S. Cambanis et I. Fakhrezakeri, FORWARD AND REVERSED TIME PREDICTION OF AUTOREGRESSIVE SEQUENCES, Journal of Applied Probability, 33(4), 1996, pp. 1053-1060
Prediction for autoregressive sequences with finite second moment and
of general order is considered. It is shown that the best predictor wi
th time reversed is linear if and only if the innovations are Gaussian
. The connection to time reversibility is also discussed.