Many forecasting models use parameters that are estimated using nonlinear optimization. This is true of many of the models developed in Chapter 6. Consider the exponential smoothing forecasting model from Section 6.2. For instance, the basic exponential smoothing model for forecasting sales is
Ft+1 = αYt + (1 - α) Ft
Where
Ft+1 = forecast of sales for period t + 1
Yt = actual value of sales for period t
Ft = forecast of sales for period t
α = smoothing constant 0 ‰¤ α ‰¤ 1

This model is used recursively; the forecast for time period t + 1 is based on the forecast for period t, Ft, the observed value of sales in period t, Yt, and the smoothing parameter α. The use of this model to forecast sales for 12 months is illustrated in Table with the smoothing constant α = 0.3. The forecast errors, Yt - Ft, are calculated in the fourth column. The value of α is often chosen by minimizing the sum of squared forecast errors, commonly referred to as the mean squared error (MSE). The last column of Table shows the square of the forecast error and the sum of squared forecast errors.
In using exponential smoothing models one tries to choose the value of α that provides the best forecasts. Build an Excel Solver or LINGO optimization model that will find the smoothing parameter, α that minimizes the sum of forecast errors squared. You may find it easiest to put Table into an Excel spreadsheet and then use Solver to find the optimal value of α.
TABLE
EXPONENTIAL SMOOTHING MODEL FOR α =0.3

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