Self-similarity of high-frequency USD-DEM exchange rates

Abstract

High frequency DEM-USD exchange rate data (resolution > 2 seconds) are analyzed for their scaling behavior as a function of the time lag. Motivated by the finding that the distribution of 1-quote returns is rather insensitive to the physical time duration between successive quotes, lags are measured in units of quotes. The mean absolute returns over lags of different sizes, shows three different regimes. The smallest time scales show no scaling, followed by two scaling regimes characterized by Hurst exponents H = 0.45 and H = 0.56, with a crossover occuring at lags of # 500 quotes. The up-down correlation coefficient, defined here, shows strong anticorrelations on scales smaller than 500. The lack of convergence to a large deviation rate function, convex tails in the logarithm of the probability distributions, strong up-down correlations and H < 0.5, show that the dynamics on small scales is more complicated than random walk models with i.i.d. increments. Nevertheless, for both scaling re..