Multivariate Skewed Student's t Copula in the Analysis of Nonlinear and Asymmetric Dependence in the German Equity Market

Abstract

Analyzing comovements in equity markets is important for risk diversification in portfolio management. Copulas have several advantages compared to the linear correlation measure in modeling comovement. This paper introduces a copula ARMA-GARCH model for analyzing the comovement of indexes in German equity markets. The model is implemented with an ARMA-GARCH model for the marginal distributions and a copula for the joint distribution. After goodness-of-fit testing, we find that the skewed Student's t copula ARMA(1,1)-GARCH(1,1) model with Lévy fractional stable noise is superior to alternative models investigated in our study where we model the simultaneous comovement of six German equity market indexes. This model is also suitable for capturing the long-range dependence, tail dependence, and asymmetric correlation observed in German equity markets.