Question

Consider the following time series data.

Week	1	2	3	4	5	6
Value	19	13	16	12	18	14

a. Which of the following is a correct time series plot for this data?

	$appletImage?dbid=759704288$
	$appletImage?dbid=1558008531$
	$appletImage?dbid=1863918557$

- Select your answer -plot #1plot #2plot #3Item 1

What type of pattern exists in the data?

- Select your answer -VerticalHorizontalScatterItem 2

b. Develop the three-week moving average forecasts for this time series. Compute MSE and a forecast for week  (to 2 decimals if necessary).

MSE
The forecast for week

c. Use  to compute the exponential smoothing forecasts for the time series. Compute MSE and a forecast for week  (to 2 decimals).

MSE
The forecast for week

d. Compare the three-week moving average approach with the exponential smoothing approach using . Which appears to provide more accurate forecasts based on MSE?
- Select your answer -The three-week moving average provides a better forecast since it has a smaller MSEThe exponential smoothing approach provides a better forecast since it has a smaller MSEThe three-week moving average provides a better forecast since it has a larger MSEItem 7

e. Use a smoothing constant of  to compute the MSE (to 2 decimals).

Does a smoothing constant of  or  appear to provide more accurate forecasts based on MSE?

The exponential smoothing forecast using  provides a - Select your answer -worsebetterItem 9 forecast than the exponential smoothing forecast using  since it has a smaller MSE.

Answer 1

a)

plot #1

Horizontal

b)

Time period	Actual Value(A)	Moving avg. Forecast(F)	Forecast error E=|A-F|	Squared Forecast Error
1	19
2	13
3	16
4	12	16.00	4.00	16.00
5	18	13.67	4.33	18.78
6	14	15.33	1.33	1.78
		Total	9.67	36.56
		Average	3.22	12.19
			MAD	MSE

MSE=12.19

The forecast for week 7 =14.67

c)

Time period	Actual Value(A)	Forecast(F)	Forecast error E=A-F	Squared Forecast Error
1	19
2	13	19.00	6.00	36.00
3	16	17.80	1.80	3.24
4	12	17.44	5.44	29.59
5	18	16.35	1.65	2.72
6	14	16.68	2.68	7.19
		Total	17.57	78.74
		Average	3.51	15.75
			MAD	MSE

MSE=15.75

The forecast for week 7 =16.15

d)

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

e)

(here smoothing constant is not given ; please revert for that)