Question

Consider the following time series data.

Week	1	2	3	4	5	6
Value	19	12	16	11	18	13

(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	19
2	12
3	16
4	11
5	18
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	19
2	12
3	16
4	11
5	18
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 smaller MSE than the smoothing 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 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.

(e)

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

Week	Time Series Value	Forecast
1	19
2	12
3	16
4	11
5	18
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 = 0.4 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.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.

Answer 1

b)

		3 week
Time period	Actual Value(A)	Moving avg. Forecast(F)
1	19
2	12
3	16
4	11	15.67
5	18	13.00
6	13	15.00

MSE =16.93

forecast for week 7 =14

c)

Time period	Actual Value(A)	Forecast(F)
1	19
2	12	19.00
3	16	17.60
4	11	17.28
5	18	16.02
6	13	16.42

MSE =21.32

forecast for week 7 =15.74

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	19
2	12	19.00
3	16	16.20
4	11	16.12
5	18	14.07
6	13	15.64

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