Simple Time - Varying Copula Estimation

This article examines the ability of time-varying Gaussian and Student t copulas to accurately predict the probability of joint extreme co-movements in stock index returns. Using a sample of more than 20 years of daily return observations of the Eurostoxx50 and Dow Jones Industrial stock indices, Gaussian and Student t copulas are calibrated daily on a rolling window of the 250 most recent observations. We do not make assumptions on the functional form of the marginal distributions. Thus, the focus remains on the examination of the appropriateness of the two types of copulas. One of our findings is that there are time periods when the assumption of a Gaussian copula seems to be accurate and when the hypothesis of a Gaussian copula cannot be rejected in favor of a Student t copula. In other time periods, the hypothesis of a Gaussian copula can be rejected, as it underestimates the probability of joint extreme co-movements. This time periods of joint extreme co-movements are typically associated with a higher volatility environment and higher correlations between stock index returns. In applying a hit test to examine the ability of both copulas to predict the probability of joint strongly negative returns of both indices, we reject the null hypothesis of a Gaussian copula while the null hypothesis of a Student t copula cannot be rejected.