Question

Consider the following time series data:

Month 1 2 3 4 5 6 7

Value 25 14 19 11 18 22 16

(a) Compute MSE using the most recent value as the forecast for the next period. If required, round your answer to one decimal place. What is the forecast for month 8? If required, round your answer to one decimal place. Do not round intermediate calculation.

(b) Compute MSE using the average of all the data available as the forecast for the next period. If required, round your answer to one decimal place. Do not round intermediate calculation. What is the forecast for month 8? If required, round your answer to one decimal place.

Answer 1

a)

Using the most recent value as the forecast:

Month	Value	Forecast	Error	Absolute Error	Error 2
1	25
2	14	25	-11	11	121
3	19	14	5	5	25
4	11	19	-8	8	64
5	18	11	7	7	49
6	22	18	4	4	16
7	16	22	-6	6	36
				Total	311

Hence,

MSE = ∑Error² / (n-1) = 311/6 = 51.8

Forecast for month 8 = 16

b)

Using the average of all the data available as the forecast for the next period

Month	Value	Forecast	Error	Absolute Error	Error 2
1	25
2	14	25	-11.00	11.00	121.00
3	19	19.50	-0.50	0.50	0.25
4	11	19.33	-8.33	8.33	69.44
5	18	17.25	0.75	0.75	0.56
6	22	17.40	4.60	4.60	21.16
7	16	18.17	-2.17	2.17	4.69
				Total	217.11

Hence,

MSE = ∑Error² / (n-1) = 217.11/6 = 36.2

Forecast for month 8 = Average of all the previous months = 17.86