Most problems in time series go far beyond serial correlation and variability or volatility clustering. It is known that major cyclical variables display asymmetric behavior during various phases of the cycle. Time reversibility is a broad concept of asymmetry or symmetry in time series. In this talk, we consider time reversibility and prediction of stationary autoregressive processes with finite variance. We obtain a simple test for time reversibility. We also discuss time reversibility and prediction of stable processes.