Nonseasonal, Damped Trend

In this Time Series model, the simple exponential smoothing forecasts are "enhanced" by a damped trend component (independently smoothed with parameters g for the trend, and f for the damping effect). For example, suppose we wanted to forecast from month to month the percentage of households that own a particular consumer electronics device (e.g., a VCR). Every year, the proportion of households owning 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.

To compute the smoothed value (forecast) for the first observation in the series, both estimates of S0 and T0 (initial trend) are necessary. By default, these values are computed as:

T0 = (1/f)*(Xn-X1)/(N-1)

where

N

is the number of cases in the series,

f

is the smoothing parameter for the damped trend,

and S0 = X1-T0/2

See also, Nonseasonal, Exponential Trend; Nonseasonal, Linear Trend (Holt's Two-Parameter Method); and Nonseasonal, No Trend.