Consider the following time series data:
Month 
1 
2 
3 
4 
5 
6 
7 
Value 
24 
13 
20 
12 
19 
23 
15 
Develop a threemonth moving average for this time series. Compute MSE and a forecast for month 8. 

If required, round your answers to two decimal places. Do not round intermediate calculation. 

MSE: 

The forecast for month 8: 

(c) 
Use α = 0.2 to compute the exponential smoothing values for the time series. Compute MSE and a forecast for month 8. 
If required, round your answers to two decimal places. Do not round intermediate calculation. 

MSE: 

The forecast for month 8: 

(d) 
Compare the threemonth moving average forecast with the exponential smoothing forecast using α = 0.2. Which appears to provide the better forecast based on MSE? 
(e) 
Use trial and error to find a value of the exponential smoothing coefficient α that results in the smallest MSE. 
If required, round your answer to two decimal places. 

α = 
b)
for 3 month forecast:
Time period  Actual Value(A)  Moving avg. Forecast(F)  Forecast error E=AF  Squared Forecast Error 
1  24  
2  13  
3  20  
4  12  19.00  7.00  49.00 
5  19  15.00  4.00  16.00 
6  23  17.00  6.00  36.00 
7  15  18.00  3.00  9.00 
Total  20.00  110.00  
Average  5.00  27.50  
MAD  MSE 
MSE: =27.50
forecast for month 8=19
c)
Time period  Actual Value(A)  Forecast(F)  Forecast error E=AF  Squared Forecast Error 
1  24  
2  13  24.00  11.00  121.00 
3  20  21.80  1.80  3.24 
4  12  21.44  9.44  89.11 
5  19  19.55  0.55  0.30 
6  23  19.44  3.56  12.66 
7  15  20.15  5.15  26.56 
19.12  31.50  252.88  
Average  5.25  42.1461  
MAD  MSE 
MSE:=42.15
forecast for month 8 =19.12
d)
threemonth moving average forecast
e)
α = 0.35
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