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.
Week Sales (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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Week	Sales (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

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












				Total