Duration time-series models with proportional hazard

The analysis of liquidity in financial markets is generally performed by means of the dynamics of the observed intertrade durations (possibly weighted by price or volume). Various dynamic models for duration data have been considered in the literature, such as the Autoregressive Conditional Duration (ACD) model. These models are often excessively constrained, introducing, for example, a deterministic link between conditional expectation and variance in the case of the ACD model. Moreover, the stationarity properties and the patterns of the stationary distributions are often unknown. The aim of this article is to solve these difficulties by considering a duration time series satisfying the proportional hazard property. We describe in detail this class of dynamic models, discuss its various representations and provide the ergodicity conditions. The proportional hazard copula can be specified either parametrically, or nonparametrically. We discuss estimation methods in both contexts, and explain why they are efficient, that is, why they reach the parametric (respectively, nonparametric) efficiency bound.