Question

Consider the following time series data. Week 1 2 3 4 5 6 Value 18 13 17 12 17 15 a. Which of the following is a correct time series plot for this data? What type of pattern exists in the data? 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? 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 forecast than the exponential smoothing forecast using since it has a smaller MSE.

Answer 1

a)

type of pattern: Horizontal

b)

		3 week
Time period	Actual Value(A)	Moving avg. Forecast(F)	Forecast error E=|A-F|	Squared Forecast Error
1	18
2	13
3	17
4	12	16.00	4.00	16.00
5	17	14.00	3.00	9.00
6	15	15.33	0.33	0.11
		Total	7.33	25.11
		Average	2.44	8.37
			MAD	MSE

  MSE =8.37

forecast =14.67

c)

Time period	Actual Value(A)	Forecast(F)	Forecast error E=A-F	Squared Forecast Error
1	18
2	13	18.00	5.00	25.00
3	17	17.00	0.00	0.00
4	12	17.00	5.00	25.00
5	17	16.00	1.00	1.00
6	15	16.20	1.20	1.44
		Total	12.20	52.44
		Average	2.44	10.49
			MAD	MSE

  MSE =10.49

forecast =15.96

d)

three-week moving average  appears to provide more accurate forecasts because of smaller MSE

e)

MSE =10.25
The exponential smoothing forecast using 0.4 provides a better forecast than the exponential smoothing forecast using 0.2 since it has a smaller MSE.