Question

Consider the following time series data.

Week	1	2	3	4	5	6
Value	18	14	15	11	19	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

Here naive forecast means forecast for a given weekis the most recent value.

Week	Value	Forecast	Abs. Error
1	18
2	14	18	4
3	15	14	1
4	11	15	4
5	19	11	8
6	14	19	5

(a) Mean absolute error = (4 + 1 + 4 +8+5)/5 = 4.4

Week	Value	Forecast	Abs. Error	Squared error
1	18
2	14	18	4	16
3	15	14	1	1
4	11	15	4	16
5	19	11	8	64
6	14	19	5	25

(b) Mean squared error = (16 +1 + 16 + 64 + 25)/5 = 24.4

Week	Value	Forecast	Abs. Error	APError
1	18
2	14	18	4	28.57%
3	15	14	1	6.67%
4	11	15	4	36.36%
5	19	11	8	42.11%
6	14	19	5	35.71%

(c) Mean absolute percentage error = 1/n

= 29.88%

(d)  forecast for week 7 = 14 (value of week 6)