This paper proposes a dynamic proportional hazard (PH) model with non-specified baseline hazard for the modelling of autoregressive duration processes. A categorization of the durations allows us to reformulate the PH model as an ordered response model based on extreme value distributed errors. In order to capture persistent serial dependence in the duration process, we extend the model by an observation driven ARMA dynamic based on generalized errors. We illustrate the maximum likelihood estimation of both the model parameters and discrete points of the underlying unspecified baseline survivor function. The dynamic properties of the model as well as an assessment of the estimation quality is investigated in a Monte Carlo study. It is illustrated that the model is a useful approach to estimate conditional failure probabilities based on (persistent) serial dependent duration data which might be subject to censoring structures. In an empirical study based on financial transaction data we present an application of the model to estimate conditional asset price change probabilities. Evaluating the forecasting properties of the model, it is shown that the proposed approach is a promising competitor to well-established ACD type models