  We present a new, non-parametric forecasting method for data where continuous
values are observed discretely in space and time. Our method, "light-cone
reconstruction of states" (LICORS), uses physical principles to identify
predictive states which are local properties of the system, both in space and
time. LICORS discovers the number of predictive states and their predictive
distributions automatically, and consistently, under mild assumptions on the
data source. We provide an algorithm to implement our method, along with a
cross-validation scheme to pick control settings. Simulations show that
CV-tuned LICORS outperforms standard methods in forecasting challenging
spatio-temporal dynamics. Our work provides applied researchers with a new,
highly automatic method to analyze and forecast spatio-temporal data.
