Question

Period	1	2	3	4	5
Sales	60	27	75	105	96

Complete the exponential for $6^{th}$ period using $\alpha =0.5$ and $\alpha =0.7$. What is the best choice for ${}^{\prime }{\alpha }^{\prime }$ ? Take the initial forecast as 60 units.

Answer 1

Period	Sales	$\alpha =0.5$	$\alpha =0.7$
1	60	-	-
2	27	60	60
3	75	43.5	36.9
4	105	59.25	63.57
5	96	82.13	92.57

$\text{Sample calculation:}$

$F_n=F_{n-1}+\alpha (D_{n-1}-F_{n-1})$

$F_3=60+0.5\times (27-60)=43.5$

To secide the best choice, we need to calculate 'MAD', $\alpha =0.5$

Period	Sales	Forecast	Absolute Error
1	60	60	0
2	27	60	33
3	75	43.5	31.50
4	105	59.25	45.75
5	96	82.13	13.89

$\sum |D_t-F_t|=124.12$

$MAD=31.03$

$\alpha =0.7$

Period	Sales	Forecast	Absolute Error
1	60	60	0
2	27	60	33
3	75	36.9	38.10
4	105	63.57	41.43
5	96	92.57	3.43

$\sum |D_t-F_t|=115.96$

$MAD=\frac{\Sigma |D_t-F_t|}{n}$

$MAD=28.99$

The $\alpha$ value of 0.7 has the lowest mean absolute deviation. Hence the best choice is $\alpha =0.7$