  Literatures in state space models focus on parametric inference and
prediction, which fail if the state space model is not fully specified and the
maximum likelihood estimation does not work. In this paper, we assume the state
transition matrix and the distribution of state noises are unknown. Under this
assumption, we provide methods to consistently estimate these terms. In
addition, we introduce an algorithm to construct consistent prediction
intervals for state vectors and future observations. We complement the
asymptotic results with several numerical experiments.
