FORECASTING WITH EXPONENTIAL TRENDS
Although, exponential smoothing of a linear, or straight-line, trend is a useful tool for business forecasting, it's not necessarily best for every forecasting problem. Sales growth is often exponential, especially early in the life cycle of a product. That is, the amount of growth increases continuously from period to period. In such a case, a linear trend is too conservative for exponential growth and lags behind.
In other situations, a linear trend is too enthusiatic about the future. When the amount of growth is slowing or when growth is erratic, a linear trend usually overshoots the data, giving forecasts that are too optimistic. A better forecasting strategy is to use a damped-exponential trend. As the name implies, a damped-exponential trend assumes a steadily diminishing amount of growth.
Figure 1 illustrates how the three types of forecasting trends behave. The solid Actual Data line represents quarterly circulation figures (in thousands) for a petroleum-industry trade magazine. There is no evidence of a seasonal pattern in circulation. The magazine enjoyed rapid growth from the fourth quarter of 1985 through the fourth quarter of 1986 (or 85-4 through 86-4). Circulation was flat during the first two quarters of 1987. Although it resumed during the third quarter, growth in the last two quarters of 1987 was much slower than in 1986. (Note that figure 1 is presented as an illustration of different types of trends. Instructions for creating this graph won't be given in this article.)
At the end of 1987, we develop forecasts based on three types of trends: damped-exponential, linear, and …