Time-Varying Correlations between Selected Exchange Rates: A Robust DCC-GARCH Model Approach

Abstract

Effective diversification of global portfolios and risk management depends to a large extent on the degree
of correlation between the returns of financial assets. The Dynamic Conditional Correlation Generalized
Autoregressive Conditional Heteroscediency (DCC-GARCH) model addresses the time-varying correlation and
volatility among financial assets. The model has a two-step process whereby the volatility of each individual
asset is first estimated using the univariate GARCH and the time-varying correlation between those assets
is then captured using the DCC framework. Although the DCC-GARCH setup allows for the use of any univariate
GARCH model for the variance of each financial asset, when constructing a DCC-GARCH model, most researchers
typically use only one univariate GARCH model for all the returns of the financial asset. This study proposes
a robust DCC-GARCH model in analyzing the dynamics of time-varying correlations of financial data in which
the optimal univariate GARCH models (with the lowest information criteria) for each financial asset are
used to build up the DCC-GARCH model. An empirical application of this model in analyzing the time-varying
conditional correlation between four exchange rates shows an improvement in results (relative to the
information criterion values) compared to the case where only one univariate GARCH model is used to
construct the DCC-GARCH model. Standardized residuals in the quasi maximum likelihood estimation (QMLE)
procedure for DCC-GARCH parameters, are typically assumed to follow a multivariate Gaussian distribution.
One stylized fact of financial data returns is that the residuals are heavy-tailed. We consider the case
where the standardized residuals follow a multivariate Gaussian, and the case where they follow either
a multivariate Student's t-distribution or a multivariate Laplace distribution. Results show that a robust
DCC-GARCH model performs better when the standardized residuals follow a multivariate Student's
t-distribution.