本研究主要目的在應用平滑轉換自我迴歸模型(Smooth Transition Autoregressive Model:STAR)探討世界七大工業國-美國、英國、德國、日本、義大利、法國、加拿大的實質有效匯率指數的非線性型態。研究期間自1964年1月至2009年1月，共541筆月觀察值，其中，前491筆資料作為樣本內資料，後50筆作為樣本外預測資料。
本研究首先進行自我迴歸模型的配適，再依照其資料特性，選取適合的轉換函數。由於自我迴歸模型的殘差經診斷檢定，發現存在異質性、厚尾及波動叢聚現象，因此，本研究應用GARCH-t捕捉殘差的異質變異及胖尾特性。本實證研究結果發現，七大工業國中，只有德國適合使用ESTAR(1)-GARCH(1,1)模型進行配適，其餘國家均拒絕線性的虛無假設。本研究進一步對德國實質有效率指數的樣本內及樣本外預測，結果發現對於德國實質有效匯率指數的預數，非線型STAR-GARCH模型明顯優於AR-GARCH模型。
除此，本研究探討離群值對於非線性模型配適度的影響，結果發現在考量極端值後，所有變數均不適用非線性STAR-GARCH模型，顯示STAR非線性型態大部分來自於極端值的影響。在實務上，有效匯率指數除了能夠明確的表達一國貨幣在匯率上相對於其他主要貿易往來國家的變動程度，有效匯率指數更是該國於在國際中是否具有競爭力的經濟指標。本研究結果有助了解實質有效匯率的動態調整過程。

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.