Question

Month	1 2 3 4 5 6 7
Value	24 15 21 13 19 21 16

a) Develop a three-month moving average for this time series. Compute MSE and a forecast for month 8. If required, round your answers to two decimal places. Do not round intermediate calculation. MSE:_______ The forecast for month 8________

b) Use α = 0.2 to compute the exponential smoothing values for the time series. Compute MSE and a forecast for month 8. If required, round your answers to two decimal places. Do not round intermediate calculation. MSE_____ The forecast for month 8 _____

c) Use trial and error to find a value of the exponential smoothing coefficient α that results in the smallest MSE. If required, round your answer to two decimal places. α =______  

Answer 1

a)

month	value	forecast	|error|	error^2
1	24
2	15
3	21
4	13	20.00	-7.00	49.00
5	19	16.33	2.67	7.11
6	21	17.67	3.33	11.11
7	16	17.67	-1.67	2.78
			total	70.00
			average	17.50
MSE=			17.50
Forecast=			18.67

b)

month	value	forecast	error	error^2
1	24
2	15	24.00	-9.00	81.00
3	21	22.20	-1.20	1.44
4	13	21.96	-8.96	80.28
5	19	20.17	-1.17	1.36
6	21	19.93	1.07	1.14
7	16	20.15	-4.15	17.20
			total	182.42
			average	30.40
MSE=			30.40
Forecast=			19.32

c()

from   trial and error : α =0.41