Scaling Exponents in Financial Markets

We study the dynamical behavior of four exchange rates in foreign exchange markets. A detrended fluctuation analysis (DFA) is applied to detect the long-range correlation embedded in the non-stationary time series. It is for our case found that there exists a persistent long-range correlation in volatilities, which implies the deviation from the efficient market hypothesis. Particularly, the crossover is shown to exist in the scaling behaviors of the volatilities.