On the multifractal properties and the local multifractality sensitivity index of euro to Japanese yen foreign currency exchange rates

We examine the high frequency dynamics of euro to Japanese yen foreign currency exchange rates for the period of January 2001 to January 2010, comprising approximately three million data entries. The probability density function is described competently by the Tsallis q-Gaussian statistics, approaching the Gaussian distribution as the time lag increases. Multifractality has been studied using the original, shuffled and surrogate data series to investigate the origin. We then extend the local Hurst exponent idea taking in account the local multifractality, using a moving window of 10,000 data points. The square of the difference of the local multifractality ranges, defined as a sensitivity index, provides a signal before the last crash.