We construct nonstationary sunspot equilibria in an unbounded growth model associated with Boldrin and Rustichini (1994) which is a variant of the Rebelo (1991) model. The constructed equilibria constitute a continuum of the balanced growth equilibria whose average growth rates are different from each other in spite of the fact that fundamental characteristics of an underlying deterministic model are identical. The equilibrium stochastic process exhibits strong statistical regularities such as a cointegrated relation, and generates both a stochastic trend and transitory cyclical fluctuations in a purely endogenous fashion.