Question

Consider the following time series data.

Month	1	2	3	4	5	6	7
Value	22	11	18	10	17	21	13

A) What type of pattern exists in the data?

The data appear to follow a seasonal pattern.

The data appear to follow a trend pattern.    

The data appear to follow a horizontal pattern.

The data appear to follow a cyclical pattern.

B) Develop the three-month moving average forecasts for this time series.

Month	Time Series Value	Forecast
1	22
2	11
3	18
4	10	____
5	17	____
6	21	____
7	13	____

Compute MSE. (Round your answer to two decimal places.)

MSE = ____

What is the forecast for month 8? ____

C) Use α = 0.2 to compute the exponential smoothing forecasts for the time series. (Round your answers to two decimal places.)

Month	Time Series Value	Forecast
1	22
2	11	____
3	18	____
4	10	____
5	17	____
6	21	____
7	13	____

Compute MSE. (Round your answer to two decimal places.)

MSE = ____

What is the forecast for month 8? (Round your answer to two decimal places.) ____

D) Compare the three-month moving average approach with the exponential smoothing approach using α = 0.2. Which appears to provide more accurate forecasts based on MSE?

The three-month moving average provides a better forecast since it has a larger MSE than the exponential smoothing using α = 0.2.

The exponential smoothing using α = 0.2 provides a better forecast since it has a smaller MSE than the three-month moving average.     

The exponential smoothing using α = 0.2 provides a better forecast since it has a larger MSE than the three-month moving average.

The three-month moving average provides a better forecast since it has a smaller MSE than the exponential smoothing using α = 0.2.

Answer 1

The data appear to follow a horizontal pattern.

b)

month	value	forecast	|error|	error^2
1	22
2	11
3	18
4	10	17.00	-7.00	49.00
5	17	13.00	4.00	16.00
6	21	15.00	6.00	36.00
7	13	16.00	-3.00	9.00
			total	110.00
			average	27.50
MSE=			27.50
Forecast=			17.00

c)

month	value	forecast	error	error^2
1	22
2	11	22.00	-11.00	121.00
3	18	19.80	-1.80	3.24
4	10	19.44	-9.44	89.11
5	17	17.55	-0.55	0.30
6	21	17.44	3.56	12.66
7	13	18.15	-5.15	26.56
			total	252.88
			average	42.15
MSE=			42.15
Forecast=			17.12

d)

The three-month moving average provides a better forecast since it has a smaller MSE than the exponential smoothing using α = 0.2.