The formula for MASE can be found here: https://en.wikipedia.org/wiki/Mean_absolute_scaled_error
I am building a multi-step time series forecaster and I want to use MASE as a measure of prediction accuracy for a horizon of $n$ steps. These $n$ steps are part of the testing set, not the training set. I've trained the model and now I choose a starting point from my test set to begin the $n$-step forecast.
When calculating the naive mean absolute error (naive = using previous time step as next time step) should I calculate it on the same interval as the multistep forecast (which is comprised of test data), or on the entire training set?
Currently I calculate the naive mean absolute error on the entire training set, and I use that constant number for very multi-step MASE calculation. I still get MASE<1, which is encouraging, but I think perhaps this comparison doesn't make sense and I need to be comparing absolute forecast error and absolute naive error on the same interval every time. But this would mean that my accuracy would depend on each interval, which also doesn't seem ideal.