Double Dynamic Max-Copula Model with Application to Financial Time Series

Accurately modeling time-varying dependence structures is essential for financial market analysis, particularly during periods of market stress. Recognizing that traditional copula models often fail to jointly capture dynamic dependence and tail behavior, this article proposes a double dynamic max-copula (DDMC) model that accommodates time variation while effectively characterizing tail dependence. To estimate the model, we introduce a maximum composite profile likelihood estimator, and establish its consistency and asymptotic normality. We also propose a test statistic to check whether the dependence parameter is time-varying, and derive the asymptotic distribution of the proposed test statistic. Simulation studies confirm the flexibility and robustness of the proposed model. In an empirical application, we analyze the evolving interdependence between U.S. financial markets, demonstrating the model’s ability to capture dynamic relationships. Furthermore, in a portfolio optimization context, the DDMC-based portfolio consistently outperforms those generated by benchmark models.