Question

Consider the following time series data.

Month	1	2	3	4	5	6	7
Value	25	14	21	13	20	24	16

(a)

Construct a time series plot.

What type of pattern exists in the data?

The data appear to follow a seasonal pattern.

The data appear to follow a cyclical pattern.    

The data appear to follow a trend pattern.

The data appear to follow a horizontal pattern.

(b)

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

Month	Time Series Value	Forecast
1	25
2	14
3	21
4	13	_____
5	20	______
6	24	______
7	16	_____

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	25
2	14	____
3	21	_____
4	13	_____
5	20	_____
6	24	______
7	16	_____

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 exponential smoothing using α = 0.2 provides a better forecast since it has a smaller 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.  

  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 larger MSE than the exponential smoothing using α = 0.2.

Answer 1

a)

The data appear to follow a horizontal pattern.

b_)

month	value	forecast	|error|	error^2
1	25
2	14
3	21
4	13	20.00	-7.00	49.00
5	20	16.00	4.00	16.00
6	24	18.00	6.00	36.00
7	16	19.00	-3.00	9.00
			total	110.00
			average	27.50
MSE=			27.50
Forecast=			20.00

c)

Period	value(A)	forecast(F)	error |A-F|	error^2
1	25
2	14	25.00	11.00	121.00
3	21	22.80	1.80	3.24
4	13	22.44	9.44	89.11
5	20	20.55	0.55	0.30
6	24	20.44	3.56	12.66
7	16	21.15	5.15	26.56
		total	31.50	252.88
		average	5.25	42.15
MSE=			42.15
Forecast=			20.12

d)

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