Using various information criteria conducts non-linear model estimation and selection for monthly real effective exchange rate of HKD of large sample data(January 1964-February 2009) and small sample data(May 2004-February 2009). Performs the multi-step forward forecast of the models through Bootstrap methods, calculates the values of relative error(RE) and root-mean-square error(RMSE), and compares the predictive accuracy of each model through the Wilcoxon Signed-Rank test so as to evaluate the fitting effect of each model. At last obtains a conclusion about the applicability of various information criteria to large and small sample datas.