Simple moving average
MA = SUM(Di) / n
A stable series with no trend or seasonality. Larger n means more smoothing and less responsiveness.
- n
- Number of periods in the moving average
- Di
- Actual demand in period i, the n most recent periods
Weighted moving average
WMA = SUM(Wi x Di), with SUM(Wi) = 1.00
When recent periods deserve more weight than older ones. Check the weights sum to 1.00 and that the largest is on the most recent period.
- Wi
- Weight for period i, between 0 and 1
- Di
- Demand in period i
Exponential smoothing
F(t) = F(t-1) + alpha ( D(t-1) - F(t-1) )
= alpha x D(t-1) + (1 - alpha) x F(t-1)
When only the last forecast and last actual are available, and the level moves but does not trend. State the starting forecast you assume.
- alpha
- Smoothing constant between 0 and 1; the fraction of the last error fed back
- F(t-1)
- Previous period's forecast
- D(t-1)
- Previous period's actual demand
Alpha and moving-average length
alpha = 2 / (n + 1)
To justify a chosen alpha, or to convert a familiar moving-average length into a smoothing constant.
- n
- Equivalent number of periods in a moving average
- alpha
- Smoothing constant with roughly the same behaviour