Question

5. [20 pts.] Historical data is often used in marketing to drive estimates of future demand. A common estimate (or forecast) used to predict future demand is the moving average. This forecasting method considers a weighted average where the m most recent observations receive the same weight, while all the remaining observations receive a weight of zero. Of course, the value of m is a parameter of the method, and it is up to the user to fine tune it for the application of his(her) choice. To compute an ?-period moving average use the following equation:

                    ?? = 1m (??-1 + ??-2 + ⋯ + ??-m )

The mean absolute deviation is a criterion used to compare forecasting models. The absolute deviation for any given period is the absolute difference between the forecast and the observed demand for the period (i.e., ?(?) = |F(?) − D(?)|). Once an absolute deviation is calculated for every single forecasting period, they are averaged to produce the estimate of the mean absolute deviation (MAD) of the model.

Period (t)	Demand D(t)	Ft m=3	Error	Ft m=4	Error	Ft m=5	Error
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20

1. For this example, apply an exponential smoothing model with m = 3 to forecast the monthly sales for months 4 through 20.


2. Use m = 4. How do these results compare to the ones in (5a)?


3. Use m = 5. How do these results compare to the ones in (5a) and (5b)?

4. Calculate the mean absolute deviation (MAD) of each model. Which value of m would you prefer for this situation? Why?

Answer 1

Period	Demand D(t)	Ft	Error	Ft	Error	Ft	Error
(t)		m=3		m=4		m=5
1	58
2	62
3	57
4	56	59	3
5	40	58.33333	18.3333333	58.25	18.25
6	56	51	5	53.75	2.25	54.6	1.4
7	48	50.66667	2.66666667	52.25	4.25	54.2	6.2
8	29	48	19	50	21	51.4	22.4
9	82	44.33333	37.6666667	43.25	38.75	45.8	36.2
10	56	53	3	53.75	2.25	51	5
11	45	55.66667	10.6666667	53.75	8.75	54.2	9.2
12	55	61	6	53	2	52	3
13	61	52	9	59.5	1.5	53.4	7.6
14	52	53.66667	1.66666667	54.25	2.25	59.8	7.8
15	50	56	6	53.25	3.25	53.8	3.8
16	48	54.33333	6.33333333	54.5	6.5	52.6	4.6
17	52	50	2	52.75	0.75	53.2	1.2
18	48	50	2	50.5	2.5	52.6	4.6
19	46	49.33333	3.33333333	49.5	3.5	50	4
20	40	48.66667	8.66666667	48.5	8.5	48.8	8.8
		MAD	8.49019608	MAD	7.890625	MAD	8.386667

m = 4 would be preferred for this situation because it has the lowest MAD value.