Question

An analyst must decide between two different forecasting techniques for weekly sales of roller blades: a linear trend equation and the naive approach. The linear trend equation is Ft = 125 + 2.0t, and it was developed using data from periods 1 through 10. Based on data for periods 11 through 20 as shown in the table, which of these two methods has the greater accuracy if MAD and MSE are used? (Round your intermediate calculations and final answers to 2 decimal places.)

Answer 1

Linear trend forecasting:

Forecast for 11th period = 125+2.0*11 = 147. Sumilarly forecast for periods 12 to 20 has been obtained as shown below:

Period	Actual	Forecast
11	148.00	147.00
12	150.00	149.00
13	149.00	151.00
14	146.00	153.00
15	156.00	155.00
16	148.00	157.00
17	156.00	159.00
18	154.00	161.00
19	159.00	163.00
20	163.00	165.00

Next I will compute MAD and MSE. MAD = (sum of absolute value of errors)/n. MSE = Sum of (actual - forecast)^2/n

Error = actual - forecast

Period	Actual	Forecast	Error	error^2	absoulte value of error
11	148.00	147.00	1.00	1.00	1.00
12	150.00	149.00	1.00	1.00	1.00
13	149.00	151.00	-2.00	4.00	2.00
14	146.00	153.00	-7.00	49.00	7.00
15	156.00	155.00	1.00	1.00	1.00
16	148.00	157.00	-9.00	81.00	9.00
17	156.00	159.00	-3.00	9.00	3.00
18	154.00	161.00	-7.00	49.00	7.00
19	159.00	163.00	-4.00	16.00	4.00
20	163.00	165.00	-2.00	4.00	2.00
		Total		215.00	37.00

MAD = 37/10 = 3.7 and MSE = 215/10 = 21.5

NAIVE approach: In this approach last period's actual will be considered as this period's forecast. Thus forecast for period 12 = actual for period 11 = 148

Period	Actual	Forecast	Error	error^2	absoulte value of error
11	148.00
12	150.00	148.00	2.00	4.00	2.00
13	149.00	150.00	-1.00	1.00	1.00
14	146.00	149.00	-3.00	9.00	3.00
15	156.00	146.00	10.00	100.00	10.00
16	148.00	156.00	-8.00	64.00	8.00
17	156.00	148.00	8.00	64.00	8.00
18	154.00	156.00	-2.00	4.00	2.00
19	159.00	154.00	5.00	25.00	5.00
20	163.00	159.00	4.00	16.00	4.00
		Total		287.00	43.00

MAD = 43/9 = 4.78 and MSE = 287/9 = 31.89

Thus MAD and MSE in case of naive method is higher.

So we can conclude that the linear trend equation is better as it has a lower MAD as well as MSE.