We obtain the complete time dependence of the velocity autocorrelation function (VACF) for lattice gas cellular automata, using ring kinetic theory. This theory accounts for the simplest correlated collisions that improve on the molecular chaos approach, and yields a dosed equation for the VACF that we evaluate for both infinite and l'mite systems. We compare our analytical results with numerical simulations at all times, as well as with long-time results of the mode coupling theories, fmding a very good agreement for all times at all densities.