The Development and Evaluation of a Forecasting System that Incorporates ARIMA Modeling with Autoregression and Exponential Smoothing

This research was designed to develop and evaluate an automated alternative to the Box-Jenkins method of forecasting. The study involved two major phases. The first phase was the formulation of an automated ARIMA method; the second was the combination of forecasts from the automated ARIMA with forecasts from two other automated methods, the Holt-Winters method and the Stepwise Autoregressive method. The development of the automated ARIMA, based on a decision criterion suggested by Akaike, borrows heavily from the work of Ang, Chuaa and Fatema. Seasonality and small data set handling were some of the modifications made to the original method to make it suitable for use with a broad range of time series. Forecasts were combined by means of both the simple average and a weighted averaging scheme. Empirical and generated data were employed to perform the forecasting evaluation. The 111 sets of empirical data came from the M-Competition. The twenty-one sets of generated data arose from ARIMA models that Box, Taio and Pack analyzed using the Box-Jenkins method. To compare the forecasting abilities of the Box-Jenkins and the automated ARIMA alone and in combination with the other two methods, two accuracy measures were used. These measures, which are free of magnitude bias, are the mean absolute percentage error (MAPE) and the median absolute percentage error (Md APE).