The financial crises of 2001-2002 and 2008-2009 had a significant impact on the world economy. In this paper, we investigate whether early warning signals can be seen in financial time series preceding the crises. In our analysis, we use data on the Dow Jones Industrial Average and Federal Reserve Interest Rate. We construct a random process describing the occurrence of positive and negative signals in a time series preceding the financial crisis of 2001-2002. We use the constructed random process and a time series for the period 2001-2008 to assess the probability of a crisis to occur in 2008-2009. We show that the probability exhibits a steady growth and conclude that the proposed method demonstrates an ability to register early warning signals on the global financial crisis of 2008-2009.