This paper establishes in a general way the existence of a connection between the stationary equilibria of an infinite horizon economy and the equilibria of a naturally related finite economy.
More specifically, the connection is established first between the cycles of a stationary overlapping generations economy and the equilibria of a related finite economy with a cyclical structure. Then the connection is shown to hold also when extrinsic uncertainty (a sunspot) is introduced in the models. The connection holds in this case between a kind of sunspot equilibria called here sunspot cycles, and the correlated equilibria of the finite economy when there is asymmetric information about the extrinsic uncertainty. Incidentally, the sunspot cycles constitute a class of sunspot equilibria that are able to generate time series fluctuating in the recurrent but irregular way characteristic to some economic time series.