This note describes a model for inflow-stock-outflow time series which are formed as sums of random numbers of subcomponents of randomly determined sizes and are related via a probabilisticly distributed lag. Such time series may be illustrated by population processes in connection with which not only numbers of units are of interest but also the sizes of the units and the sums of the sizes. Such series may also be illustrated by economic phenomena like new loans made, loans outstanding and loans repaid of a commercial bank; new capital investments, capital stock and depreciated capital for a group of firms as well as accessions to the labor force, labor force outstanding, and secessions from the labor force.