Benjamin Kauper, Karl-Kuno Kunze

• This paper offers empirical evidence on the power of Sornette et al's [2001] model of bubbles and crashes regarding the German stock market between 1960 and 2009. We identify relevant time periods and describe them with the function given by Sornette et al's model. Our results show some evidence in predicting crashes with the understanding of logarithmic periodic structures that are hidden in the stock price trajectories. It was shown that for the DAX most of the relevant parameters determining the shape of the logarithmic periodic structures are lying in the expected interval researched by Sornette et al. Further more the paper implicitly shows that the point of time of former crashes can be predicted with the presented formula. We conclude that the concept of financial time series conceived as purely random objects should be generalised as to admit complexity.