Skip to main content Accessibility help
×
Home

DETECTING FINANCIAL DATA DEPENDENCE STRUCTURE BY AVERAGING MIXTURE COPULAS

  • Guannan Liu (a1), Wei Long (a2), Xinyu Zhang (a3) and Qi Li (a4)

Abstract

A mixture copula is a linear combination of several individual copulas that can be used to generate dependence structures not belonging to existing copula families. Because different pairs of markets may exhibit quite different dependence structures in empirical studies, mixture copulas are useful in modeling the dependence in financial data. Therefore, rather than selecting a single copula based on certain criteria, we propose using a model averaging approach to estimate financial data dependence structures in a mixture copula framework. We select weights (for averaging) by a J-fold Cross-Validation procedure. We prove that the model averaging estimator is asymptotically optimal in the sense that it minimizes the squared estimation loss. Our simulation results show that the model averaging approach outperforms some competing methods when the working mixture model is misspecified. Using 12 years of data on daily returns from four developed economies’ stock indexes, we show that the model averaging approach more accurately estimates their dependence structures than some competing methods.

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      DETECTING FINANCIAL DATA DEPENDENCE STRUCTURE BY AVERAGING MIXTURE COPULAS
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      DETECTING FINANCIAL DATA DEPENDENCE STRUCTURE BY AVERAGING MIXTURE COPULAS
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      DETECTING FINANCIAL DATA DEPENDENCE STRUCTURE BY AVERAGING MIXTURE COPULAS
      Available formats
      ×

Copyright

Corresponding author

*Address correspondence to Xinyu Zhang, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China; and Qingdao University, Qingdao, China; email: xinyu@amss.ac.cn.

Footnotes

Hide All

We would like to thank the Editor, Peter C.B. Phillips, Co-Editor, Dennis Kristensen, and three anonymous referees for their insightful comments that greatly improved our article. We would also like to thank Yanqin Fan and Xiaohong Chen for their help during the revision process of this article. Liu’s research is supported by the National Natural Science Foundation of China (Grant No. 71803160) and the Fundamental Research Funds for the Central Universities (project number 20720171061). Long’s research is partially supported by the Carol Lavin Bernick Faculty Grants at Tulane University. Zhang and Li’s research is partially supported by National Natural Science Foundation of China (projects 71522004, 11471324, and 71631008 for Zhang; 71722011 and 71601130 for Li).

Footnotes

References

Hide All
Aloui, R., Aïssa, M., & Nguyen, D. (2011) Global financial crisis, extreme interdependences, and contagion effects: The role of economic structure? Journal of Banking & Finance 35, 130141.10.1016/j.jbankfin.2010.07.021
Ando, T. & Li, K. (2014) A model-averaging approach for high-dimensional regression. Journal of the American Statistical Association 109, 254265.10.1080/01621459.2013.838168
Andrews, D.W.K. (1991) Heteroskedasticity and autocorrelation consistent covariance matrix estimation. Econometrica 59, 817858.10.2307/2938229
Cai, Z. & Wang, X.. (2014) Selection of mixed copula model via penalized likelihood. Journal of the American Statistical Association 109, 788801.10.1080/01621459.2013.873366
Chen, X. & Fan, Y. (2006a) Estimation of copula-based semiparametric time series models. Journal of Econometrics 130, 307335.10.1016/j.jeconom.2005.03.004
Chen, X. & Fan, Y. (2006b) Estimation and model selection of semiparametric copula-based multivariate dynamic models under copula misspecification. Journal of Econometrics 135, 125154.10.1016/j.jeconom.2005.07.027
Cheng, X. & Hansen, B. (2015) Forecasting with factor-augmented regression: A frequentist model averaging approach. Journal of Econometrics 186, 280293.10.1016/j.jeconom.2015.02.010
Chollete, L., Peña, V., & Lu, C.. (2005) Comovement of international financial markets. Unpublished manuscript.10.2139/ssrn.675382
Chollete, L., Heinen, A., & Valdesogo, A. (2009) Modeling international financial returns with a multivariate regime-switching copula. Journal of Financial Econometrics 7, 437480.10.1093/jjfinec/nbp014
Fan, J. & Li, R. (2001) Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of the American Statistical Association 96, 13481360.10.1198/016214501753382273
Fan, Y. & Patton, A. (2014) Copulas in econometrics. Annual Review of Economics 6, 179200.10.1146/annurev-economics-080213-041221
Gao, Y., Zhang, X., Wang, S., Chong, T., & Zou, G. (2018). Frequentist model averaging for threshold models. Annals of the Institute of Statistical Mathematics, first published online 12 January 2018. doi:10.1007/s10463-017-0642-9.
Genest, C. & Rivest, L. (1993) Statistical inference procedures for bivariate Archimedean copulas. Journal of the American Statistical Association 88, 10341043.10.1080/01621459.1993.10476372
Hansen, B. & Racine, J. (2012) Jackknife model averaging. Journal of Econometrics 167, 3846.10.1016/j.jeconom.2011.06.019
Hansen, B. (2007) Least squares model averaging. Econometrica 75, 11751189.10.1111/j.1468-0262.2007.00785.x
Hu, L. (2006) Dependence patterns across financial markets: A mixed copula approach. Applied Financial Economics 16, 717729.10.1080/09603100500426515
Joe, H. (1997) Multivariate Models and Dependence Concepts. Chapman & Hall.10.1201/b13150
Li, D. (2000) On default correlation: A copula function approach. Journal of Fixed Income 9, 4354.10.3905/jfi.2000.319253
Longin, F. & Solnik, B. (2001) Extreme correlation of international equity markets. The Journal of Finance 56, 649676.10.1111/0022-1082.00340
Ma, Y. & Zhu, L. (2012) A semiparametric approach to dimension reduction. Journal of the American Statistical Association 497, 168179.10.1080/01621459.2011.646925
Manner, H. & Reznikova, O. (2012) A survey on time-varying copulas: Specification, simulations and application. Econometric Reviews 31, 654687.10.1080/07474938.2011.608042
Nelsen, R. (2006) An Introduction to Copulas, 2nd ed. Springer.
Patton, A. (2006) Modelling asymmetric exchange rate dependence. International Economic Review 47, 527556.10.1111/j.1468-2354.2006.00387.x
Patton, A. (2012) A review of copula models for economic time series. Journal of Multivariate Analysis 110, 418.10.1016/j.jmva.2012.02.021
Rodriguez, J. (2007) Measuring financial contagion: A copula approach. Journal of Empirical Finance 14, 401423.10.1016/j.jempfin.2006.07.002
Shao, J. (1997) An asymptotic theory for linear model selection. Statistica Sinica 7, 221264.
Sklar, A. (1959) Fonctions de répartition à n dimensions et leurs marges. Publication de l’Institut de Statistique de l’Universite de Paris 8, 229231.
Zhang, X. (2010) Model Averaging and its Applications. Ph.D. thesis, Academy of Mathematics and Systems Science, Chinese Academy of Sciences.
Zhang, X., Wan, A.T.K., & Zou, G. (2013) Model averaging by Jackknife criterion in models with dependent data. Journal of Econometrics 174, 8294.10.1016/j.jeconom.2013.01.004
Zhang, X., Yu, D., Zou, G., & Liang, H. (2016) Optimal model averaging estimation for generalized linear models and generalized linear mixed-effects models. Journal of the American Statistical Association 111, 17751790.10.1080/01621459.2015.1115762
Zimmer, D.M. (2012) The role of copulas in the housing crisis. Review of Economics and Statistics 94, 607620.10.1162/REST_a_00172

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed