Question

Consider the following time series data:

Month 1 2 3 4 5 6 7

Value 23 13 21 13 19 21 17

b)	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:
(c)	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: Forecast for month 8:

e)	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

b)

month	value	forecast	|error|	error^2
1	23
2	13
3	21
4	13	19.00	-6.00	36.00
5	19	15.67	3.33	11.11
6	21	17.67	3.33	11.11
7	17	17.67	-0.67	0.44
		19.00	total	58.66
			average	14.67
MSE=			14.67
Forecast=			19.00

c)

for exponential smoothing: next period forecast =α*last period actual+(1-α)*last period forecast

month	value	forecast	error	error^2
1	23
2	13	23.00	-10.00	100.00
3	21	21.00	0.00	0.00
4	13	21.00	-8.00	64.00
5	19	19.40	-0.40	0.16
6	21	19.32	1.68	2.82
7	17	19.66	-2.66	7.05
			total	174.04
			average	29.01
MSE=			29.01
Forecast=			19.13

e)

alpha= 0.32