Bayesian analysis of the stochastic conditional duration model

A Bayesian Markov chain Monte Carlo methodology is developed for estimating the stochastic conditional duration model. The conditional mean of durations between trades is modelled as a latent stochastic process, with the conditional distribution of durations having positive support. Regressors are included in the model for the latent process in order to allow additional variables to impact on durations. The sampling scheme employed is a hybrid of the Gibbs and Metropolis-Hastings algorithms, with the latent vector sampled in blocks. Candidate draws for the latent process are generated by applying a Kalman filtering and smoothing algorithm to a linear Gaussian approximation of the non-Gaussian state space representation of the model. Monte Carlo sampling experiments demonstrate that the Bayesian method performs better overall than an alternative quasi-maximum likelihood approach. The methodology is illustrated using Australian intraday stock market data, with Bayes factors used to discriminate between different distributional assumptions for durations.