Problem 15-07 (Algorithmic) Refer to the gasoline sales time series data in the
ID: 419539 • Letter: P
Question
Problem 15-07 (Algorithmic)
Refer to the gasoline sales time series data in the given table.
Compute four-week and five-week moving averages for the time series. Round your answers to two decimal places.
Compute the MSE for the four-week and five-week moving average forecasts. Round your intermediate calculations and final answers to two decimal places.
MSE for four-week moving average =
MSE for five-week moving average =
What appears to be the best number of weeks of past data (three, four, or five) to use in the moving average computation? Recall that MSE for the three-week moving average is 12.67.
3? 4? 5?
Explanation / Answer
Formula to be used are as follows:
4-week forecast for week 5 = (sales of week 1 + sales of week 2 + sales of week 3 + sales of week 4)/4
5-week forecast for week 6 = (sales of week 1 + sales of week 2 + sales of week 3 + sales of week 4 + sales of week 5)/5
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MSE for 4 week MA forecast = (7.56 + 20.25 + 16+ 4+ 10.56 + 5.06 + 39.06 + 22.56)/8 = 15.63
MSE for 5 week MA forecast = (17.64 + 11.56 + 3.24 + 5.76 + 6.76+ 27.04 + 16)/7 = 12.57
Above calculation is based on the following data.
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5-week moving average data is best, because it has lowest MSE that is 12.57 among all the three forecasted data. The lowest MSE means highest accuracy of the forecasted data.
Week Sales 4-Week Moving Average 5-Week Moving Average 1 18 2 21 3 18 4 22 5 17 19.75 6 15 19.5 19.2 7 22 18 18.6 8 17 19 18.8 9 21 17.75 18.6 10 21 18.75 18.4 11 14 20.25 19.2 12 23 18.25 19