# Why do percentage-based forecast error measures assume a meaningful zero?

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.

• If we are forecasting the year in which something would occur, is there is a meaningful zero? – user1205901 - Reinstate Monica Feb 3 '13 at 11:40
• 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. – Rob Hyndman Feb 3 '13 at 22:45