A family of autoregressive conditional duration models

This paper develops a family of autoregressive conditional duration (ACD) models that encompasses most specifications in the literature. The nesting relies on a Box–Cox transformation with shape parameter λ to the conditional duration process and a possibly asymmetric shocks impact curve. We establish conditions for the existence of higher-order moments, strict stationarity, geometric ergodicity and β -mixing property with exponential decay. We next derive moment recursion relations and the autocovariance function of the power λ of the duration process. Finally, we assess the practical usefulness of our family of ACD models using New York stock exchange (NYSE) transactions data, with special attention to IBM price durations. The results warrant the extra flexibility provided either by the Box–Cox transformation or by the asymmetric response to shocks.