Exchange Rate Analysis Between the U.S. Dollar and the Japanese Yen

Abstract: The exchange data between the U.S. Dollar and Japanese Yen are analyzed with three models called the Auto-Regressive Integrated Moving- Average (ARIMA) model, the Generalized Auto-Regressive Conditional Heteroscedastic (GARCH) model, and the Fractional Differencing model. We mainly use log-transformed data with one difference taken because the residuals of the ARIMA model with log-transformed data is closer to normal distribution than other residuals of ARIMA models with squareroot- transformation or without transformation. Furthermore, the Akaike Information Criteria (AIC), the Mean Absolute Error (MAE) and the Root Mean Square Error (RMSE) are used to evaluate performances of each models. The Bayesian Information Criterion (BIC) is also used for GARCH models and we do the Ljung-Box tests for ARIMA models. In conclusion, the fractional differencing model is the best one in the three types of models because its MAE and its RMSE are the smallest values in those of all models we make in this analysis.