Part 2. MM4XL Tools > 1. Strategic Tools > Forecast Manager > 3. Technicalities > Opening the black box of Forecast Manager > How to find optimized unknowns

Forecast Manager

How to find optimized unknowns

Forecast Manager assigns to each forecasting method a portion of the hidden sheet, and it handles each as a separate model in order to use Solver for finding optimized unknown values, when required. Read also the notes in the example file Forecast.xls for an explanation of how setting up optimization models using Solver.

An optimized unknown is one that best satisfies the constraints of the chosen measure of fit accuracy. Imagine you were to select the best fitted model using MSE, the optimum unknown is the one that produces the lowest MSE value. When the unknown value lays between 0 and 1 and we test values at intervals of 0.001 it may take 1000 trials for finding the optimal value. Two unknowns may require exploring 1000000 values. We stress the may because often finding the first minimum value is not enough in order to reach the optimal solution. Indeed, in real life it is only seldom the case when working with uni-modal equations, and multi-modal functions require repeating the optimization process in order to make sure reaching the really lowest value. The picture below shows this concept graphically.

Sales Forecast Software with Sales History Data

Forecast Managers runs automatically the optimization algorithm until the measure of accuracy satisfies its constraints, e.g. minimum value for MSE or maximum value for R squared.

It must be noted that in the literature there are references to autoadaptive optimization. This is a special case of optimization where the unknown variables are allowed changing between time periods. We found this methodology viable for fitting the series but not for forecasting. In fact, the estimation process for forecasts did not produce robust enough outcome results due to the approximation of unknown values.

Lewandowski (1974) offers a detailed explanation of the concept of optimized unknown parameters. Beside the method we apply, called linear optimization, he also describes Friedmans and Gradient methods.

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