most prevalent means of describing long-term trends (Makridakis, 1990, pp. 70-71). The arithmetic trend is a linear equation with a constant absolute change in level per time period. The arithmetic linear trend for a data series is obtained most frequently by finding the linear regression between a dependent and independent variable, using all prior values of the variables.
Both simple regression analysis and multiple regression analysis may be applied in the curve fitting process for moving average trend projections. As the number of past time periods included in a moving average trend projection are increased, the forecast produced becomes closer to the forecast produced through the use of arithmetic trend projection; thus, most trend projections relying on the moving average use only a fraction of the total available data.
Exponential smoothing is an exponentially weighted moving average (Tersine, 1993, p. 432). The exponential smoothing approach assumes that a model which makes use of all data, with appropriate weighting, is superior to a model which discards data. In the exponential smoothing approach, the "weight given to past data decreases geometrically with increasing age of the data" (Tersine, 1993, p. 432). Thus, while all data are represented, as is true in the arithmetic mean approach, greater weight is given to the most recent data. The exponential smoothing approach, thus, attempts to incorporate the best of each of these approaches to trend analysis in a single superior model. Exponential trend projection discards the assumption of some absolute change in the value of the variable being projected through the use of trend analysis, and holds, instead, that proportional changes in the value of the projected variable will occur (Summers, Peters, & Armstrong, 1993, p. 550). Thus, the trend equation for the exponential trend approach "describes percentage rates of change in the exponential expression" (p. 550...