The paper presents selected specifications of autoregressive conditional duration models (ACD). Over the past years, ACD models became very popular in describing conditional expectations of durations between successive financial market events, such as order submissions, trades or changes in transaction price. Described models are classified according to (1) specification used for conditional expectation of duration and (2) probability distribution applied. Selected methods for evaluating the goodness-of-fit of the models are presented, such as density forecasts and the nonparametric D-test. Theoretical presentation is illustrated by the empirical example. The models and the testing procedures are applied to intertrade durations of two Polish stocks from the Warsaw Stock Exchange: Telekomunikacja Polska S.A. and PGF S.A. The results show that the best specification for the data under study is the most general one, i.e. the Box-Cox ACD2 model based on generalized gamma distribution. Keywords: intertrade durations, autoregressive conditional duration models, ultra-high-frequency data, density forecasting
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