Question: MOVING AVERAGES Consider first the case in which forecasts are generated by moving averages. Then the forecast error is
et = Ft - Dt, where Ft is given by
This is the standard deviation of the forecast error for simple moving averages in terms of the standard deviation of each observation. Having derived the mean and the variance of the forecast error, we still need to specify the form of the forecast error distribution. By assumption, the values of Dt form a sequence of independent, identically distributed, normal random variables. Since Ft is a linear combination of Dt-1, Dt-2, . . . . , Dt-N, it follows that Ft is normally distributed and independent of Dt. It now follows that et is normal as well. Hence, the distribution of et is completely specified by its mean and variance. As the expected value of the forecast error is zero, we say the method is unbiased. Notice that this is a result of the assumption that the demand process is stationary. Consider the variance of the forecast error. The value of N that minimizes e is.
This means that the variance is minimized if the forecast is the average of all the past data. However, our intuition tells us that we can do better if we use more recent data to make our forecast. The discrepancy arises because we really do not believe our assumption that the demand process is stationary for all time. A smaller value of N will allow the moving-average method to react more quickly to unforeseen changes in the demand process.