Question

Consider the following time series data:

Month	1	2	3	4	5	6	7
Value	24	13	20	12	18	23	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.
(c)	Which method appears to provide the better forecast? (options are: naive, all data average)

Answer 1

a)

month	value	Forecast	|error|	|error|^2
1	24
2	13	24	11	121
3	20	13	7	49
4	12	20	8	64
5	18	12	6	36
6	23	18	5	25
7	16	23	7	49
		total	44	344
		average	7.33	57.33
MSE =				57.3
forecast =				16.0

b)

month	value	Forecast	(error)^2
1	24
2	13	24.00	121.00
3	20	18.50	2.25
4	12	19.00	49.00
5	18	17.25	0.56
6	23	17.40	31.36
7	16	18.33	5.44
		total	209.62
		average	34.94
MSE =			34.9
forecast =			18.0

c)

all data average is better due to smallest MSE