On Fréchet autoregressive conditional duration models

• We propose a new autoregressive conditional duration model by introducing the Fréchet distribution to the innovations.
• This new model is able to capture the features of heavy tails and extreme values in trade durations data, which can usually be found in block trades.
• We consider the maximum likelihood estimation for the model, and derive its asymptotic properties.
• A diagnostic tool based on the residual autocorrelations is proposed.

Some durations such as those of block trades may have the properties of both heavy tails and extreme values. To model such type of data, we suggest the Fréchet distribution for the innovations of the autoregressive conditional duration (ACD) model, and hence the Fréchet ACD model. Some statistical inference tools including the maximum likelihood estimation and diagnostic tools for model adequacy are derived, and their finite-sample performance is evaluated by Monte Carlo simulation experiments. The usefulness of the new model is demonstrated by analyzing the durations of block trades on two stock exchanges.