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Forecasting, Problem2-4, pg 732

# Forecasting, Problem2-4, pg 732 - Problem 2 pg.732 Gasoline...

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Problem 2, pg.732: Gasoline sales data a) compute 3-, 4- and 5-week moving averages for the time series. Compute the MSE. Which is better? week Sales 3-monthMA Error Error^2 4-month MA Error Error^2 5-month MA Error Error^2 t Yt Ft Yt-Ft (Yt-Ft)^2 Ft Yt-Ft (Yt-Ft)^2 Ft Yt-Ft (Yt-Ft)^2 1 17 2 21 3 19 4 23 19.00 4.00 16.00 5 18 21.00 -3.00 9.00 20.00 -2.00 4.00 6 16 20.00 -4.00 16.00 20.25 -4.25 18.06 19.60 -3.60 12.96 7 20 19.00 1.00 1.00 19.00 1.00 1.00 19.40 0.60 0.36 8 18 18.00 0.00 0.00 19.25 -1.25 1.56 19.20 -1.20 1.44 9 22 18.00 4.00 16.00 18.00 4.00 16.00 19.00 3.00 9.00 10 20 20.00 0.00 0.00 19.00 1.00 1.00 18.80 1.20 1.44 11 15 20.00 -5.00 25.00 20.00 -5.00 25.00 19.20 -4.20 17.64 12 22 19.00 3.00 9.00 18.75 3.25 10.56 19.00 3.00 9.00 MSE= 10.22 MSE= 9.65 MSA= 7.41 Forecast for week 13: 19.00 19.75 19.40

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Problem 3, pg.732: Gasoline sales data a) compute 3--week weighted moving averages for the time series. Use 1/2 for the most recent, 1/3 for the next, and 1/3 for the third most recent observation. Caculate the MSA. Which is better: The 3-month MA, or the 3-month Weighter moving average? w1= 0.5 week Sales 3-monthMA Error Error^2 30month WMA w2= 0.3 t Yt Ft Yt-Ft (Yt-Ft)^2 w3= 0.2 1 17 2 21 3 19 4 23 19.00 4.00 16.00 19.33 3.67 13.44 5 18 21.00 -3.00 9.00 21.33 -3.33 11.11 6 16 20.00 -4.00 16.00 19.83 -3.83 14.69 7 20 19.00 1.00 1.00 17.83 2.17 4.69 8 18 18.00 0.00 0.00 18.33 -0.33 0.11 9 22 18.00 4.00 16.00 18.33 3.67 13.44 10 20 20.00 0.00 0.00 20.33 -0.33 0.11 11 15 20.00 -5.00 25.00 20.33 -5.33 28.44 12 22 19.00 3.00 9.00 17.83 4.17 17.36 MSE= 10.22 MSA= 11.49 forecast for week13: 19.33 Prefer the unweighted moving average here. However, one could always find a weighted moving average at least as good as the unweighted one
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Forecasting, Problem2-4, pg 732 - Problem 2 pg.732 Gasoline...

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