a. If Y(t) is the value for month t, the forecast for month t+1 using exponential smoothing model is
We will set the first month forecast as the the actual value, that is F(1) = 20. The forecast for month 2 is
We compute the 2 month moving average forecast using
For example the forecast for month 3 is
Since we want to compare a 2 month moving average with exponential forecast, we will calculate the MSE (Mean Square error) using the data from 3rd month to month 11
Prepare the following sheet
We have kept the value of alpha in a separate cell so that we can do the trial and error required in part c)
get this
a) MSE for exponential forecast with alpha=0.025 is 34.99, Forecast for the month of 12 is 19.09
b) The MSE for 2 month moving average forecast is 48.81 and it is larger than the MSE for exponential smoothing forecast. Hence we can say that exponential smoothing method provides a better forecast based on MSE
c. Now we can use trial and error by changing the value of alpha in cell C1. Try values between 0 and 1 starting from 0.01 to 1.
Or we can use the solver in excel to find the value of alpha which will give the lowest MSE.
Set up the solver using data---> solver
get this
We can see that for alpha=0.03, results in a smaller MSE than we calculated for alpha=0.25
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