  In finance, durations between successive transactions are usually modeled by
the autoregressive conditional duration model based on a continuous
distribution omitting zero values. Zero or close-to-zero durations can be
caused by either split transactions or independent transactions. We propose a
discrete model allowing for excessive zero values based on the zero-inflated
negative binomial distribution with score dynamics. This model allows to
distinguish between the processes generating split and standard transactions.
We use the existing theory on score models to establish the invertibility of
the score filter and verify that sufficient conditions hold for the consistency
and asymptotic normality of the maximum likelihood of the model parameters. In
an empirical study, we find that split transactions cause between 92 and 98
percent of zero and close-to-zero values. Furthermore, the loss of decimal
places in the proposed approach is less severe than the incorrect treatment of
zero values in continuous models.
