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# Time series analysis

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Data covering the most recent 30 days are given in the following table for the price per gallon of regular gasoline at a location station

Day Price Day Price
1 2.53 16 2.46
2 2.35 17 2.6
3 1.91 18 2.1
4 2.2 19 2.01
5 1.77 20 2.14
6 3.26 21 2.03
7 1.63 22 2.68
8 2.73 23 2.59
9 2.41 24 2.99
10 2.72 25 2.94
11 2.87 26 1.77
12 1.49 27 2.62
13 2.92 28 3.19
14 3.53 29 3.01
15 2.74 30 2.1

a. Compute a forecast for the next day's price by using a 3-day moving average. What is the forecast? What is the MSE for the last five observations?

b. Can you reduce the MSE for the last five observations by changing the moving average window (try 4- to 10-day windows)?

c. Compute a forecast for the next day's price by using exponential smoothing with &#940;=0.25. What is the forecast? What is the MSE for the last five observations?

d. Can you improve the MSE for the last five observations by changing the smoothing constant &#940;?