Bayesian Inference of Multiscale Stochastic Conditional Duration Models

There is evidence to suggest that a single factor of duration running on single time scale is not adequate to capture the dynamics of the duration process of financial transaction data. This assertion is motivated by the observation that some existing one-factor stochastic duration models have had difficulty in successfully fitting the left tail of the marginal distribution of the observed durations. This empirical poor fit of the left tail of the duration distribution may be indicative of the possible existence of multiple stochastic duration factors running on different time scales. This paper proposes multiscale stochastic conditional duration (MSCD) models to describe the dynamics of financial transaction data. Novel algorithms of Markov Chain Monte Carlo (MCMC) are developed to fit the resulting MSCD models under three distributional assumptions about the innovation of the measurement equation. In addition, instead of subjecting the observation equation to a logarithmic transformation, we work on the MSCD model directly. Simulation studies suggest that our proposed models and corresponding estimation methodology work quite well. We also apply an auxiliary particle filter technique to construct one-step-ahead in-sample and out-of-sample duration forecasts based on the fitted models. Applications to two duration data sets of FIAT and IBM indicate the existence of at least two factors that determine the dynamics of the two stock transactions.