Question

Weekly sales of the Weber Dicamatic food processor for the past ten weeks have been:

Week	Sales	Week	Sales
1	980	6	990
2	1040	7	1030
3	1120	8	1260
4	1050	9	1240
5	960	10	1100

Determine, on the basis of minimizing the mean square error, whether a three-period or four-period simple moving average model gives a better forecast for this problem.

Answer 1

Answer:

Given that,

Weekly sales of the Weber Dicamatic food processor for the past ten weeks have been:

Week	Sales	Week	Sales
1	980	6	990
2	1040	7	1030
3	1120	8	1260
4	1050	9	1240
5	960	10	1100

Determine, on the basis of minimizing the mean square error, whether a three-period or four-period simple moving average model gives a better forecast for this problem.

Mean Square Error (MSE)= $\sum$ (Actual-Forecast)2/(n-1)
			Error	Error2
Month	Demand	3 Month MA	Absolute error	Square error
	A	B	C=A-B	D=C2
1	980
2	1040
3	1120
4	1050	1046.6667	3.3333	11.1111
5	960	1070.0000	-110.0000	12100.0000
6	990	1043.33333	-53.3333	2844.4444
7	1030	1000.0000	30.0000	900.0000
8	1260	993.3333	266.6667	21511.1111
9	1240	1093.3333	146.6667	21511.1111
10	1100	1176.6667	-76.6667	5877.7778
			-160.0000	14955.5556

Eg Forecast Calculation
Month 4	=(month 1+month 2 +month 3)/3
	=(980+1040+1120)/3
	=3140/3=1046.6667
MSE=14955.5556/(7-1)
=2492.593
			Error	Error2
Month	Demand	4 Month MA	Absolute error	square error
	A	B	C=A-B	D=C2
1	980
2	1040
3	1120
4	1050
5	960	1047.5000	-87.5000	7656.2500
6	990	1042.5000	-52.5000	2756.2500
7	1030	1030.0000	0.0000	0.0000
8	1260	1007.5000	252.5000	63756.2500
9	1240	1060.0000	180.0000	32400.0000
10	1100	1130.0000	-30.0000	900.0000
			-140.0000	10412.5000
Eg Forecast Calculation
Month 5	=(month 1+month 2+month 3+ month 4)/4
	=(980=1040+1120+1050)/4
	=4190/4=1047.50
MSE=10412.50/(6-1)
=2082.50
Four month moving average gives better forecast,
Forecast for period 11
Using 3 month moving average
=(month 8+ month 9+ month 10)/3
=(1260+1240+1100)/3
=3600/3
=1200
Using 4 month moving average
=(month 7+month 8+month 9+month 10)/4
=(1030+1260+1240+1100)/4
=4630/4
=1157.50