Task: Here are the gasoline sales time series data: Week Sales (1000s of gallons)
1 17
2 21
3 19
4 23
5 18
6 16
7 20
8 18
9 22
10 20
11 15
12 22
Problem 1. Use a weight of 1/2 for the most recent observation, 1/3 for the second most recent, and 1/6 for the third most recent to compute a 3-week weighted moving average for the time series.
Problem 2. Compute the MSE for the weighted moving average in part (a). Now, calculate the unweighted moving average and the corresponding MSE. Which method do you prefer: the unweighted or weighted from part a) and why?
Problem 3. Suppose that 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?
Problem 4. Use exponential smoothing with α=0.35 Calculate the MSE.