Question

Consider the following time series data: Month 1 2 3 4 5 6 7 Value 23 15 20 12 18 22 15 (a) Choose the correct time series plot. (i) (ii) (iii) (iv)
	- Select your answer -Graph (i)Graph (ii)Graph (iii)Graph (iv)Item 1
	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 average exponential 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.
	α =

Answer 1

a)

horizontal

b)

month	value	forecast	|error|	error^2
1	23
2	15
3	20
4	12	19.33	-7.33	53.78
5	18	15.67	2.33	5.44
6	22	16.67	5.33	28.44
7	15	17.33	-2.33	5.44
		18.33	total	93.10
			average	23.28
MSE=			23.28
Forecast=			18.33

c)

month	value	forecast	error	error^2
1	23
2	15	23.00	-8.00	64.00
3	20	21.40	-1.40	1.96
4	12	21.12	-9.12	83.17
5	18	19.30	-1.30	1.68
6	22	19.04	2.96	8.78
7	15	19.63	-4.63	21.43
			total	181.03
			average	30.17
MSE=			30.17
Forecast=			18.70

d)

The three-month moving average provides a better forecast since it has a smaller MSE=

e)

alpha =0.37