MGARCH models: tradeoff between feasibility and flexibility

The parameters of popular multivariate GARCH (MGARCH) models are restricted so that their estimation is feasible in large systems and covariance stationarity and positive definiteness of conditional covariance matrices are guaranteed. These restrictions limit the dynamics that the models can represent, assuming, for example, that volatilities evolve in an univariate fashion, not being related neither among them nor with the correlations. This paper updates previous surveyson parametric MGARCH models focusing on their limitations to represent the dynamics observed in real systems of financial returns. The conclusions are illustrated using simulated data and a five-dimensional system of exchange rate returns.The first author was supported by grants of 0969/13-3 CAPES, Coordination of Improvement of Higher Education Personnel. The second author acknowledges financial support from CAPES, grant 10600/13-2, São Paulo Research Foundation (FAPESP), grant 2013/00506-1, and Laboratory EPIFISMA. Financial support from ECO2012-32401 project by the Spanish Government is gratefully acknowledged by the third author