Question

Consider the following time series data:

Month	1	2	3	4	5	6	7
Value	23	13	21	13	19	21	17

(a)	Create a time series plot.

What type of pattern exists in the data?
	- Select your answer -Positive trend patternHorizontal patternVertical patternNegative trend patternItem 2
(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:
	The forecast for month 8:
(d)	Compare the three-month moving average forecast with the exponential smoothing forecast using α = 0.2. Which appears to provide the better forecast based on MSE?
	- Select your answer -3-month moving averageexponential smoothingItem 7
(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.

Answer 1

a)

Horizontal

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
			total	58.67

MSE=14.67

forecast =19

c)

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

MSE=29.01

forecast =19.13 (try 19.12 if this comes wrong)

d) three-month moving average forecast o provide the better forecast due to smaller MSE

e)

alpha =0.32