Financial data modeling by Poisson mixture regression

Abstract

In many financial applications, Poisson mixture regression models are commonly used to analyze heterogeneous count data. When fitting these models, the observed counts are supposed to come from two or more subpopulations and parameter estimation is typically performed by means of maximum likelihood via the Expectation–Maximization algorithm. In this study, we discuss briefly the procedure for fitting Poisson mixture regression models by means of maximum likelihood, the model selection and goodness-of-fit tests. These models are applied to a real data set for credit-scoring purposes. We aim to reveal the impact of demographic and financial variables in creating different groups of clients and to predict the group to which each client belongs, as well as his expected number of defaulted payments. The model's conclusions are very interesting, revealing that the population consists of three groups, contrasting with the traditional good versus bad categorization approach of the credit-scoring systems.

Keywords:

• Poisson mixture regression models
• EM algorithm
• count data
• overdispersion
• credit scoring

Acknowledgements

This research was financed by FEDER Funds through “Programa Operacional Factores de Competitividade – COMPETE” and by Portuguese Funds through “FCT – Fundação para a Ciência e Tecnologia”, within the Project Est-C/MAT/UI0013/2011.