Multifractality in time series

We apply the concepts of multifractal physics to financial time series in o rder to characterize the onset of crash for the Standard & Poor 500 (S&P500 ) stock index x(t). It is found that within the framework of multifractalit y, the 'analogous' specific heat of the S&P500 discrete price index display s a shoulder to the right of the main peak for low time-lag values. For dec reasing T, the presence of the shoulder is a consequence of the peaked, tem poral x(t+T) - x(t) fluctuations in this regime. For large time lags (T > 8 0), we have found that C-q displays typical features of a classical phase t ransition at a critical point. An example of such dynamic phase transition in a simple economic model system, based on a mapping with multifractality phenomena in random multiplicative processes, is also presented by applying former results obtained with a continuous probability theory for describin g scaling measures.