Inventory decisions relating to items that are demanded intermittently are particularly challenging. Decisions relating to termination of sales of product often rely on point estimates of the mean demand, whereas replenishment decisions depend on quantiles from interval estimates. It is in this context that modelling intermittent demand becomes an important task. In previous research, this has been addressed by generalised linear models or integer-valued ARMA models, while the development of models in state space framework has had mixed success. In this paper, we propose a general state space model that takes intermittence of data into account, extending the taxonomy of single source of error state space models. We show that this model has a connection with conventional non-intermittent state space models used in inventory planning. Certain forms of it may be estimated by Croston’s and Teunter–Syntetos–Babai (TSB) forecasting methods. We discuss properties of the proposed models and show how a selection can be made between them in the proposed framework. We then conduct a simulation experiment, empirically evaluating the inventory implications.