Question

Please answer every fill in the blank shown, I will make sure to up vote, thank you!

Consider the following gasoline sales time series data. Click on the datafile logo to reference the data Week Sales (1000s of gallons) 18 18 18 16 19 18 23 21 15 23 10 12 a. Using a weight of-for the most recent observation for the second most recent observation, and time series (to 2 decimals). Enter negative values as negative numbers. third the most recent observation, compute a three-week weighted moving average for the Weighted Moving Average Forecast Forecast Time-Series Value Error (Error)2 Week 10 12 Total 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 10.91 Prefer the unweighted moving average here; it has a Select your answer- 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? Select your answer -

Answer 1

Answer a)

Following is the table showing Weighted Moving Average:

All values to be filled in table are highlighted in blue color

ErrorA2 Week Time-Series Vale Weighted Moving Average Forecast Forecast Error (Actual -Forecast) 18 2 18 7.11 7.11 2.67 2.67 3.33 1.33 0.17 5.00 0.33 19.33 20.67 19.33 17.67 17.83 18.00 20.67 21.17 18.33 20.00 4 18 16 19 18 23 21 15 23 1.78 0.03 25.00 0.11 38.03 21.78 112.06 12.45 9 10 4.67 12 Total 13 Forecasted Value MSE (ZErrorA2)/n

Forecast value corresponding to week 4 is calculated using actual values of week 1, 2, and 3 as follows:

Week 4 Forecast = 18*(1/2) + 22*(1/3) + 18*(1/6) = 19.33

Similarly, all the other values are calculated.

Answer b)

MSE for weighted moving average in part (a) = Average of Error² = 12.45

MSE for weighted moving average = 12.45 is greater than MSE of unweighted moving average. Thus, we prefer MSE of unweighted moving average

Prefer unweighted moving average here, it has smaller MSE.

Answer c)

You can always find weighted average at least as good as the unweighted one; actually unweighted average is the special case of the weighted ones where weights are equal.