Modeling corporate defaults: Poisson autoregressions with exogenous covariates (PARX)

We develop a class of Poisson autoregressive models with additional covariates (PARX) that can be used to model and forecast time series of counts. We establish the time series properties of the models, including conditions for stationarity and existence of moments. These results are in turn used in the analysis of the asympotic properties of the maximum-likelihood estimators of the models. The PARX class of models is used to analyse the time series properties of monthly corporate defaults in the US in the period 1982-2011 using financial and economic variables as exogeneous covariates. Results show that our model is able to capture the time series dynamics of corporate defaults well, including the well-known default counts clustering found in data. Moreover, we find that while in general current defaults do indeed affect the probability of other firms defaulting in the future, in recent years economic and financial factors at the macro level are capable to explain a large portion of the correlation of US firms defaults over time.