Problem 15-08 (Algorithmic) Refer again to the gasoline sales time series data i
ID: 3314002 • Letter: P
Question
Problem 15-08 (Algorithmic)
Refer again to the gasoline sales time series data in the following table.
a. Using a weight of 1/2 for the most recent observation, 1/3 for the second most recent, and 1/6 for third most recent, compute a three-week weighted moving average for the time series. Use rounded for two decimal places values for intermediate colculations.
b. Compute the MSE for the weighted moving average in part a. Do you prefer this weighted moving average to the unweighted moving average? Remember that the MSE for the unweighted moving average is 10.22. Round your answer to two decimal places.
MSE =
Prefer the weighted or unweighted moving average here?
c. Suppose you are allowed to choose any weights as long as they sum to 1. Could you always find a set of weights that would make the MSE smaller for a weighted moving average than for an unweighted moving average? Why or why not?
Week Sales (1000s of gallons) 1 16 2 21 3 20 4 25 5 19 6 17 7 20 8 17 9 23 10 23 11 14 12 21Explanation / Answer
a)
b) MSE = 206.4987/ 9 = 29.5
c) Moving average
MSE = 18.8333
Moving average MSE is smaller than weighted moving average, so moving average best method of this problem
Error Week Tickets Sold Weights y-Forecast Error Square 1 16 0.5 2 21 0.333333 3 20 0.333333 4 25 21.6667 3.3333 11.11089 5 19 25.5 -6.5 42.25 6 17 24.6667 -7.6667 7 20 24.5 -4.5 20.25 8 17 21.8333 -4.8333 23.36079 9 23 20.8333 2.1667 4.694589 10 23 23.3333 -0.3333 0.111089 11 14 23.8333 -9.8333 96.69379 12 21 23.8333 -2.8333 8.027589 Total: 206.4987