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We introduce a schematic formalism for the time evolution of a random open population divided into classes. With a Markov chain model, allowing for population entrances, we consider the flow of incoming members modeled by a time series - either ARIMA for the number of new incomings or SARMA for the residuals of a deterministic sigmoid type trend - and we detail the time series structure of the elements in each class. A practical application to real data from a credit portfolio is presented.