Problem 15-05 (Algorithmic) Consider the following time series data. A. Develop
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Question
Problem 15-05 (Algorithmic)
Consider the following time series data.
A. Develop a three-week moving average for this time series. Compute MSE and a forecast for week 7. Round your answers to two decimal places.
MSE:
The forecast for week 7:
B. Use = 0.2 to compute the exponential smoothing values for the time series. Compute MSE and a forecast for week 7. Round your answers to two decimal places.
MSE:
The forecast for week 7:
C. Compare the three-week moving average forecast with the exponential smoothing forecast using = 0.2. Which appears to provide the better forecast based on MSE?Explain.
D. Use trial and error to find a value of the exponential smoothing coefficient that results in a smaller MSE than what you calculated for = 0.2. Find a value of for the smallest MSE. Round your answer to three decimal places.
=
Explanation / Answer
The values are given in table
Forecast for week 7 = 14
Mean square error = (4.672 + 3.672 + 0.672 )/3 = 35.67/3 = 11.89
b. Exponential smoothing formula where = 0.2
Ft+1 = Ft + (1- ) yt
so the calculated values are in the below given table
SME = (25 + 1 + 33.64 + 1.8496 + 3.6557)/5 = 13.029
Forecast for week 14 = 15.53
C. When we compare MSE of first and second method, we find first method better as its MSE is less than the second's MSE.
D. By doing trial and error by changing values we find minimum MSE for alpha = 0.367
and MSE = 12.061
Week Value (A) 3 - WMA (F) l (A -F) l 1 18 #N/A 2 13 #N/A 3 16 #N/A 4 11 15.67 4.67 5 17 13.33 3.67 6 14 14.67 0.67 7 14