Question

Consider the following time series data:

Month	1	2	3	4	5	6	7	8
Value	24	13	21	12	20	23	15	25

1. Compute MSE using the most recent value as the forecast for the next period. What is the forecast for month 9?
2. Compute MSE using the average of all the data available as the forecast for the next period. What is the forecast for month 9?
3. Which method appears to provide the better forecast?

Answer 1

a)

period	demand	forecast	forecast error=demand value-forecast value	absolute forecast error	squared forcast error
t	Dt	Ft	et=Dt-Ft	| et |	(et)²
1	24
2	13	24	-11.00	11.00	121.0
3	21	13	8.00	8.00	64.0
4	12	21	-9.00	9.00	81.0
5	20	12	8.00	8.00	64.0
6	23	20	3.00	3.00	9.0
7	15	23	-8.00	8.00	64.0
8	25	15	10.00	10.00	100.0

forecast for month 9 = 25

MSE=   Σ(et)²/n =    71.86

2)

period	demand	forecast	forecast error=demand value-forecast value	absolute forecast error	squared forcast error
t	Dt	Ft	et=Dt-Ft	| et |	(et)²
1	24
2	13	24	-11.00	11.00	121.0
3	21	18.5	2.50	2.50	6.3
4	12	19.33	-7.33	7.33	53.8
5	20	17.5	2.50	2.50	6.3
6	23	18	5.00	5.00	25.0
7	15	18.8333333	-3.83	3.83	14.7
8	25	18.2857143	6.71	6.71	45.1

forecast for month 9 = 18.43

MSE=   Σ(et)²/n =    38.86

c)

MSE in part b) is lower than that of part a)

so,  average of all the data available as the forecast is better forecast