Most companies store demand data periodically and make periodic demand forecasts, whereas many demand processes in inventory control need parameter estimates at the individual customer level. Guidance on estimating the parameters of a continuous-time demand process from period demand data is lacking, in particular for the popular and well-studied compound Poisson class of demand. Whereas the statistics literature typically focuses on asymptotic properties, parameters for inventory control have to be estimated based on a limited number of periodic historical demand observations. We show that the standard Method-of-Moments (MM) estimator – the default choice in applied inventory control research – is severely biased for finite samples. The Maximum Likelihood (ML) estimator – which needs to be obtained by a numerical search – performs better, but both estimators lack robustness to misspecification of the demand size distribution. We propose an intuitive, consistent, closed-form MM alternative that dominates standard MM and ML in terms of estimation accuracy and on-target inventory performance. Its closed form does not depend on the specific demand size distribution, making it robust and easily applicable in large-scale applications with many items. In a case study, we find that the accuracy loss due to storing demand periodically is four times as high under standard MM as under the proposed estimator.