Question

Problem 15-03 (Algorithmic) Consider the following time series data.

Week 1 2 3 4 5 6

Value 20 13 15 11 18 13

Using the naïve method (most recent value) as the forecast for the next week, compute the following measures of forecast accuracy: Mean absolute error (MAE) Mean squared error (MSE) Mean absolute percentage error (MAPE) Round your answers to two decimal places.

MAE =

MSE =

MAPE =

Using the average of all the historical data as a forecast for the next period, compute the same three values. Round your answers to two decimal places.

MAE =

MSE =

MAPE =

Which method appears to provide the more accurate forecasts for the historical data? Explain.

Answer 1

a)

Naïve method:

Time period	Actual Value(A)	Moving avg. Forecast(F)	Forecast error E=|A-F|	Squared Forecast Error	|A-F|A
1	20
2	13	20	7	49	0.5385
3	15	13	2	4	0.1333
4	11	15	4	16	0.3636
5	18	11	7	49	0.3889
6	13	18	5	25	0.3846
7		13
		Total	25	143	1.81
		Average	5.00	28.60	36.18%
			MAD	MSE	MAPE
a) mean absolute error=			5.00
b) mean squared error =			28.60
c) mean absolute % error=			36.18%
d) forecast for week 7 =			13

2)

Historical data method:

Time period	Actual Value(A)	historical Data Forecast(F)	Forecast error E=|A-F|	Squared Forecast Error	|A-F|A
1	20
2	13	20.00	7.00	49.00	0.54
3	15	16.50	1.50	2.25	0.10
4	11	16.00	5.00	25.00	0.45
5	18	14.75	3.25	10.56	0.18
6	13	15.40	2.40	5.76	0.18
7		15.00
		Total	19.15	92.5725	1.46
		Average	3.83	18.51	29.16%
			MAD	MSE	MAPE

a) mean absolute error=		3.83
b) mean squared error =		18.51
c) mean absolute % error=		29.16%
d) forecast for week 7 =		15.00

3)

average of all data method provide better forecast because of lower value of MAE, MSE and MAPE