Structural and predictive analyses with a mixed copula-based vector autoregression model

Abstract

In this study, we introduce a mixed copula-based vector autoregressive (VAR) model for investigating the relationship between random variables. The one-step maximum likelihood estimation is used to obtain point estimates of the autoregressive parameters and mixed copula parameters. More specifically, we combine the likelihoods of the marginal and mixed copula to construct the full likelihood function. The simulation study is used to confirm the accuracy of the estimation as well as the reliability of the proposed model. Various mixed copula forms from a combination of Gaussian, Student's t, Clayton, Frank, Gumbel, and Joe copulas are introduced. The proposed model is compared to the traditional VAR model and single copula-based VAR models to assess its performance. Furthermore, the real data study is also conducted to validate our proposed method. As a result, it is found that the one-step maximum likelihood provides accurate and reliable results. Also, we show that if we ignore the complex and nonlinear correlation between the errors, it causes significant efficiency loss in the parameter estimation in terms of |Bias| and MSE. In the application study, the mixed copula-based VAR is the best fitting copula for our application study.