Tutors Please Expedite these questions.. (ANSWER ALL QUESTIONS PLEASE) Here are

Question

Tutors Please Expedite these questions.. (ANSWER ALL QUESTIONS PLEASE)

Here are the gasoline sales time series data:

Week Sales (1000s of gallons)

10 20

11 15

12 22

a.(10 points) To calculate forecasts 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 and compute a 3-week weighted moving average for the time series. Calculate the MSE. b. (10 points) Calculate forecasts by using the 3-period unweighted moving averages and the corresponding MSE.
c. (10 points) Calculate forecasts by using exponential smoothing with =0.35 Calculate the MSE.
d) (5 points) Which method do you prefer and why?

Thank you very much!!

Explanation / Answer

MSE = [(Dt-MAt)²]/n

a) WMA3
W ..; WMA(3)
4 ..';. 19.33
5 ..';. 21.33
6 ..';. 19.83
7 ..';. 17.83
8 ..';. 18.33
9 ..';. 18.33
10 ..'; 20.33
11 ..'; 20.33
12 ..'; 17.83
13 ..'; 19.33 (f)

n=12-3=9
(Dt-MAt)² 103.4166667
MSE 103.4166667/9 11.49074074

b) MA3
W ... MA(3)
4 ..'; 19.00
5 ..'; 21.00
6 ..'; 20.00
7 ..'; 19.00
8 ..'; 18.00
9 ..'; 18.00
10 ..' 20.00
11 ..' 20.00
12 ..' 19.00
13 ..' 19.00 (f)

n=12-3=9
(Dt-MAt)² 92
MSE 92/9 10.22222222

c) SES(0.35)
W .. S[t]
1 ..';. 17.00
2 ..';. 18.40
3 ..';. 18.61
4 ..';. 20.15
5 ..';. 19.40
6 ..';. 18.21
7 ..';. 18.83
8 ..';. 18.54
9 ..';. 19.75
10 ..'; 19.84
11 ..'; 18.15
12 ..'; 19.49
13 ..'; 19.49

St = X[t-1] + (1-)•S[t-1]
n=12-1=11
(Dt-MAt)² 44.77226698
MSE 44.77226698/11 4.070206089

d) I would prefer minimal MSE = SES(0.35)

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

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