Agosto, G. Cavaliere, D. Kristensen and A. Rahbek
Journal of Empirical Finance (2016), 38, pp.640-663.

We develop a class of Poisson autoregressive models with exogenous 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 asymptotic properties of the maximum-likelihood estimators of the models. The PARX class of models is used to analyze the time series properties of monthly corporate defaults in the US in the period 1982–2011 using financial and economic variables as exogenous 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.