Autoregressive-type multivariate GARCH (MGARCH) models have been widely adopted by scholars to measure time-varying correlation structures. It is a well-known stylized fact that conditional correlations generated by these models tend to exhibit a highly unstable and erratic behavior under certain conditions. Therefore, the value added of these scientifically demanding MGARCH techniques remains sometimes ambiguous. In this paper, we provide a measure for the autocovariance structure of conditional correlations generated by a DCC MGARCH under the assumption that true conditional correlations are constant. This allows us to formally demonstrate that autocovariances of conditional correlations generated by an autoregressive-type MGARCH model are highly sensitive to small changes in model parameters. We provide empirical evidence for the impact of parameter changes on forecasting accuracy and show under which conditions a simple rolling window estimator yields superior results.