Question

Consider the following time series data.

Week	1	2	3	4	5	6
Value	18	13	16	11	17	14

Using the naïve method (most recent value) as the forecast for the next week, compute the following measures of forecast accuracy.

(a)	Mean absolute error
	If required, round your answer to one decimal place.
(b)	Mean squared error
	If required, round your answer to one decimal place.
(c)	Mean absolute percentage error
	If required, round your intermediate calculations and final answer to two decimal places.
(d)	What is the forecast for week 7?

Answer 1

most recent value is used as forecast in naive method

period	demand	forcast	forecast error=demand value-forecast value	absolute forecast error	squared forcast error	Abs %error
t	Dt	Ft	et=Dt-Ft	| et |	(et)²	| et/Dt |
1	18
2	13	18.000	-5.00	5.00	25.00	38.46%
3	16	13.000	3.00	3.00	9.00	18.75%
4	11	16.000	-5.00	5.00	25.00	45.45%
4	17	11.000	6.00	6.00	36.00	35.29%
6	14	17.000	-3.00	3.00	9.00	21.43%

	forecast error=demand value-forecast value	absolute forecast error	squared forcast error	Abs %error
	et=Dt-Ft	| et |	(et)²	| et/Dt |
total sum=	-4.00	22.00	104.00	159.39%
n=	5	5	5	5
average=	-0.80	4.40	20.80	31.88%

a)

(a)   Mean absolute error=Σ |et|/n =    4.4

(b)   Mean squared error=Σ(et)²/n =    20.8
(c)   Mean absolute percentage error = Σ | et/Dt |/n =    31.88%

(d)   forecast for week 7 = 14