Smoothing linear, exponential, and damped trends (TRENDSMOOTH)

  Exponential smoothing with a trend works much like simple smoothing except that two components must be updated each period:  level and trend.  The level is a smoothed estimate of the value of the data at the end of each period.  The trend is a smoothed estimate of average growth at the end of each period.

To explain this type of forecasting, let's review an application at Alief Precision Arms, a company that manufactures high-quality replicas of the Colt Single-Action Army revolver and other revolvers from the nineteenth century.  Alief was founded in 1987 and experienced rapid growth through about 1994.  Since 1994, growth has slowed and Alief is uncertain about the growth that should be projected in the future.

The worksheet was developed to help Alief compare several different types of trend forecasts.  This worksheet can produce a linear or straight-line trend, a damped trend in which the amount of growth declines each period in the future, or an exponential trend in which the amount of growth increases each period in the future.

TRENDSMOOTH is a robust model, relatively insensitive to smoothing parameters provided that they are approximately correct.