Influence diagnostics for multivariate GARCH processes

This article presents diagnostics for identifying influential observations when estimating multivariate generalized autoregressive conditional heteroscedasticity (GARCH) models. We derive influence diagnostics by introducing minor perturbations to the conditional variances and covariances. The derived diagnostics are applied to a bivariate GARCH model of daily returns of the S&P500 and IBM. We find that univariate diagnostic procedures may be unable to identify the influential observations in a multivariate model. Importantly, the proposed curvature-based diagnostic identified influential observations where the correlation between the two series had a major change. These observations were not identified as influential using the univariate diagnostics for each asset separately. When estimating the bivariate GARCH model allowing for weights at influential observations, we found that the time-varying correlations behaved differently from that implied by the model ignoring influential observations. The application therefore highlights the importance of extending univariate diagnostic procedures to multivariate settings.