If I understand this answer correctly, it is not a problem for a Gaussian ARMA(p,q) process to be non-invertible (ie some of the roots of the MA part of the process are inside or on the unit circle). We restrict the parameter space to that of invertible processes just to make the model identifiable (and because we get the possibility of writing the model as an AR(∞)).
Anyway, almost (roots inside the unit circle) any Gaussian, non-invertible MA() model can be changed to an invertible MA() model representing the same exact process, so restricting the parameter space is not a problem for almost any case, it's just a convenient choice.
Now, if some of the roots of the MA part of a process are ON the unit circle (not inside), is there an invertible representation of the same process?
I don't think there is, so, are there any problems that arise from having roots of the MA part of a process on the unit circle?
