Consider the following gasoline sales time series data. Click on the datafile logo to reference the data.
a. Using a weight of 1/2 for the most recent observation, 1/3 for the second most recent observation, and 1/6 the most recent observation, compute a three-week weighted moving average for the time series (to 2 decimals). Enter negative values as negative numbers.
b. Compute the MSE for the weighted moving average in part (a).MSE =
Do you prefer this weighted moving average to the unweighted moving average? Remember that the MSE for the unweighted moving average is 8.90.Prefer the unweighted moving average here; it has a (greater/smaller) MSE.
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 at least as small for a weighted moving average than for an unweighted moving average? (Yes/ No)
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