  Arguably the most important problem in quantitative finance is to understand
the nature of stochastic processes that underlie market dynamics. One aspect of
the solution to this problem involves determining characteristics of the
distribution of fluctuations in returns. Empirical studies conducted over the
last decade have reported that they arenon-Gaussian, scale in time, and have
power-law(or fat) tails. However, because they use sliding interval methods of
analysis, these studies implicitly assume that the underlying process has
stationary increments. We explicitly show that this assumption is not valid for
the Euro-Dollar exchange rate between 1999-2004. In addition, we find that
fluctuations in returns of the exchange rate are uncorrelated and scale as
power-laws for certain time intervals during each day. This behavior is
consistent with a diffusive process with a diffusion coefficient that depends
both on the time and the price change. Within scaling regions, we find that
sliding interval methods can generate fat-tailed distributions as an artifact,
and that the type of scaling reported in many previous studies does not exist.
