Why is it so difficult to beat the random walk forecast of exchange rates?

Recent empirical evidence suggests that the time series behavior of the real exchange rate is well approximated by a nonlinear, exponential smooth transition autoregressive (ESTAR) model. This nonlinearity helps resolve a number of puzzles concerning the persistence and volatility of real exchange rates. In this paper, we explore whether it may also help resolve the well-known difficulties of exchange rate forecasting. We develop a bootstrap test of the random walk hypothesis of the nominal exchange rate, given ESTAR real exchange rate dynamics. We find strong evidence of predictability at horizons of 2 to 3 years, but not at shorter horizons.