I see. I made a quick figure of the ZTAE loss function for different true values with mean=0 and standard deviation=1. So the function becomes more asymmetric as the true value increases from the mean. But because it flattens off “infinite” values in the correct direction (relative to the mean) can receive quite low losses, which is what we’re seeing above.
This is how losses look for a topic with an MSE loss function. The scatter around the expected loss function is I think related to uncertainty on how the ground truth is defined (see here), plus differences between data providers. So the “true” values I’ve used (from Tiingo, rounded to the nearest minute) might be slightly different from what the reputers used, which is why the scatter increases as the difference from ground truth decreases. Still, inferences with much larger differences than the ground truth uncertainty should largely be unaffected, and indeed they have the largest losses.
