In this paper we construct sunspot equilibria that arise from chaotic deter
ministic dynamics. These equilibria are stationary and have absolutely cont
inuous stationary measures. We prove that they can be learned by a simple r
ule based on the histograms of past state variables. This work gives a theo
retical justification for complex deterministic models that might compete w
ith stochastic models to explain real data. Also we prove the stochastic st
ability of the indeterminate equilibrium. JEL Classification Numbers: C61,
E32.