Directional dependence via Gaussian copula beta regression model with asymmetric GARCH marginals

ABSTRACT

This article proposes a new directional dependence by using the Gaussian copula beta regression model. In particular, we consider an asymmetric Generalized AutoRegressive Conditional Heteroscedasticity (GARCH) model for the marginal distribution of standardized residuals to make data exhibiting conditionally heteroscedasticity to white noise process. With the simulated data generated by an asymmetric bivariate copula, we verify our proposed directional dependence method. For the multivariate direction dependence by using the Gaussian copula beta regression model, we employ a three-dimensional archemedian copula to generate trivariate data and then show the directional dependence for one random variable given two other random variables. With West Texas Intermediate Daily Price (WTI) and the Standard & Poor’s 500 (S&P 500), our proposed directional dependence by the Gaussian copula beta regression model reveals that the directional dependence from WTI to S&P 500 is greater than that from S&P 500 to WTI. To validate our empirical result, the Granger causality test is conducted, confirming the same result produced by our method.

KEYWORDS:

• Asymmetric Garch models
• Beta regression model
• Copula
• Directional dependence
• Generalized autoregressive conditional heteroscedasticity

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 62H11 (Directional data)
• Secondary 62M10

Acknowledgments

The authors would like to thank the Editor, Associate Editor, and the anonymous learned referee whose helpful suggestions and insightful comments greatly improved the quality of this article. S.Y. Hwang’s work was supported by Basic Science Research Program through the NRF of Korea funded by the Ministry of Education (2015-057031).