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Exponential smoothing is a technique that is relatively easy to implement, yet has proven to be an effective tool at forecasting sales. In its simplest form, this technique assumes, on average, sales are constant, but include a random error term about the average. It is also assumed the underlying average can drift from period to period. These assumptions lead to the following smoothing equation:
St = a Xt + (1 - a) St-1where,
St = predicted sales, or signal, in period t,From this equation, we can see the closer a is to 1 the more the current observation affects our signal. Subsequently, the less "memory" our equation has. Frequently, a value for a is chosen in the range of .01 to .3. In this example, we will solve for an a that minimizes the sum of the squared prediction errors.
Xt = observed sales in period t, and
a = a constant term between 0 and 1.