Functional sunspot equilibria

Consider a one step forward looking model where agents believe that the equilibrium values of the state variable are determined by a function whose domain is the current value of the state variable and whose range is the value for the subsequent period. An agent's forecast for the subsequent period uses the belief, where the function that is chosen is allowed to depend on the current realization of an extrinsic random process, and is made with knowledge of the past values of the state variable but not the current value. The paper provides (and characterizes) the conditions for the existence of sunspot equilibria for the model described.