Study on Nonlinear Approximation of Exchange Rate with Regime Switching Models

We test the linearity of the returns on the nominal exchange rate against the alternative hypothesis of the regime switching models. We find that the switches between the regimes can be a gradual transition and the smooth transition autoregressive (STAR) model is appropriate to estimate and forecast nonlinear behavior of the process. We also evaluate the out-of-sample forecasting performance of the model in comparison to that of the linear AR model. Although the out-of-sample forecasting performance of the STAR model is not superior to that of the linear AR model, the qualitative difference among the forecast evaluation criteria is conspicuous in the median squared prediction error (MedSPE). Considering the fact that the MedSPE criterion takes the aberrant behavior of the forecast error into account in setting up the statistic, the MedSPE criterion is appropriate if we have quite a number of outliers in the process. The forecasting performance of the regime switching model is dependent upon which regime the process is going to be during the out-of-sample forecast period. Although the in-sample fit of the estimated regime switching model is better than the benchmark, this does not guarantee better out-of-sample predictability of the nonlinear models if the regime during the out-of-sample period is not correctly predicted. We find somewhat mixed evidence on the superiority of the out-of-sample forecasting performance of the self-exciting threshold autoregressive model and the Markov switching model to that of the linear AR model.