Hi. May I get some general advice about when a transformation of the training data does or does not get applied to the testing data that is used to test the accuracy of a forecast?

If I am transforming independent variables such as by doing 1/x, √x. or e^(-x), I assume I want to do this to both the training data and the testing data.

If I am transforming the dependent variable such as by doing √y, arcsin √y, or ln(y), I assume I want to do this to both the training data and the testing data, but then the predicted values in the testing data are the inverse of the transformation.

If I am reducing the number of independent variables such as by doing a principal component analysis, I assume I want to do this to both the training data and the testing data.

If I am adjusting the sampling of the training data due to an imbalance of the distribution of the dependent variable (not really a transformation?), I assume this is an instance where I would NOT adjust the testing data but rather I would apply the model to the original unadjusted testing data.

Are there other common examples where a transformation of the training data does not require an adjustment to the testing data?

Also, is all of the above independent of the choice of the accuracy metric?

Thank you.