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The main purpose of this study is to apply the Smooth Transition Autoregressive(STAR) Model in exploring the dynamic adjustment processes of the real effective foreign exchange rate(REER) indices for the G7 countries, including the U.S., the U.K., Germany, Japan, France, and Canada. The sample used in this study covers 541 monthly observations, collecting from January 1964 to January 2009. We define the first 491 observaions as in-sample data, and the remaining 50 observations are used as out-of-sample forecast.
To build the STAE model, we establish the linear autoregressive(AR) model and choose the appropriate transition function for the REER indices under study. Since the residuals of the AR models exhibit heteroskedasticity, fat-tail, and volatility-clustering, we use the GARCH-t framework in capturing the nonlinear dynamic processes of the REER indices. The empirical result shows that only Germany is suitable for adopting the STAR-EGARCH model among the G7 countries. To compare the predictive performance of the STAR model, we further undertake the in-sample and out-of-sample predictive performance comparison using German REER index. Our evidence suggests that the nonlinear STAR-GAECH model obviously dominates the AR-GARCH model.
Moreover, this study discussed how outliers affect the fitness of nonlinear STAR models. The result reveala that after controlling the outliers, none of the G7 REER indices exhibits nonlinear STAR patterns. It suggests that the nonlinear STAR process can be explained by the existence of the extreme values. This paper helps us better understand the nonlinear dynamic process of the REER indices and provides further insights into literature.
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