The quality of radio astronomical images made with an antenna array depends upon atmospheric behavior. As baselines and frequencies increase, phase variations become increasingly erratic. The phase fluctuations are time dependent and we found them to be correlated in time order in each baseline. We can represent these correlations by stochastic models. Models obtained by the Box-Jenkins method are referred to as autoregressive integrated moving average processes (ARIMA). ARIMA models of VLA phase provide good short-term predictions that may be useful for improving present calibration techniques. ARIMA models of VLA phase are data dependent and can be used in a variety of situations. A technique that works in all cases can be programmed into a software package such that modeling can be accomplished with no operator interactions. Another important application of ARIMA models involves the use of Kalman filtering to reduce the atmospheric effects when self-calibration does not work well. The performance of the Kalman filter critically depends upon the models of the processes. An ARIMA model of the phase fluctuation can be represented in a state space form as noise in the Kalman filter equations.