On the devolatised returns and dynamic conditional correlations GARCH modelling in selected European indices

Typical issues of multivariate GARCH models are dimensionality, which is time-consuming both in terms of computations and their programming, and the availability of very few distributional schemes, since linear correlations are a natural dependence measure, only if the joint distribution of the variables is elliptical. We consider the new approach of devolatised returns, computed as returns standardised by realised volatilities rather than by GARCH-type volatilities estimates. As a case study, we examine several European indices, and the methodology incorporates a multivariate t-student version of the dynamic conditional correlations GARCH model. The time series under consideration and the results are subjected to several diagnostic tests, including the temporal volatilities and correlations of the asset returns, the validity of the t-DCC model using value-at-risk, the empirical cumulative distribution function of the probability integral transform variable, and forecasts of the conditional volatility and correlations. The concluding remarks are consistent, and in agreement with the new devolatised returns concept.