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Consider the following gasoline sales time series data. Click on the datafile logo to reference the...

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Basic Math

Consider the following gasoline sales time series data. Click onthe datafile logo to reference the data.

WeekSales (1000s of gallons)
1    17   
2    21   
3    19   
4    24   
5    18   
6    15   
7    21   
8    19   
9    22   
10    19   
11    15   
12    23   

a. Using a weight of 1/2 for the most recentobservation,1/3 for the second most recent observation, and 1/6third the most recent observation, compute a three-week weightedmoving average for the time series (to 2 decimals). Enter negativevalues as negative numbers.


Week
Time-Series Value		Weighted Moving
Average Forecast		Forecast
Error
(Error)2
Total

b. Compute the MSE for the weighted movingaverage in part (a).
MSE =

Do you prefer this weighted moving average to the unweightedmoving average? Remember that the MSE for the unweighted movingaverage is 14.39 .
Prefer the unweighted moving average here; it has a - Select youranswer -greatersmallerItem 42 MSE.

c. Suppose you are allowed to choose anyweights as long as they sum to 1. Could you always find a set ofweights that would make the MSE at least as small for a weightedmoving average than for an unweighted moving average?
- Select your answer -YesNoItem 43

Answer & Explanation Solved by verified expert
4.5 Ratings (675 Votes)
Let Yt be the actual sales for period tthe forecast for period t using the weighted moving average Ftis calculated asWeighted moving average isWeekSales 1000s of gallonsWeighted MovingAverage Forecast1 172 213 194 241219132116171933335 181224131916212183336 151218132416192016677 211215131816241758 191221131516181859 221219132116151910 1912221319162120833311    See Answer
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