Question

Consider the following time series data:

Month	1	2	3	4	5	6	7
Value	25	12	20	11	20	23	15

(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? (Naiive or all data coverage)

Answer 1

Answer:

a)

Given,

let us consider,

F1 be no forecast

F2 = A1 = 25

F3 = A2 = 12

Month	Actual value (A)	Forecast(F)	Error E = A-F	Error^2 = E^2
1	25
2	12	25	13	169
3	20	12	-8	64
4	11	20	9	81
5	20	11	-9	81
6	23	20	-3	9
7	15	23	8	64
Total				E^2 = 468

Now mean square error = E^2 / n

= 468 / 6

MSE = 78

Now to give forecast for month 8

Here we take n = 6

Due to the addition of 6 values the forecast for the month 8 = F8 = A7 = 15

b)

Now to give the MSE

Average = (25+12+20+11+20+23+15)/7

= 126/7

Average = Forecast = 18 for all months

Month	A	F	E=A-F	E^2
1	25	18	-7	49
2	12	18	6	36
3	20	18	-2	4
4	11	18	-7	49
5	20	18	-2	4
6	23	18	-5	25
7	15	18	3	9
Total				E^2 = 176

Mean square error = E^2 / n

= 176 / 7

= 25.1429

MSE = 25

Now forecast for month 8 = Average of the previous seven month values = 18

c)

Here we can say that the second method is better for the forecast. It is due to the mean square error MSE which is lower in this second method.