We consider a class of nonlinear dynamic economic models inwhich the actual realizations of a certain variable (e.g., price) dependon the agents' expectations about this variable. We define a consistentexpectations equilibrium (CEE) by the property that the sample averageand the sample autocorrelations of the realizations of the actual lawof motion equal the average and the autocorrelations of the perceived lawof motion. Along a CEE agent's expectations are thus self-fulfilling interms of the observable sample average and sample autocorrelations.Restricting ourselves to the case in which beliefs are described byan AR(1) process, we study existence and stability of three differenttypes of CEE: steady-state, two-cycle, and chaotic. We illustrate howthese equilibria can emerge in the nonlinear cobweb model. Learningdynamics based on sample average and sample autocorrelations areintroduced and stability of CEE under this learning process isinvestigated.