Modelling multivariate moments in European Stock Markets

Abstract

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.

Keywords:

• Multivariate ES density
• co-skewness
• co-kurtosis and co-volatility
• European stock markets

Acknowledgements

The comments and suggestions of the participants at the 32nd meeting of the Euro Working Group on Financial Modelling held at the Imperial College (London, 2003), without implicating them, are gratefully acknowledged. The research assistance of Raúl Sánchez Larrión is also gratefully acknowledged. Special thanks deserve two anonymous referees and the editor of this journal, as well. The author is solely responsible for any possible remaining error.

Notes

¹I am grateful to both referees, for pointing out some errors.