A new time-varying optimal copula model identifying the dependence across markets

Abstract

This paper proposes a new time-varying optimal copula (TVOC) model to identify and capture the optimal dependence structure of bivariate time series at every time point. In the TVOC model, half-rotated copulas are constructed to measure the nonlinear and asymmetric negative dependence, and the distribution-free test for independence is introduced to verify the dependent relationship and reduce the computational time. The TVOC model is then employed to research the dependence structure between security and commodity markets. We find evidence that the dependence structures across different markets vary over time and that emergencies are usually the major cause of sudden changes in the dependence structure. We also show that the TVOC model captures the dynamic characteristics of the direction and intensity of the dependence as well as the dynamic characteristics of the types of dependence structure. In particular, the half-rotated copulas can accurately describe the asymmetric negative extreme dependence across different markets.

Keywords:

• Tail dependence
• Co-movement across markets
• Half-rotated copulas
• Time-varying optimal copula approach

Acknowledgements

The authors appreciate the weekly seminars at CEEP in CAS, from where the earlier draft of the paper got improved.

Notes

¹ Given the historical information set at time t Ω_t-1, the marginal distribution.

and then .