Consider the following time series data. Develop a three-week moving average for
ID: 376323 • Letter: C
Question
Consider the following time series data.
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: ??
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: ??
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.
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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
a) 3-week moving average forecast and MSE
Forecast is calculated by formula Ft = (Ft-1 + Ft-2 + Ft-3)/3
MSE is calculated as Average of Squared Errors, where square error = (At - Ft)2 , where At is the actual time series value and Ft is the forecast in time period t
Forecast for week 7 = (12+18+15)/3 = 15
MSE = (13.44+18.78+0.11)/3 = 10.78
b) Exponential smoothing forecast is calculated by formula
Ft = Ft-1 + (At-1 - Ft-1)
MSE = 9.77
Forecast for week 7 = 16.02
c) MSE of exponential smoothing with =0.2 is lesser. Therefore it gives less error and hence is a better forecasting model as compared to 3 week moving average method.
d) Using trial and error, =0.3 gives a better forecast (smaller MSE)
Week Time Series Value Forecast Squared Error 1 18 2 13 3 16 4 12 15.67 13.44 5 18 13.67 18.78 6 15 15.33 0.11 7 15.00