Directional time-varying partial correlation with the Gaussian copula–DCC–GARCH model

ABSTRACT

This article suggests a directional time-varying partial correlation based on the dynamic conditional correlation (DCC) method. A recent study proposed the copula DCC based on the vine structure. Due to the arbitrary variable selection, their method can produce unnecessary dependence in the multivariate structure, with extra economic and computational burdens. To overcome this limitation, we incorporate directional dependence by copula to track the causal relationship among multiple variables and then extend the copula bivariate DCC method to a directional time varying partial correlation in the multivariate structure. Our proposed method provides a reasonable and efficient conditional dependence structure, without the trial and error process. We offer an application of our method to the U.S. stock market as an illustrated example.

KEYWORDS:

• Directional dependence
• time-varying partial correlation
• dynamic conditional correlation

JEL CLASSIFICATION:

• C32
• G10

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ Each conditional correlation is estimated by the cgarchspec command in the R package rmgarch, which implements the Gaussian copula.

² In the first step, we estimate the parameters of univariate marginal distributions and then the dependence parameters can be estimated in the second step by using the estimates obtained from the first step.

³ Poignard and Fermanian (2015) deduce the partial correlation from a vine structure.

⁴ We examine such a long time horizon at roughly 7-year intervals before and after the financial crisis in order to account for the possibility of structural change in the U.S. stock market. All stock index prices are retrieved from http://quote.yahoo.comhttp://quote.yahoo.com.