A model is constructed for three related time series: an inflow, a stock, and an outflow. The inflow and outflow time series are related via a truly stochastic distributed lag and the three time series are viewed as cumulations of a random number of units of randomly determined size. Among the interesting results are the serial correlations of the stock and outflow time series viewed singly and the cross and cross serial correlations between outflow in t and stock at t - 1, outflow in t, and inflow in t - 1, as well as between stock in t and inflow in t - i. These relations and others make it possible to evaluate the comparative advantage of lead series in forecasting lag series and as such may be of methodological value for the evaluation of stabilization policies. The model may be viewed as a description of several inflow-stock-outflow phenomena: trade credit and consumer credit processes, demand deposits of commercial banks, population and labor force, the formation and decay of aggregates of capital projects, and some aspects of the income-expenditure process.