The Vasicek distribution autoregressive time-series model for aggregated data of default and delinquency rates

Abstract

Is it possible to analyse time series of aggregated data of default and delinquency rates with a simple model that includes both cross-sectional and serial dependence? To address this question, this paper proposes an autoregressive time-series model for Vasicek-distributed random variables. A direct result from the proposed model is that it leads to a novel out-of-time validation test for aggregated default and delinquency rates. The motivation for the model comes from an analysis of a time series of aggregated US credit card delinquencies, for which the Poisson or binomial distribution cannot be used. The proposed model can also be employed to analyse a time series of the average default probability of a portfolio.