Predicting critical crashes? A new restriction for the free variables

Several authors have noticed the signature of log-periodic oscillations prior to large stock market crashes. Unfortunately, the prediction of crashes with this method is difficult, since good fits of the corresponding log-periodic equation to stock market prices are also observed in quiet times. We deduce a new inequality among the free variables in this equation, that must be satisfied before a crash. This inequality alone yields crash predictions with a 25% success rate for the Dow Jones index. This compares to a 9% success rate obtained by previous approaches. Combining our method with previous ones we obtain a success rate of 54%.