Abstract: Forecasting ability of several parameterizations of ACD models are compared to benchmark linear autoregressions for inter-trade durations. The estimation of parametric ACD models requires both the choice of a conditional density for durations and the specification of a functional form for the conditional mean duration. Our results provide guidance for choosing among different parameterizations and for developing better forecasting models to predict one-step-ahead, multi-step-ahead, and the whole density of time durations. For evaluating density forecasts, we propose a new constructive test, which is based on the series of probability integral transforms. The choice of the conditional distribution for inter-trade durations does not seem to affect the out-of sample performances of the ACD at short, as well as longer, horizons. Yet, this choice becomes critical when forecasting the density.