A Conditionally Beta Distributed Time-Series Model with Application to Monthly US Corporate Default Rates

Abstract

We consider an observation driven, conditionally Beta distributed model for variables restricted to the unit interval. The model includes both explanatory variables and autoregressive dependence in the mean and precision parameters using the mean-precision parametrization of the beta distribution suggested by Ferrari and Cribari-Neto (2004). Our model is a generalization of the βARMA model proposed in Rocha and Cribari-Neto (2009), which we generalize to allow for covariates and a ARCH type structure in the precision parameter. We also highlight some errors in their derivations of the score and information which has implications for the asymptotic theory. Included simulations suggests that standard asymptotics for estimators and test statistics apply. In an empirical application to Moody’s monthly US 12-month issuer default rates in the period 1972-2015, we revisit the results of Agosto et al. (2016) in examining the conditional independence hypothesis of Lando and Nielsen (2010). Empirically we find that: (1) the current default rate influence the default rate of the following periods even when conditioning on explanatory variables. (2) The 12 month lag is highly significant in explaining the monthly default rate. (3) There is evidence for volatility clustering beyond what is accounted for by the inherent mean-precision relationship of the Beta distribution in the default rate data.