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Appendix DForecasting process detailsin the SAS forecastingsystemSection 1: Extrapolative projection with SAS(Yaffee, 1996)Extrapolative methods consist of a variety of exponential smoothing techniques.First, there is simple exponential smoothing, with or without a constant (a baselinelevel for the series). Second, there is Holt exponential smoothing with a trend (adeterministic tendency over time) for long-term patterns. Third, there is Wintersexponential smoothing, which involves a linear or quadratic trend with a multiplicativeor additive seasonal (regular variation around the trend) component. There is alsostepwise autoregressive exponential smoothing for more short-run fluctuations.Exponential smoothing is based on the concept of moving averages. If a mean of thefirst twelve data points (of, say, fifty) is computed and recorded, and is moved onetime period ahead from the previous starting position to compute the average forpoints two through thirteen, and then this process is reiterated until the end of theseries is reached. The new data series recorded is called a moving average of ordertwelve. The moving average smooths out irregular fluctuation, and a double movingaverage—a moving average of a moving average—smooths it out even more.Exponential smoothing represents an improvement on moving average smoothing.Simple moving averages give more weights to mid-range data values, whereasexponential smoothing has the decided advantage of giving more weight to recentobservations and exponentially smaller weight to historically distant observations. Asimple exponential forecast for one time period in the future is the forecast of thecurrent value plus the average error. The average error of the series at the presenttime is the quantity of the value of the series at the present time, divided by the totalnumber of values, minus the quantity of the forecast of the current value, divided bythe total number of values.Coupled with this moving average concept, the Holt model accommodates a constant,linear trend for long-run forecasts, or a quadratic trend (for projections of a recentchange in the series). The Winters model accommodates seasonal fluctuations in theseries as well. SAS allows for a multiplicative as well as an additive Winters model andalso permits custom-designed smoothing and forecasting.The relative fit of these models is generally assessed by the sum of squared errors. SASproduces a wide variety of measures of fit (see section 3). The model with the best fitis the chosen model. It can handle additive as well as multiplicative seasonal models.It also has a quadratic trend option which provides for fixing selected parameters.It is possible to have a custom design models. Stepwise autoregression algorithmsmay be used in forecasting. With the stepwise autoregression, a time trend is foundand the differences between the actual data and the trend line are computed. Theseresiduals are then fit using autoregressive estimation.255