Question

Consider the following time series data.

Week	1	2	3	4	5	6
Value	17	11	14	10	16	13

(a)

(b)

Develop the three-week moving average forecasts for this time series. (Round your answers to two decimal places.)

Week	Time Series Value	Forecast
1	17
2	11
3	14
4	10
5	16
6	13

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

MSE =

What is the forecast for week 7?

(c)

Use α = 0.2 to compute the exponential smoothing forecasts for the time series.

Week	Time Series Value	Forecast
1	17
2	11
3	14
4	10
5	16
6	13

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

MSE =

What is the forecast for week 7? (Round your answer to two decimal places.)

(d)

Compare the three-week moving average approach with the exponential smoothing approach using

α = 0.2.

Which appears to provide more accurate forecasts based on MSE? Explain.

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

(e)

Use a smoothing constant of α = 0.4 to compute the exponential smoothing forecasts.

Week	Time Series Value	Forecast
1	17
2	11
3	14
4	10
5	16
6	13

Does a smoothing constant of 0.2 or 0.4 appear to provide more accurate forecasts based on MSE? Explain.

The exponential smoothing using α = 0.4 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 exponential smoothing using α = 0.4.     The exponential smoothing using α = 0.4 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 exponential smoothing using α = 0.4.

Answer 1

b)

Time period	Actual Value(A)	Moving avg. Forecast(F)	Forecast error E=|A-F|	Squared Forecast Error
1	17
2	11
3	14
4	10	14.00	4.00	16.00
5	16	11.67	4.33	18.78
6	13	13.33	0.33	0.11
		Total	8.67	34.89
		Average	2.89	11.63
			MAD	MSE
MSE =			11.63
forecast for week 7 =			13.00

c)

Time period	Actual Value(A)	Forecast(F)	Forecast error E=A-F	Squared Forecast Error
1	17
2	11	17.00	6.00	36.00
3	14	15.80	1.80	3.24
4	10	15.44	5.44	29.59
5	16	14.35	1.65	2.72
6	13	14.68	1.68	2.83
		Total	16.57	74.38
		Average	3.31	14.88
			MAD	MSE
MSE =			14.88
forecast for week 7 =			14.34

d)

.The three-week moving average provides a better forecast since it has a smaller MSE than the smoothing approach.

e)

Time period	Actual Value(A)	Forecast(F)
1	17
2	11	17.00
3	14	14.60
4	10	14.36
5	16	12.62
6	13	13.97

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