A new approach to calculate and forecast dynamic conditional correlation - the use of a multivariate heteroskedastic mixture model

Much research in finance has been directed towards forecasting time varying volatility of unidimensional macroeconomic variables such as stock index, exchange rate and interest rate. However, comparatively little is devoted to modelling time varying correlation. In this research, we extend the current literature on correlation modelling by reviewing existing time-series tools, performing empirical analysis and developing two new conditional heteroscedastic models based on mixture techniques. Specifically, Engle’s standard DCC is augmented with an asymmetric factor and then modified so that disturbances (conditional returns) can be modelled using multivariate Gaussian mixture distribution and multivariate T mixture distribution. A key motivation of proposing mixture models is to account for the bi-modality observed in unconditional distribution of realized correlation. Besides, the ultimate purpose of incorporating this assumption to a multivariate GARCH is to account for a variety of stylized features frequently presented in financial returns such as volatility clustering, correlation clustering, leverage effect, fat tails, skewness and leptokurtosis. Since the model flexibility given this assumption can be greatly enhanced, after a thorough comparison we find significant evidence of outperformance of our models over other alternative models from a range of perspectives. Besides, in this research we also study a new type of correlation model using multivariate skew-t as basis for quantifying the density values of conditional returns. Note that, the ADCC skew-t and AGDCC skew-t model analyzed in this research are both new to the financial literature