Testing the Adequacy of Markov Chain and Mover-Stayer Models as Representations of Credit Behavior

Abstract

We summarize methodology for testing the compatibility of discrete time stochastic processes—stationary and nonstationary Markov chains and an extension, the mover-stayer model—with longitudinal data from an unknown empirical process. We apply this methodology to determine the suitability of these models to represent the payment behavior of a sample of retail revolving credit accounts. We are led to reject stationary and also nonstationary Markov chain models for our data and for our state space definition in favor of the mover-stayer model. The mover-stayer model, in contrast to Markov chains, incorporates a simple form of population heterogeneity. Stationary Markov chains have been used extensively in finance literature to model payment behavior of credit accounts. Our empirical study suggests, however, that stationary Markov chains may not appropriately model payment behavior. It also indicates that incorporating heterogeneity in modeling payment behavior may be more important than incorporing nonstationarity.