| Forecasting is a key activity in most organizations. The Box-Jenkins autoregressive moving average (ARMA) approach to forecasting has been popular with statisticians for years. However, ARMA model specification requires considerable time, experience, and technical skill to be used successfully. Because of the complexity of model specification, nontechnical managers have avoided using ARMA models, especially where forecasts are needed for a large number of products or locations.; Automatic model specification procedures may help overcome managers' resistance to using the ARMA approach. Several researchers, in recent years, have attempted to partially automate model building with procedures for automatically identifying the correct order of an ARMA model. Their efforts have not been very successful, especially when the data sets are small.; It is known, however, that ARMA models of different orders can be exactly equivalent. Even approximately equivalent models may produce indistinguishable forecasts. This means that automatic model specification procedures may not have to identify the exact order of the model to be useful.; One objective of this dissertation is to develop mathematically the concept of approximate equivalence between ARMA models. The method used to characterize approximately equivalent models is to represent them in terms of their impulse response weights as elements of a normed linear space. Approximately equivalent ARMA models turn out to be those that are close to each other in this space. Models that are close are shown to produce forecasts that are close. The distance in model space, at which a change in forecast becomes important, represents the additional error one is willing to tolerate.; The other objective of this dissertation is to apply this concept to advance the art of model specification. First, a new approach to ARMA model portfolio selection, based on a distance constraint, increases the usefulness of the portfolio for forecasting and provides a framework for automatic identification. Next, a new procedure for deciding the feasibility of using a common ARMA model for several related time series eases the burden of multiple model specification. Finally, procedures for automatic identification are evaluated allowing for reclassification in the case of approximately equivalent models. |
