  We study the statistical properties of a cellular automata model of traffic
flow with the look-ahead potential. The model defines stochastic rules for the
movement of cars on a lattice. We analyze the underlying statistical
assumptions needed for the derivation of the coarse-grained model and
demonstrate that it is possible to relax some of them to obtain an improved
coarse-grained ODE model. We also demonstrate that spatial correlations play a
crucial role in the presence of the look-ahead potential and propose a simple
empirical correction to account for the spatial dependence between neighboring
cells.
