An important problem in physics concerns the origin of very large events in the dynamics of complex systems, such as large earthquakes, pandemics, mass extinctions and financial crashes. Here we review recent advances that suggest that the largest events in the dynamics of stock markets are due to long-range memory effects. We have studied the distributions of stock returns measured over different time lags tau and compared the results with those obtained after shuffling the data to reduce the memory. Specifically, destroying all correlations by shuffling the order of the returns, but without changing the tau = 1 d distribution, significantly reduces the probability of very large events. The distribution of returns for tau > 1 d loses the fat tails and acquires a more Gaussian shape. However, shuffling only the signs-but not the modulus-of the returns allows the fat tails and large events to persist for tau > 1 d. From these results, one can conclude that the very large events are caused by known multifractal long-range correlations in the modulus of the financial time series.
econophysics; long-rang correlations; fat-tailed distributions
