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

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.

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:
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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).

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Econometric Theory
  • ISSN: 0266-4666
  • EISSN: 1469-4360
  • URL: /core/journals/econometric-theory
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