Humboldt-Universität zu Berlin - High Dimensional Nonstationary Time Series

Trending Mixture Copula Models with Copula Selection

Bingduo Yang
Zongwu Caib
Christian M. Hafner
Guannan Liu

Abstract
Modeling the joint tails of multiple nancial time series has important im-
plications for risk management. Classical models for dependence often encounter a lack
of t in the joint tails, calling for additional exibility. In this paper we introduce a new
nonparametric time-varying mixture copula model, in which both weights and depen-
dence parameters are deterministic functions of time. We propose penalized trending
mixture copula models with group smoothly clipped absolute deviation (SCAD) penal-
ty functions to do the estimation and copula selection simultaneously. Monte Carlo
simulation results suggest that the shrinkage estimation procedure performs well in s-
electing and estimating both constant and trending mixture copula models. Using the
proposed model and method, we analyze the evolution of the dependence among four
international stock markets, and nd substantial changes in the levels and patterns of
the dependence, in particular around crisis periods.

Keywords:
Copula, Time-Varying Copula, Mixture Copula, Copula Selection

JEL Classification: