Modelling multivariate moments in European Stock Markets

This research extends the results of Mauleón and Perote, and derives analytically a general framework for the multivariate Edgeworth Sargan (ES) density. Its capability to account for multivariate moments beyond correlation is shown–mainly, co-skewness, co-kurtosis and co-volatility. The multivariate ES is then fitted to the residuals of a VAR model applied to three European stock market series of daily data (FTSE, DAX, CAC40), accounting for univariate as well as multivariate departures from normality. The complete model – with nearly 60 parameters – is set up and estimated jointly by maximum likelihood. Two alternative multivariate probability density functions, student's t and the normal skewed, are also estimated and compared to the ES. The empirical results show: (1) in spite of the high nonlinearity and complexity of the model, it is feasible to fit it to empirical data; (2) statistically significant multivariate effects, other than correlations, are found, and (3) the tail fit of the ES is significantly better.