In finance, durations between successive transactions are usually modeled by the autoregressive conditional duration model based on a continuous distribution omitting frequent zero values. 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. We establish the invertibility of the score filter . Additionally, we derive sufficient conditions for the consistency and asymptotic normality of the maximum likelihood of the model parameters. In an empirical study of DJIA stocks, we find that split transactions cause on average 63\% of zero values. Furthermore, the loss of decimal places in the proposed model is less severe than incorrect treatment of zero values in continuous models.
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 of DJIA stocks, we find that split transactions cause on average 63\% of close-to-zero values. Furthermore, the loss of decimal places in the proposed approach is less severe than incorrect treatment of close-to-zero values in continuous models.
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This model allows to distinguish between the processes generating split and standard transactions. We use the existing theory on score models to
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. Additionally, we derive sufficient conditions
and verify that sufficient conditions hold
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