Forecasting the Real US/DEM Exchange Rate: TAR vs. AR

Abstract

The out-of-sample forecasting performances of two univariate time series presentations for the USD/DEM real exchange rate are compared using quarterly data for the period 1957Q1-1998Q4. The linear AR process is frequently fitted to real exchange rate series because it is sufficient for capturing the reported slow mean reversion in real exchange rates and it has some predictive ability for the long run. A simple nonlinear alternative, the threshold autoregressive (TAR) model, allows for the possibility that there is a band of slow or no convergence around the purchasing power parity level in the real exchange rate, due to transportation costs or other market frictions that create barriers to arbitrage. The TAR model is theoretically and empirically appealing, and it has been fitted to real exchange rates in many recent papers. However, the ultimate test of its usefulness is its out-of-sample forecasting accuracy. We compare the TAR model to its simple linear AR alternative in terms of out-of-sample forecast accuracy. Preliminary results using the RMSE criterion indicate that TAR forecasts are more sensitive to the estimation period and that they involve considerably more uncertainty at long horizons, as compared with the simple AR model.