Robust M-estimation of multivariate conditionally heteroscedastic time series models with elliptical innovations

This paper proposes new methods for the econometric analysis of outlier contaminated multivariate conditionally heteroscedastic time series. Robust alternatives to the Gaussian quasi-maximum likelihood estimator are presented. Under elliptical symmetry of the innovation vector, consistency results for M-estimation of the general conditional heteroscedasticity model are obtained. We also propose a robust estimator for the cross-correlation matrix and a diagnostic check for correct specification of the innovation density function. In a Monte Carlo experiment, the effect of outliers on different types of M-estimators is studied. We conclude with a financial application in which these new tools are used to analyse and estimate the symmetric BEKK model for the 1980-2006 series of weekly returns on the Nasdaq and NYSE composite indices. For this dataset, robust estimators are needed to cope with the outlying returns corresponding to the stock market crash in 1987 and the burst of the dotcom bubble in 2000.