In this article, we consider financial markets as complex dynamical systems, and check whether the critical slowing down indicators can be used as early warning signals to detect a phase transition. Using various rolling windows, we analyze the evolution of three indicators: i) First-order autocorrelation, ii) Variance, and iii) Skewness. Using daily data for ten European stock exchanges plus the United States, and focusing on the Global Financial Crisis, our results are mitigated and depend both on the series used and the indicator. Using the main log-indices, critical slowing down indicators seem weak to predict the Global Financial Crisis. Using cumulative returns, for almost all countries, an increase in variance and skewness does precede the crisis. However, first-order autocorrelations of both log-indices and cumulative returns do not provide any useful information about the Global Financial Crisis. Thus, only some of the reported critical slowing down indicators may have informational content, and could be used as early warnings.