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DETECTING FINANCIAL DATA DEPENDENCE STRUCTURE BY AVERAGING MIXTURE COPULAS

Published online by Cambridge University Press:  10 September 2018

Guannan Liu ,
Wei Long ,
Xinyu Zhang  and
Qi Li
Guannan Liu
Affiliation:
School of Economics, Xiamen University
Wei Long
Affiliation:
Tulane University
Xinyu Zhang*
Affiliation:
Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Qingdao University
Qi Li
Affiliation:
Texas A&M University, Capital University of Economics and Business
*
*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.
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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.

Type
ARTICLES
Information
Econometric Theory , Volume 35 , Issue 4 , August 2019 , pp. 777 - 815
Copyright
Copyright © Cambridge University Press 2018 

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Footnotes

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).

References

REFERENCES

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, 130–141.10.1016/j.jbankfin.2010.07.021CrossRefGoogle Scholar
Ando, T. & Li, K. (2014) A model-averaging approach for high-dimensional regression. Journal of the American Statistical Association 109, 254–265.10.1080/01621459.2013.838168CrossRefGoogle Scholar
Andrews, D.W.K. (1991) Heteroskedasticity and autocorrelation consistent covariance matrix estimation. Econometrica 59, 817–858.10.2307/2938229CrossRefGoogle Scholar
Cai, Z. & Wang, X.. (2014) Selection of mixed copula model via penalized likelihood. Journal of the American Statistical Association 109, 788–801.10.1080/01621459.2013.873366CrossRefGoogle Scholar
Chen, X. & Fan, Y. (2006a) Estimation of copula-based semiparametric time series models. Journal of Econometrics 130, 307–335.10.1016/j.jeconom.2005.03.004CrossRefGoogle Scholar
Chen, X. & Fan, Y. (2006b) Estimation and model selection of semiparametric copula-based multivariate dynamic models under copula misspecification. Journal of Econometrics 135, 125–154.10.1016/j.jeconom.2005.07.027CrossRefGoogle Scholar
Cheng, X. & Hansen, B. (2015) Forecasting with factor-augmented regression: A frequentist model averaging approach. Journal of Econometrics 186, 280–293.10.1016/j.jeconom.2015.02.010CrossRefGoogle Scholar
Chollete, L., Peña, V., & Lu, C.. (2005) Comovement of international financial markets. Unpublished manuscript.10.2139/ssrn.675382CrossRefGoogle Scholar
Chollete, L., Heinen, A., & Valdesogo, A. (2009) Modeling international financial returns with a multivariate regime-switching copula. Journal of Financial Econometrics 7, 437–480.10.1093/jjfinec/nbp014CrossRefGoogle Scholar
Fan, J. & Li, R. (2001) Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of the American Statistical Association 96, 1348–1360.10.1198/016214501753382273CrossRefGoogle Scholar
Fan, Y. & Patton, A. (2014) Copulas in econometrics. Annual Review of Economics 6, 179–200.10.1146/annurev-economics-080213-041221CrossRefGoogle Scholar
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.Google Scholar
Genest, C. & Rivest, L. (1993) Statistical inference procedures for bivariate Archimedean copulas. Journal of the American Statistical Association 88, 1034–1043.10.1080/01621459.1993.10476372CrossRefGoogle Scholar
Hansen, B. & Racine, J. (2012) Jackknife model averaging. Journal of Econometrics 167, 38–46.10.1016/j.jeconom.2011.06.019CrossRefGoogle Scholar
Hansen, B. (2007) Least squares model averaging. Econometrica 75, 1175–1189.10.1111/j.1468-0262.2007.00785.xCrossRefGoogle Scholar
Hu, L. (2006) Dependence patterns across financial markets: A mixed copula approach. Applied Financial Economics 16, 717–729.10.1080/09603100500426515CrossRefGoogle Scholar
Joe, H. (1997) Multivariate Models and Dependence Concepts. Chapman & Hall.10.1201/b13150CrossRefGoogle Scholar
Li, D. (2000) On default correlation: A copula function approach. Journal of Fixed Income 9, 43–54.10.3905/jfi.2000.319253CrossRefGoogle Scholar
Longin, F. & Solnik, B. (2001) Extreme correlation of international equity markets. The Journal of Finance 56, 649–676.10.1111/0022-1082.00340CrossRefGoogle Scholar
Ma, Y. & Zhu, L. (2012) A semiparametric approach to dimension reduction. Journal of the American Statistical Association 497, 168–179.10.1080/01621459.2011.646925CrossRefGoogle Scholar
Manner, H. & Reznikova, O. (2012) A survey on time-varying copulas: Specification, simulations and application. Econometric Reviews 31, 654–687.10.1080/07474938.2011.608042CrossRefGoogle Scholar
Nelsen, R. (2006) An Introduction to Copulas, 2nd ed. Springer.Google Scholar
Patton, A. (2006) Modelling asymmetric exchange rate dependence. International Economic Review 47, 527–556.10.1111/j.1468-2354.2006.00387.xCrossRefGoogle Scholar
Patton, A. (2012) A review of copula models for economic time series. Journal of Multivariate Analysis 110, 4–18.10.1016/j.jmva.2012.02.021CrossRefGoogle Scholar
Rodriguez, J. (2007) Measuring financial contagion: A copula approach. Journal of Empirical Finance 14, 401–423.10.1016/j.jempfin.2006.07.002CrossRefGoogle Scholar
Shao, J. (1997) An asymptotic theory for linear model selection. Statistica Sinica 7, 221–264.Google Scholar
Sklar, A. (1959) Fonctions de répartition à n dimensions et leurs marges. Publication de l’Institut de Statistique de l’Universite de Paris 8, 229–231.Google Scholar
Zhang, X. (2010) Model Averaging and its Applications. Ph.D. thesis, Academy of Mathematics and Systems Science, Chinese Academy of Sciences.Google Scholar
Zhang, X., Wan, A.T.K., & Zou, G. (2013) Model averaging by Jackknife criterion in models with dependent data. Journal of Econometrics 174, 82–94.10.1016/j.jeconom.2013.01.004CrossRefGoogle Scholar
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, 1775–1790.10.1080/01621459.2015.1115762CrossRefGoogle Scholar
Zimmer, D.M. (2012) The role of copulas in the housing crisis. Review of Economics and Statistics 94, 607–620.10.1162/REST_a_00172CrossRefGoogle Scholar