If, over several periods, a time series shows a change of the average value which corresponds to the trend model, the forecast values always lag behind the actual values by one or several periods in the first-order exponential smoothing procedure. You can achieve a more efficient adjustment of the forecast to the actual consumption values pattern by using the second-order exponential smoothing procedure.
The second-order exponential smoothing model is based on a linear trend and consists of two equations (see formulae (11) below). 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 in the second equation as initial values and are smoothed again.
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