Pretesting for multi-step-ahead exchange rate forecasts with STAR models

It is well known that a linear model may forecast better than a nonlinear one, even when the nonlinear model is consistent with the actual data-generating process. Moreover, forecasting with nonlinear models can be quite programming-intensive, as multi-step-ahead forecasts need to be simulated. We propose a simple pretest to help determine whether it is worthwhile to forecast a series using a STAR model. In particular, we extend Teräsvirta's in-sample test for LSTAR and ESTAR behavior to multi-step-ahead out-of-sample forecasts. We apply our pretest to the real exchange rates of various OECD countries. When the test strongly rejects the null of linearity, a nonlinear model clearly outperforms a linear one in terms of multi-step-ahead forecasting accuracies (i.e., lower mean absolute percentage errors). However, when it fails to reject the null or does so only mildly, a direct approach based on an autoregressive model yields forecasts that are slightly superior to those generated from a logistic model. We also find that, when the proposed test strongly rejects the null of linearity, the “direct” method of forecasting and the bootstrap predictor yield similar performances, with the latter outperforming in terms of lower mean absolute percentage errors.