# 19-004/III (2019-01-11)

Francisco Blasques, VU University Amsterdam; Vladimir Holy, University of Economics Prague; Petra Tomanova, University of Economics Prague
Financial High-Frequency Data, Autoregressive Conditional Duration Model, Zero-Inflated Negative Binomial Distribution, Generalized Autoregressive Score Model
JEL codes:
C22, C41, C58

In finance, durations between successive transactions are usually modelled 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.