Higher RMSE lower MAPE

Question

I have a time series model that forecast next K days. For example when I forecast next 50 days my MAPE is 20.3% and RMSE is 2943 and when I forecast next 200 days is the MAPE is 10.25 % but RMSE is 9872. If I want to describe in a word which one is a better forecast the next 50 days or the next 200 days, how can I compare the MAPE and RMSE scores given this model?

For next 50 days range of outputs is smaller so it makes sense that RMSE is smaller and the same thing goes for 200 days since numbers are bigger therefore 200 days have larger RMSE however does this mean that model predict longer horizon better than shorter one?

Is there any other metrics I should take into consideration before making final decisions.

I have looked at this post but I still need more explanations:

https://datascience.stackexchange.com/questions/37168/high-rmse-and-mae-and-low-mape

Answer 1

Note that different accuracy measures (such as the MAPE or the RMSE) are minimized in expectation by different functionals of the unknown future distribution. See Kolassa (2020, International Journal of Forecasting) for an explanation. The MAPE in particular rewards a biased forecast: What are the shortcomings of the Mean Absolute Percentage Error (MAPE)?

Thus, what is a "better" forecast depends on your error measure. Or, it might be better to turn this around: decide beforehand what functional of your future distribution you want to elicit and then choose the error measure based on that. If you want an unbiased forecast, use the (R)MSE. If you want the median of the future distribution, use the MAE. If you want the (-1)-median (Gneiting, 2011, JASA) , use the MAPE. If you actually need a quantile, use a hinge loss.