Question

Consider the following time series data:

Month	1	2	3	4	5	6	7
Value	24	15	21	12	19	21	16

(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 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.

α =  

Answer 1

a)

horizontal

b)

month	value	forecast	|error|	error^2
1	24
2	15
3	21
4	12	20.00	-8.00	64.00
5	19	16.00	3.00	9.00
6	21	17.33	3.67	13.44
7	16	17.33	-1.33	1.78
		18.67	total	88.22
			average	22.06
MSE=			22.06
Forecast=			18.67

c)

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	12	21.96	-9.96	99.20
5	19	19.97	-0.97	0.94
6	21	19.77	1.23	1.50
7	16	20.02	-4.02	16.16
			total	200.24
			average	33.37
MSE=			33.37
Forecast=			19.22

d)

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

e)

alpha =0.40