Scaling, Self-Similarity and Multifractality in FX Markets

This paper presents an empirical investigation of scaling and multifractal properties of U.S. Dollar-Deutschemark (USD-DEM) returns. The data set is ten years of 5-minute returns. The cumulative return distributions of positive and negative tails at di.erent time intervals are linear in the double logarithmic space. This presents strong evidence that the USD-DEM returns exhibit power-law scaling in the tails. To test the multifractal properties of USD-DEM returns, the mean moment of the absolute returns as a function of time intervals is plotted for di.erent powers of absolute returns. These moments show di.erent slopes for these powers of absolute returns. The nonlinearity of the scaling exponent indicates that the returns are multifractal.