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Forecast Accuracy Measures

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See attached Excel data file.

For each forecast, set up columns and calculate:
Squared error
Absolute error
Absolute % error
The numerator of Thiel"s U statistic
The denominator of Thiel"s U statistic
Calculate ME, MSE, RMSE, MAPE, and U.


1/ The absolute percentage error for the data point 9/24/2008 returns #DIZ/0! Value. The appropriate action is...
a/ exclude 9/24/2008 entirely from data set
b/ Treat the reported error as a missing value when calculating the error statistics
c/ Replace the error by zero
d/ Replace the actual value of calls offered by a very small number e.g 1
e/ do nothing

2/ The following statement about the error statistics for the two variables is true.
a/ the calculated mean squared error for both models are too large to be interpreted
b/ Model 1 systematically over predicts number of calls
c/ Thiel's U statistic indicate that naïve forecasting will produce better forecast than either model 1 or 2
d/ Model 2 is far superior to Model 1 in terms of mean error
e/ Neither model has any substantial bias.

3/ The root mean squared error for models 1 and 2 respectively are
a/ 1018 and 1075
b/ 31 and 2
c/ .048 and .52
d/ 1036949 and 1156669
e/ .097 and .102

4/ The mean absolute percentage error for models 1 and 2 respectively are
a/ 1018 and 1075
b/ 0.097 and .102
c/ .48 and .52
d/ 1036949 and 1156669
e/ 31 and 2

5/ The error statistic indicate
a/ Naïve forecasting will produce better results than either model 1 or model 2
b/ Model 2 is better than model 1 based on RMSE and MAPE
c/ model 2 is better than model 1 because it has the lowest mean error
d/ model 1 is better than model 2 based on RMSE, MAPE, and Thiel's U statistic
e/ Both model 1 and model 2 provide reasonable forecast of calls offered based on MAPE.

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Solution Summary

This solution is comprised of detailed step-by-step calculations and explanation of various Forecast Accuracy Measures like Forecast Error, Absolute Error, Thiel's U Statistic, ME, MSE, RMSE, MAPE etc. in EXCEL. Comparison of these Forecast Techniques based on these Forecast Accuracy measures has also been shown.

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  • MSc, Osmania University
  • MSc, Indian Institute of Technology - Roorkee (I.I.T.-ROORKEE)
  • BSc, Banaras Hindu University
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