The copula directional dependence by stochastic volatility models

ABSTRACT

This paper proposes a copula directional dependence by using a bivariate Gaussian copula beta regression with Stochastic Volatility (SV) models for marginal distributions. With the asymmetric copula generated by the composition of two Plackett copulas, we show that our SV copula directional dependence by the Gaussian copula beta regression model is superior to the Kim and Hwang (2016) copula directional dependence by an asymmetric GARCH model in terms of the percent relative efficiency of bias and mean squared error. To validate our proposed method with the real data, we use Brent Crude Daily Price (BRENT), West Texas Intermediate Daily Price (WTI), the Standard & Poor’s 500 (SP) and US 10-Year Treasury Constant Maturity Rate (TCM) so that our copula SV directional dependence is overall superior to the Kim and Hwang (2016) copula directional dependence by an asymmetric GARCH model in terms of precision by the percent relative efficiency of mean squared error. In terms of forecasting using the real financial data, we also show that the Bayesian SV model of the uniform transformed data by a copula conditional distribution yields an improvement on the volatility models such as GARCH and SV.

KEYWORDS:

• Beta regression model
• Copula
• Directional dependence
• Stochastic volatility model

MATHEMATICS SUBJECT CLASSIFICATION:

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

Acknowledgment

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).

Additional information

Funding

Basic Science Research Program through the NRF of Korea funded by the Ministry of Education [2015-057031].