In massive MIMO systems, which rely on uplink pilots to estimate the channel, the time interval between pilot transmissions constrains the length of the downlink. Since switching between up-and downlink takes time, longer downlink blocks increase the effective spectral efficiency. We investigate the use of low-complexity channel models and Kalman filters for channel prediction, to allow for longer intervals between the pilots. Specifically, we quantify how often uplink pilots have to be sent when the downlink rate is allowed to degrade by a certain percentage. To this end, we consider a time-correlated channel aging model, whose spectrum is rectangular, and use autoregressive moving average (ARMA) processes to approximate the time-variations of such channels. We show that ARMA-based predictors can increase the interval between pilots and the spectral efficiency in channels with high Doppler spreads. We also show that Kalman prediction is robust to mismatches in the channel statistics.