Abstract: 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 asymptotic properties of the maximum-likelihood estimators of the models. The PARX class of models is used to analyse the time serie properties of monthly corporate defaults in the US in the period 1980-2011 using Önancial and economic variables as external 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. An out-of-sample analysis shows that in terms of forecast performance, the inclusion of covariates in the PARX specification is important. Finally, our empirical analysis allows us to shed some light on the presence of contagion effects over time.
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