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.

翻译：金融领域中，连续交易之间的持续期通常采用基于忽略零值的连续分布的零膨胀自回归条件持续期模型进行建模。零值或接近零值的持续期可能由分笔交易或独立交易导致。本文提出一种基于零膨胀负二项分布与得分动态的离散模型，该模型允许处理大量零值，并能区分分笔交易与标准交易的生成过程。我们利用现有得分模型理论证明得分滤波器的可逆性，并验证模型参数极大似然估计的一致性与渐近正态性充分条件成立。实证研究发现，分笔交易导致92%至98%的零值及接近零值的持续期。此外，相较于连续模型对零值的错误处理方式，本文方法在小数位数损失方面表现更优。