Spatio-Temporal Modeling of Credit Default Rates

• Activity Number: 134
• Type: Contributed
• Date/Time: Monday, August 1, 2011 : 8:30 AM to 10:20 AM
• Sponsor: Business and Economic Statistics Section
• Author(s): Sathyanarayan Anand*+ and Robert Stine
• Companies: University of Pennsylvania and University of Pennsylvania
• Keywords: autoregressive ; conditional ; bayesian ; spatial ; temporal ; mcmc

Abstract

The availability of cheap computing power and pervasiveness of MCMC methods allow for the fitting of complex models that can account for intricate dependencies within data. We focus here on spatio-temporal models that have been widely studied with data on agricultural yields, disease mapping and climate. More specifically, we investigate the use of conditional autoregressive (CAR) models for fitting and predicting credit default rates in the US by county and by quarter. We begin with a hierarchical model that assumes default rates to be binomially distributed, but is computationally intractable, and derive a normal approximation that is validated and gives conjugate posterior distributions for efficient Gibbs sampling. We address issues of parameter identifiability when using CAR models along two dimensions, namely space and time. We draw inspiration from two-factor ANOVA models and re-parameterize the CAR spatio-temporal effects in terms of contrasts, and derive prior distributions for the latter while maintaining the desired CAR structure. We compare the predictive performance of our model to other established methods on a full-scale simulated dataset and the credit default data.