This paper considers a new class of time series models called autoregressive conditional duration (ACD) models. These models have been developed and applied to investigate the price discovery process in the context of financial markets. The various statistical properties of this class of ACD models are examined. A minimum mean square error (MMSE) forecast function is obtained as it plays an important role in many practical applications. The theory and utilisation of these models are illustrated using a potential application based on a sample of high frequency transactions based stock price data for News Corporation.