We consider a class of nonlinear dynamic economic models in which the actual realizations of a certain variable (e.g., price) depend on the agents' expectations about this variable. We define a consistent expectations equilibrium (CEE) by the property that the sample average and the sample autocorrelations of the realizations of the actual law of motion equal the average and the autocorrelations of the perceived law of motion. Along a CEE agent's expectations are thus self-fulfilling in terms of the observable sample average and sample autocorrelations. Restricting ourselves to the case in which beliefs are described by an AR(1) process, we study existence and stability of three different types of CEE: steady-state, two-cycle, and chaotic. We illustrate how these equilibria can emerge in the nonlinear cobweb model. Learning dynamics based on sample average and sample autocorrelations are introduced and stability of CEE under this learning process is investigated.