Adjusted Exponential Smoothing:

We have seen that the simple exponential smoothing is fairly flexible, as the smoothing effect may be increased or decreased easily by lowering or raising the value of α. But, if a trend exists in the data, the series shall always lag behind the trend (for an enhancing trend the forecasts will be consistently low and for decreasing trend the forecasts shall be consistently high). Therefore, in that case, the forecast needs to be adjusted to take care of trend effects by adding a trend correction factor.

                F_{(t +1) adj} = F_{t +1} + (1 -β  /β)T_{t +1}

where  F(t + 1) adj = trend-adjusted forecast,

F_{t + 1} = simple exponential smoothing forecast,

β = smoothing constant for trend, and

T_{t + 1} = exponentially smoothed trend factor.

The value of the exponentially smoothed trend factor T_{t + 1} is computed in the same manner as the original forecast, and may be written as :

                                                    T_{t +1}  = β (F_{t +1}  - F_t ) + (1 - β) T_t        

where T_t is the trend factor for the current period.

Eq. (2) illustrates that the trend factor consists of a portion (β) of the trend evidenced from the difference among the unadjusted forecasts for the future period and the current period (F_{t + 1} - F_t) plus a portion (1 - β) of the current trend adjustment (T_t).