TY - UNPB

T1 - A Conditionally Beta Distributed Time-Series Model With Application to Monthly US Corporate Default Rates

AU - Nielsen, Thor Pajhede

PY - 2017

Y1 - 2017

N2 - We consider an observation driven, conditionally Beta distributed model for variables restricted to theunit interval. The model includes both explanatory variables and autoregressive dependence in the meanand precision parameters using the mean-precision parametrization of the beta distribution suggested byFerrari and Cribari-Neto (2004). Our model is a generalization of the βARMA model proposed in Rocha andCribari-Neto (2009), which we generalize to allow for covariates and a ARCH type structure in the precisionparameter. We also highlight some errors in their derivations of the score and information which has implicationsfor the asymptotic theory. Included simulations suggests that standard asymptotics for estimators andtest statistics apply. In an empirical application to Moody’s monthly US 12-month issuer default rates in theperiod 1972 − 2015, we revisit the results of Agosto et al. (2016) in examining the conditional independencehypothesis of Lando and Nielsen (2010). Empirically we find that; (1) the current default rate influence thedefault rate of the following periods even when conditioning on explanatory variables. (2) The 12 monthlag is highly significant in explaining the monthly default rate. (3) There is evidence for volatility clusteringbeyond what is accounted for by the inherent mean-precision relationship of the Beta distribution in thedefault rate data.

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

KW - Faculty of Social Sciences

KW - Beta regression

KW - credit risk default rates

KW - contagion

KW - C12

KW - C22

KW - C32

KW - C50

M3 - Working paper

T3 - University of Copenhagen. Institute of Economics. Discussion Papers (Online)

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

ER -