Forecasting with ARMA models:A case study of the exchange rate between the US Dollar and a unit of the British Pound

This paper employs the R software in identifying the most suitable ARMA model for forecasting the growth rate of the exchange rate between the US dollar and a unit of the British pound. The data is systematically split into two distinct periods identified as the in-sample period and the out of sample period. The best model selected for the in-sample period is used to make forecasts for the out of sample period. Both traditional and rolling window forecasting methods are employed. This research uses the MSE, MAE, MAPE and correct sign prediction criterion to compare the forecasting performance of the rolling window forecasting method and the traditional forecasting method. The results obtained suggest that the traditional forecasting method performs better judging by MSE, MAE and MAPE. In other words, the traditional forecasting method is more suitable for predicting the magnitude (i.e., size) by which the US /UK exchange rate changes over time. However, the results also suggest that the rolling window forecasting method performs better based on the correct sign prediction criterion. In other words, the rolling window forecasting method is more appropriate for predicting the changes in the sign of the US /UK exchange rate. Key Words: Rolling Window Forecast, ARMA, MSE, MAE, MAPE