Outperforming a random walk model when trying to forecast nominal exchange rate movements is notoriously difficult. Meese and Rogoff (1983) famously admitted that, while theories suggest the exchange rate is determined by key macroeconomic fundamentals, forecasting the exchange rate to remain unchanged was a better prediction than using various fundamentals-based models.
In recent years, however, studies have shown that global risk factors could help when forecasting the dollar. A new NBER explains why this may not be the case, and under which conditions using the level of the log of the nominal exchange rate is actually better. Specifically, they find the following:
Including the nominal exchange rate as a predictor in a forecasting model of future changes in the nominal exchange rate improves its performance relative to a random walk.
Over a one-month horizon, there is evidence that the detrended S&P 500 level, the Repo and the 10-year to two-year US term spread are helpful in forecasting the nominal exchange rate.
A bivariate model that includes the nominal and real exchange rates as predictors is perhaps the best model for predicting the nominal exchange rate over 36- and 60-month horizons.
The above results hold only when assuming the nominal exchange rate is stationary. Otherwise, the models are not generally better than a random walk, except for EUR/USD movements.
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