Abstract
Recently, several copula-based approaches have been proposed for modeling stationary multivariate time series. All of them are based on vine copulas, and they differ in the choice of the regular vine structure. In this article, we consider a copula autoregressive (COPAR) approach to model the dependence of unobserved multivariate factors resulting from two dynamic factor models. However, the proposed methodology is general and applicable to several factor models as well as to other copula models for stationary multivariate time series. An empirical study illustrates the forecasting superiority of our approach for constructing an optimal portfolio of U.S. industrial stocks in the mean-variance framework.
Highlights
It took almost four decades before the statistical usefulness and attractiveness of copulas was widely recognized after the seminal papers by Frees and Valdez (1998), Li (2000), and Embrechts et al (2002).Copulas are a standard tool for modeling a dependence structure of multivariate identically and independently distributed data in applied science
The foundation of the copula theory was laid by the famous Sklar’s theorem, which states that any multivariate distribution can be represented through its copula and marginal distributions
Czado (2015) and Beare and Seo (2015) assume the existence of a key variable, whose temporal dependence was explicitly modeled, and this assumption combined with C- or drawable vines (D-vines) for the cross-sectional dependence results in a corresponding R-vine for a multivariate time series
Summary
It took almost four decades before the statistical usefulness and attractiveness of copulas was widely recognized after the seminal papers by Frees and Valdez (1998), Li (2000), and Embrechts et al (2002). Brechmann and Czado (2015), Beare and Seo (2015), and Smith (2015) simultaneously developed copula-based models for stationary multivariate time series These models differ from each other, their generality consists of an underlying R-vine pair-copula construction (see Aas et al 2009) to describe the cross-sectional and temporal dependence jointly. Czado (2015) and Beare and Seo (2015) assume the existence of a key variable, whose temporal dependence was explicitly modeled, and this assumption combined with C- or D-vine for the cross-sectional dependence results in a corresponding R-vine for a multivariate time series. Our approach allows several estimated dynamic factor models to be coupled with a copula and admits a non-Gaussian dependence structure of simulated latent factors. Appendix F summarizes testing results of Granger causality between estimated factors
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