Question

# Consider the following time series data. Week 1 2 3 4 5 6 Value 19 12...

Consider the following time series data.

 Week Value 1 2 3 4 5 6 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

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

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.

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

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