Is MAPE a good error measurement statistic? And what alternatives are there? I have a time series that deals with rainfall. It is a period of 10 years (daily resolution), and covers climate variables.
I'm going to feed the data into an Artificial Neural Network to predict the rainfall variable (PP).
As what I've been reading, MAPE's formula involves dividing by the actual observed value. But since its rainfall, there will be days with little or zero precipitation values.
This is bad (dividing by zero = black hole). So how am I going to go about this? I could do data replacement on the zero or close to zero values, but that's stupid - if I do that, I inflate a lot of things, and am pretty much tampering with the data in a way (unlike missing values, which should be imputed by way of other data and not filled in with some other arbitrary value).
My professor is stubborn as a mule. Is there any alternative to MAPE? Or are there any methods to circumvent the issues of MAPE?
EDIT
THERE ARE SMALL AND ZERO VALUES IN THE DATASET... Am I just screwed now?
 A: No, actually MAPE is very poor error measure as discussed by Stephan Kolassa in Best way to optimize MAPE and Prediction Accuracy - Another Measurement than MAPE and Minimizing symmetric mean absolute percentage error (SMAPE) and on those slides. You can also check the following paper:

Tofallis, C. (2015). A better measure of relative prediction accuracy
  for model selection and model estimation. Journal of the Operational
  Research Society, 66(8), 1352-1362.

It is also discussed by Goodwin and Lawton (1999) in the On the asymmetry of the symmetric MAPE paper

Despite its widespread use, the MAPE has several disadvantages 
  (Armstrong & Collopy,  1992; Makridakis,  1993).  In  particular, 
  Makridakis  has argued that the MAPE  is  asymmetric  in  that 
  ‘equal  errors above  the  actual  value  result  in  a  greater  APE 
  than those  below  the  actual  value’.  Similarly, Armstrong and Collopy   argued   that ‘the MAPE ... puts a heavier penalty on
  forecasts  that  exceed  the  actual than those that are less than the
  actual. For example, the MAPE is bounded on the low side by an error
  of 100%, but there is no bound on the high side’.

The quoted (Makridakis, 1993) paper gives a nice example for the asymmetry, when the predicted value is $150$ and the forecast is $100$, MAPE is $|\tfrac{150-100}{150}| = 33.33\%$, while when the predicted value is $100$ and the forecast is $150$ MAPE is $|\tfrac{100-150}{100}| = 50\%$ despite the fact that both forecasts are wrong by $50$ units!
What the above references, and the number of other sources, show is that if you use MAPE as a criterion for selecting your forecasts, this would lead to biased and underestimated results. Moreover you run into problems when the predicted value is equal to zero.
In the How to interpret error measures in Weka output? thread you can find a brief review of other error measures.
