# MAPE and SMAPE shift invariance (bias)

MAPE (Mean Absolute Percentage Error) and SMAPE (Symmetric Mean Absolute Percentage Error) both are sensitive when the TRUE values is 0.

Thus I've come to the conclusion to add some epsilon to all data points to eliminate having zero in determinator.

But after that, I put attention that the resulting SMAPE or MAPE significantly depends on such epsilon.

For example, if I choose $$\epsilon=0.1$$ the MAPE is much lower, than if I choose $$\epsilon=0.01$$.

What should be done?