukov & Iván Fernández-Val, 2006. "Quantile Regression under Misspecification, with an Application to the U.S. Wage Structure," Econometrica, Econometric Society, vol. 74(2), pages 539-563, March.
    10. Han, Heejoon & Linton, Oliver & Oka, Tatsushi & Whang, Yoon-Jae, 2016. "The cross-quantilogram: Measuring quantile dependence and testing directional predictability between time series," Journal of Econometrics, Elsevier, vol. 193(1), pages 251-270.
    11. Kenourgios, Dimitris & Dimitriou, Dimitrios, 2015. "Contagion of the Global Financial Crisis and the real economy: A regional analysis," Economic Modelling, Elsevier, vol. 44(C), pages 283-293.
    12. Girardi, Giulio & Tolga Ergün, A., 2013. "Systemic risk measurement: Multivariate GARCH estimation of CoVaR," Journal of Banking & Finance, Elsevier, vol. 37(8), pages 3169-3180.
    13. Fabrizio Durante & Roberta Pappadà & Nicola Torelli, 2015. "Clustering of time series via non-parametric tail dependence estimation," Statistical Papers, Springer, vol. 56(3), pages 701-721, August.
    14. Bashtannyk, David M. & Hyndman, Rob J., 2001. "Bandwidth selection for kernel conditional density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 36(3), pages 279-298, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Xianling Ren & Xinping Yu, 2024. "Hedging performance analysis of energy markets: Evidence from copula quantile regression," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 44(3), pages 432-450, March.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zhou, Wei & Chen, Yan & Chen, Jin, 2022. "Risk spread in multiple energy markets: Extreme volatility spillover network analysis before and during the COVID-19 pandemic," Energy, Elsevier, vol. 256(C).
    2. Ojea Ferreiro, Javier, 2020. "Disentangling the role of the exchange rate in oil-related scenarios for the European stock market," Energy Economics, Elsevier, vol. 89(C).
    3. Ye, Wuyi & Li, Mingge & Wu, Yuehua, 2022. "A novel estimation of time-varying quantile correlation for financial contagion detection," The North American Journal of Economics and Finance, Elsevier, vol. 63(C).
    4. Chao Xu & Jinchuan Ke & Xiaojun Zhao & Xiaofang Zhao, 2020. "Multiscale Quantile Correlation Coefficient: Measuring Tail Dependence of Financial Time Series," Sustainability, MDPI, vol. 12(12), pages 1-24, June.
    5. Jaworski Piotr, 2017. "On Conditional Value at Risk (CoVaR) for tail-dependent copulas," Dependence Modeling, De Gruyter, vol. 5(1), pages 1-19, January.
    6. Yuri Salazar & Wing Ng, 2015. "Nonparametric estimation of general multivariate tail dependence and applications to financial time series," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(1), pages 121-158, March.
    7. Pavel Krupskii & Harry Joe, 2015. "Tail-weighted measures of dependence," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(3), pages 614-629, March.
    8. Li, Wei-Zhen & Zhai, Jin-Rui & Jiang, Zhi-Qiang & Wang, Gang-Jin & Zhou, Wei-Xing, 2022. "Predicting tail events in a RIA-EVT-Copula framework," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 600(C).
    9. Laih, Yih-Wenn, 2014. "Measuring rank correlation coefficients between financial time series: A GARCH-copula based sequence alignment algorithm," European Journal of Operational Research, Elsevier, vol. 232(2), pages 375-382.
    10. Guillaume Carlier & Victor Chernozhukov & Alfred Galichon, 2014. "Vector quantile regression," CeMMAP working papers CWP48/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    11. Hua, Lei & Joe, Harry, 2014. "Strength of tail dependence based on conditional tail expectation," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 143-159.
    12. Shahzad, Syed Jawad Hussain & Arreola-Hernandez, Jose & Bekiros, Stelios & Shahbaz, Muhammad & Kayani, Ghulam Mujtaba, 2018. "A systemic risk analysis of Islamic equity markets using vine copula and delta CoVaR modeling," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 56(C), pages 104-127.
    13. Labidi, Chiaz & Rahman, Md Lutfur & Hedström, Axel & Uddin, Gazi Salah & Bekiros, Stelios, 2018. "Quantile dependence between developed and emerging stock markets aftermath of the global financial crisis," International Review of Financial Analysis, Elsevier, vol. 59(C), pages 179-211.
    14. Hua, Lei & Joe, Harry, 2012. "Tail comonotonicity: Properties, constructions, and asymptotic additivity of risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 492-503.
    15. Krupskii, Pavel & Joe, Harry, 2013. "Factor copula models for multivariate data," Journal of Multivariate Analysis, Elsevier, vol. 120(C), pages 85-101.
    16. Lu, Xun & Su, Liangjun, 2015. "Jackknife model averaging for quantile regressions," Journal of Econometrics, Elsevier, vol. 188(1), pages 40-58.
    17. Komunjer, Ivana & Vuong, Quang, 2010. "Efficient estimation in dynamic conditional quantile models," Journal of Econometrics, Elsevier, vol. 157(2), pages 272-285, August.
    18. Guo, Dong & Zhou, Peng, 2021. "Green bonds as hedging assets before and after COVID: A comparative study between the US and China," Energy Economics, Elsevier, vol. 104(C).
    19. Ojea-Ferreiro, Javier & Reboredo, Juan C., 2022. "Exchange rates and the global transmission of equity market shocks," Economic Modelling, Elsevier, vol. 114(C).
    20. Han, Xuyuan & Liu, Zhenya & Wang, Shixuan, 2022. "An R-vine copula analysis of non-ferrous metal futures with application in Value-at-Risk forecasting," Journal of Commodity Markets, Elsevier, vol. 25(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:stpapr:v:63:y:2022:i:4:d:10.1007_s00362-021-01268-7. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.