Example: Method 10: Linear Smoothing

This method is similar to Method 9, WMA. However, instead of arbitrarily assigning weights to the historical data, a formula is used to assign weights that decline linearly and sum to 1.00. The method then calculates a weighted average of recent sales history to arrive at a projection for the short term. Like all linear moving average forecasting techniques, forecast bias and systematic errors occur when the product sales history exhibits strong trend or seasonal patterns. This method works better for short range forecasts of mature products than for products in the growth or obsolescence stages of the life cycle.

Forecast specifications:

n equals the number of periods of sales history to use in the forecast calculation. For example, specify n equals 4 in the processing option to use the most recent four periods as the basis for the projection into the next time period. The system automatically assigns the weights to the historical data that decline linearly and sum to 1.00. For example, when n equals 4, the system assigns weights of 0.4, 0.3, 0.2, and 0.1, with the most recent data receiving the greatest weight.

Minimum required sales history: n plus the number of time periods that are required for evaluating the forecast performance (periods of best fit).

This table is history used in the forecast calculation:

Past Year	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
1	None	None	None	None	None	None	None	None	131	114	119	137

Here are the Calculation of Weights, given n = 4:

(n² + n) / 2 = (16 + 4) /2 = 10

Month	Weight
September	1 / 10
October	2 / 10
November	3 / 10
December	4 / 10
Total Weight	10 / 10

This is the calculation of Moving Average, given n = 4:

[(131 * 0.1) + (114 * 0.2) + (119 * 0.3) + (137 * 0.4)] / (0.1 + 0.0.2 + 0.3 + 0.4) = 126.4 rounded to 126.

This table is the Linear Smoothing forecast for next year, given n = 4:

Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
126	127	128	128	128	128	128	128	128	128	128	128