Semiparametric autoregressive conditional proportional hazard models

A new semiparametric proportional hazard rate model is proposed which extends standard models to include a dynamic specification. Two main problems are resolved in the course of this paper. First, the partial likelihood approach to estimate the components of a standard proportional hazard model is not available in a dynamic model involving lags of the log integrated baseline hazard. We use a discretisation approach to obtain a semiparametric estimate of the baseline hazard. Second, the log integrated baseline hazard is not observed directly, but only through a threshold function. We employ a special type of observation driven dynamic which allows for a computationally simple maximum likelihood estimation. This specifications approximates a standard ARMA model in the log integrated baseline hazard and is identical if the baseline hazard is known. It is shown that this estimator is quite flexible and easily extended to include unobserved heterogeneity, censoring and state dependent hazard rates. A Monte Carlo study on the approximation quality of the model and an empirical study on BUND future trading at the former DTB complement the paper.