### Abstract

We introduce a schematic formalism for the time evolution of a random population entering some set of classes and such that each member of the population evolves among these classes according to a scheme based on a Markov chain model. We consider that the flow of incoming members is modeled by a time series and we detail the time series structure of the elements in each of the classes. We present a practical application to data from a credit portfolio of a Cape Verdian bank; after modeling the entering population in two different ways - namely as an ARIMA process and as a deterministic sigmoid type trend plus a SARMA process for the residues - we simulate the behavior of the population and compare the results. We get that the second method is more accurate in describing the behavior of the populations when compared to the observed values in a direct simulation of the Markov chain.

Original language | English |
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Title of host publication | AIP Conference Proceedings |

Pages | 1-4 |

Number of pages | 4 |

Publication status | Published - 2016 |

Event | International Conference of Numerical Analysis and Applied Mathematics 2015, ICNAAM 2015 - Rhodes, Greece Duration: 23 Sep 2015 → 29 Sep 2015 |

### Conference

Conference | International Conference of Numerical Analysis and Applied Mathematics 2015, ICNAAM 2015 |
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Country | Greece |

City | Rhodes |

Period | 23/09/15 → 29/09/15 |

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## Cite this

Guerreiro, G. R. D., Esquível, M. L., & Fernandes, J. M. (2016). An Open Markov Chain Scheme Model for a Credit Consumption Portfolio fed by ARIMA and SARMA Processes. In

*AIP Conference Proceedings*(pp. 1-4). [19003]