Question

In a time-series decompostion of sales (in millions of units), the following trend has been estimated:

CMAT=12.315+0.196(T)

The seasonal indices have been found to be:

Quarter	Seasonal Index
1	1.27
2	1.02
3	0.73
4	0.98

For the coming year, the time index and cycle factors are:

Quarter	T	CF
1	21	1.01
2	22	1.04
3	23	1.06
4	24	1.04

a. From this information, prepare a forecast for each quarter of the coming year.

b. Actual sales for the year you forecast in part (a) were 17.2, 13.2, 10.8, and 14.2 for quarters 1, 2, 3, and 4, respectively. Use these actual sales figures along with your forecasts to calculate the mean absolute percentage error for the forecast period.

Answer 1

Part (a)

Please see the table below. The last column highlighted in yellow is your answer.

Quarter	T	CMAT=12.315+0.196(T)	CF	Season Index	Forecast = CMAT x CF x Seasonal Index
1	21	16.431	1.01	1.27	21.1
2	22	16.627	1.04	1.02	17.6
3	23	16.823	1.06	0.73	13.0
4	24	17.019	1.04	0.98	17.3

Part (b)

Actual	Forecast	Absolute Error = |Actual - Forecast|	%age error = Absolute Error / Actual
17.2	21.1	3.9	22.54%
13.2	17.6	4.4	33.62%
10.8	13.0	2.2	20.53%
14.2	17.3	3.1	22.15%