We consider dynamic stochastic economies with heterogeneous agents and introduce the concept of uniformly self-justified equilibria (USJE) -- temporary equilibria for which forecasts are best uniform approximations to a selection of the equilibrium correspondence. In a USJE, individuals' forecasting functions for the next period's endogenous variables are assumed to lie in a compact, finite-dimensional set of functions, and the forecasts constitute the best approximation within this set. We show that USJE always exist and develop a simple algorithm to compute them. Therefore, they are more tractable than rational expectations equilibria that do not always exist. As an application, we discuss a stochastic overlapping generations exchange economy and provide numerical examples to illustrate the concept of USJE and the computational method.