Question

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Tutorial Exercise

Consider the following time series data.

Month	1	2	3	4	5	6	7
Value	16	24	20	25	21	20	25

(a)

Compute MSE using the most recent value as the forecast for the next period. What is the forecast for month 8?

(b)

Compute MSE using the average of all the data available as the forecast for the next period. What is the forecast for month 8?

(c)

Which method appears to provide the better forecast?

Answer 1

a)

naïve
month	value	Forecast	|error|	|error|^2
1	16
2	24	16	8	64
3	20	24	4	16
4	25	20	5	25
5	21	25	4	16
6	20	21	1	1
7	25	20	5	25
		total	27	147
		average	4.50	24.50
MSE =				24.50
forecast =				25.00

b)

avereage of all data
month	value	Forecast	(error)^2
1	16
2	24	16.00	64.00
3	20	20.00	0.00
4	25	20.00	25.00
5	21	21.25	0.06
6	20	21.20	1.44
7	25	21.00	16.00
		total	106.50
		average	17.75
MSE =			17.75
forecast =			21.57

c)

average of all data method is better forecast because of smallest MSE