If, over several periods, a time series shows a change in the average value such that a trend pattern is revealed, first-order exponential smoothing produces forecast values that lag behind the actual values by one or several periods. You can achieve a more efficient adjustment of the forecast to the actual values pattern by using second-order exponential smoothing.

The second-order exponential smoothing model is based on a linear trend and consists of two equations (see formula (11)). The first equation corresponds to that of first-order exponential smoothing except for the indices in brackets. In the second equation, the values calculated in the first equation are used as initial values and are smoothed again.