Question

Consider the following time series data:

Month	1	2	3	4	5	6	7
Value	23	14	20	12	19	23	14

(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.
(c)	Which method appears to provide the better forecast? Naive or All data average

Answer 1

a)

month	value	Forecast	|error|^2
1	23
2	14	23	81
3	20	14	36
4	12	20	64
5	19	12	49
6	23	19	16
7	14	23	81
		total	327
		average	54.50
MSE =			54.50
forecast =			14.00

b)

month	value	Forecast	(error)^2
1	23
2	14	23.00	81.00
3	20	18.50	2.25
4	12	19.00	49.00
5	19	17.25	3.06
6	23	17.60	29.16
7	14	18.50	20.25
		total	184.72
		average	30.79
MSE =			30.8
forecast =			14.00

c)

  average of all the data available as its MSE is smaller