Choosing the best forecast based on MAD,MAPE,MSE

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Two independent methods of forecasting based on judgement and experience have been prepared each month for the past 10 months. The forecasts and actual sales are as follows…

Month Sales Forecast 1 Forecast 2
1 770 771 769
2 789 785 787
3 794 790 792
4 780 784 798
5 768 770 774
6 772 768 770
7 760 761 759
8 775 771 775
9 786 784 788
10 790 788 788

A) Compute the MSe and MAd for each forecast. Does either forecast seem superior? Explain.

B) Compute MAPE for each forecast.

C) Compute a tracking signal for the 10th month for each forecast using the cumulative error for months 1 to 10. Use action limits of +/- 4. Is there bias present? Explain.

D) Compute 2x control limits for each forecast.

E) Prepare a naive forecast for periods 2 through 11 using the given sales data. Compute each of the following; 1) MSE 2) MAD 3) tracking signal at month 10 4) 2x control limits. How do the naive results compare with the other two forecasts?

Plot 3 error control charts for parts c and d.

Discuss comparative conclusions for each technique based on the control charts.
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Solution Preview

Please see attached file.

Two independent methods of forecasting based on judgment and experience have been prepared each month for the past 10 months. The forecasts and actual sales are as follows…

Month Sales Forecast 1 Forecast 2
1 770 771 769
2 789 785 787
3 794 790 792
4 780 784 798
5 768 770 774
6 772 768 770
7 760 761 759
8 775 771 775
9 786 784 788
10 790 788 788

A) Compute the MSe and MAd for each forecast. Does either forecast seem superior? Explain.
MAD = where n= number of observations =10

Month sales (1) Forecast1(2) Error(3) =(1)-(2) Absolute error(4) =|(3)| Forecast2 (5) Error(6) =(1)-(5) Absolute error(4) =|(6)|
1 770 771 -1 1 769 1 1
2 789 785 4 4 787 2 2
3 794 790 4 4 792 2 2
4 780 784 -4 4 798 -18 18
5 768 770 -2 2 774 -6 6
6 772 768 4 4 770 2 2
7 760 761 -1 1 759 1 1
8 775 771 4 4 775 0 0
9 786 784 2 2 788 -2 2
10 790 788 2 2 788 2 2
Sum 28 36

MAD1 = 28/10 =2.8
MAD2 = 36/10 =3.6

MSE =

Month sales (1) Forecast1(2) Error(3) =(1)-(2) Error ^2 =(3)2 Forecast2 (5) Error(6) =(1)-(5) Error ^2 …