Additive Season, Damped Trend

In this Time Series model, the simple exponential smoothing forecasts are "enhanced" both by a damped trend component (independently smoothed with the single parameter , this model is an extension of Brown's one-parameter linear model, see Gardner, 1985, p. 12-13) and an additive seasonal component (smoothed with parameter ). For example, suppose we wanted to forecast from month to month the number of households that purchase a particular consumer electronics device (e.g., VCR). Every year, the number of households that purchase a VCR will increase, however, this trend will be damped (i.e., the upward trend will slowly disappear) over time as the market becomes saturated. In addition, there will be a seasonal component, reflecting the seasonal changes in consumer demand for VCR's from month to month (demand will likely be smaller in the summer and greater during the December holidays). This seasonal component may be additive, for example, a relatively stable number of additional households may purchase VCR's during the December holiday season.
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