I've seen this comment made in various textbooks and papers. For example, the online textbook by Rob J Hyndman and George Athanasopoulos states at http://otexts.com/fpp/2/5/ that

Another prob­lem with per­cent­age errors that is often over­looked is that they assume a mean­ing­ful zero. For exam­ple, a per­cent­age error makes no sense when mea­sur­ing the accu­racy of tem­per­a­ture fore­casts on the Fahren­heit or Cel­sius scales.

Why is this the case?


Think about temperature. If I predict that tomorrow it will be 30 degrees Celsius and it is actually 31, my "percentage" error is 100*1/31 = 3.2%. However, on the Fahrenheit scale, my prediction is 86 degrees, and it is actually 87.8, giving a "percentage" error of 100*1.8/87.8 = 2.05%.

If there is a meaningful zero, such as in measurements of length, then this problem doesn't occur. A percentage error using inches will give the same answer as a percentage error using centimetres.

  • $\begingroup$ If we are forecasting the year in which something would occur, is there is a meaningful zero? $\endgroup$ – user1205901 - Reinstate Monica Feb 3 '13 at 11:40
  • 1
    $\begingroup$ It depends. If you are forecasting the number of years until X occurs, then the zero is meaningful. But if you are forecasting the year on the Gregorian calendar in which X occurs, then no, it makes no sense to treat zero as meaningful as you could have used the Islamic calendar just as easily and got a different result. $\endgroup$ – Rob Hyndman Feb 3 '13 at 22:45

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.