Question

Actual sales for January through April are shown below:

Observation	Month	Actual Sales (A)	Forecasted Sales (F)
1	January	18
2	February	23
3	March	20
4	April	16
5	May

a. Use exponential smoothing with α = 0.2 to calculate smoothed averages and forecast sales for May from the above data. Assume the forecast for the initial period (January) is 18.

b. Calculate MSE, and MAPE.

Answer 1

a)

b)

Observation	Month	Actual Sales (A)	Forcasted Sales (F)	|Error|	(Error)2	% error
1	January	18	18	0	0	0
2	February	23	18	5	25	100*5/23 = 21.7%
3	March	20	19	1	1	100*1/20 = 5%
4	April	16	19.2	3.2	10.24	3.2*100/16 = 20%
5	May		18.56		total = 36.24	total = 46.7%

MSE = 36.24 / 4 = 9.06 [divided by 4 as 4 observations]

MAPE =Sum of [ Error * 100 / actual sale ] / no.of observations = 46.7% /4 = 11.7%