Foreign exchange rates don℗t follow a random walk

"The paper documents a new empirical result that a high level of aggregate U.S. idiosyncratic stock return volatility is usually associated with a future appreciation in U.S. dollars. The relation is highly significant for most foreign currencies. For example, idiosyncratic volatility accounts for over 20 percent variations of the subsequent change in the Deutsche mark/U.S. dollar rate in the non-overlapping semi-annual data and its improvements over the random walk model in the out-of-sample forecast are statistically significant. We find the similar result--a positive and significant relation between a country's aggregate idiosyncratic volatility and the future U.S. dollar price of its currency--in France, Germany, and Japan. Moreover, the U.S. default premium provides additional information about future exchange rates. Given that idiosyncratic volatility and the default premium are strong predictors of fundamentals, our results are consistent with monetary models of foreign exchange rates"--Federal Reserve Bank of St. Louis web site.