The finite sample properties of the state space methods applied to long memory time series are analyzed through Monte Carlo simulations. The state space setup allows to introduce a novel modeling approach in the long memory framework, which directly tackles measurement errors and random level shifts. Missing values and several alternative sources of misspecification are also considered. It emerges that the state space methodology provides a valuable alternative for the estimation of the long memory models, under different data generating processes, which are common in financial and economic series. Two empirical applications highlight the practical usefulness of the proposed state space methods.