Question

Consider the following time series data:

Month	1	2	3	4	5	6	7
Value	24	12	20	13	18	24	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?

Answer 1

A. The given time series data is as follows

Month	1	2	3	4	5	6	7
Value	24	12	20	13	18	24	14

The formula for MSE is as follows:

MSE= Average of the sum squared value of the forecast error= Total of the sum squared of the forecast errors divided by the number of months

Calculate the absolute value of the forecast error as follows

Month	Time series value	forecast	forecast error	squared forecast error
1	24
2	12	24	-12	144
3	20	12	8	64
4	13	20	-7	49
5	18	13	5	25
6	24	18	6	36
7	14	24	-10	100
Total				418

Here the forecast value is the previous month time series value

forecast error= time series value-forecast value

Value of MSE = 418/6=69.67

Forecast for month 8 is the time series value of month 7. Thus the forecast value for month 8 is 14.

B. Calculate the squared value of the forecast errors as follows

Month	Time series value	forecast	forecast error	squared forecast error
1	24
2	12	24	-12	144
3	20	18	2	4
4	13	18.67	-5.67	32.15
5	18	17.25	0.75	0.56
6	24	17.4	6.6	43.56
7	14	18.5	-4.5	20.25
Total				244.52

Forecast value= Average of previous time series data (ie month 2 its the previous month data i.e 24, for month 3 its the average of 24 & 12, month 4 its the average of 24,12 & 20 and so on)

Forecast error = Time series value - forecast value

Value of MSE = 244.52/ 6 = 40.75

The forecast value for the month 8 = Average of the previous time series data = (24+12+20+13+18+24+14)/7=17.86

C. From the answer to part A, value of MSE =69.7 (rounded to one decimal)

  From the answer to part B, Value of MSE =40.8 (rounded to one decimal)

From the results it can be observed that the forecast accuracy is better with the average of all the previous data as the MSE is less in this method.