The object of this paper is to show that under certain auxiliary assumptions a stationary autoregressive sequence has a best predictor in mean square that is linear if and only if the sequence is minimum phase or is Gaussian when all moments are finite.
"Prediction and Non-Gaussian Autoregressive Stationary Sequences." Ann. Appl. Probab. 5 (1) 239 - 247, February, 1995. https://doi.org/10.1214/aoap/1177004838