Bayesian Estimation and Prediction for ACD Models in the Analysis of Trade Durations from the Polish Stock Market

Abstract

In recent years, autoregressive conditional duration models (ACD models)
introduced by Engle and Russell in 1998 have become very popular in modelling
of the durations between selected events of the transaction process (trade
durations or price durations) and modelling of financial market microstructure
effects. The aim of the paper is to develop Bayesian inference for the ACD
models. Different specifications of ACD models will be considered and compared
with particular emphasis on the linear ACD model, Box-Cox ACD model,
augmented Box-Cox ACD model and augmented (Hentschel) ACD model. The
analysis will consider models with the Burr distribution and the generalized
Gamma distribution for the innovation term. Bayesian inference will be
presented and practically used in estimation of and prediction within ACD
models describing trade durations. The MCMC methods including MetropolisHastings algorithm are suitably adopted to obtain samples from the posterior
densities of interest. The empirical part of the work includes modelling of trade
durations of selected equities from the Polish stock market.