This thesis builds upon recent developments in the areas of international economics, econometrics and computational statistics, to provide a robust framework for specifying, modelling and forecasting real exchange rates. The main research topics addressed are the following. First, the impact of conditional heteroskedas-ticity on linearity tests. Second, the parsimonious modelling and forecasting of the dollar-sterling real exchange rate using a long span of data. Third, the reexamination of the well-documented real exchange rate-consumption anomaly from the viewpoint of nonlinear dynamics. Finally, the relationship between real exchange rate persistence and time-varying trade costs.