Zero-Inflated Autoregressive Conditional Duration Model for Discrete Trade Durations With Excessive Zeros

Abstract

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 in correct treatment of zero values in continuous models.