Detection of outliers in multivariate GARCH models.

In multivariate time series, correct estimation of the correlations among the series plays a key role in portfolio selection. In the univariate case, presence of outliers in financial data is known to lead parameter estimation biases, invalid inferences and poor volatility forecasts. The aim is to analyze the impact of outliers in multivariate time series. It is found that the impact in volatility follows a similar pattern to that in univariate time series, but, more interesting, the multivariate approach allows to analyze the impact on correlations. A general outlier detection procedure for multivariate time series is proposed, extending the wavelet-based method proposed in a previous work for the univariate case. The proposal is to extend this procedure to the context of multivariate GARCH models by considering random-projections of multivariate residuals. The method is general enough to deal with different multivariate GARCH models, such as the Constant Conditional Correlation, the Dynamic Conditional Correlation and the Diagonal BEKK. The effectiveness of this new procedure is evaluated through an intensive Monte Carlo study considering isolated and patches of additive level outliers and additive volatility outliers.