A Threshold Stochastic Conditional Duration Model for Financial Transaction Data

This paper proposes a threshold stochastic conditional duration (TSCD) model to capture the asymmetric property of financial transactions. The innovation of the observable duration equation is assumed to follow a threshold distribution with two component distributions switching between two regimes. The distributions in different regimes are assumed to be Exponential, Gamma or Weibull. To account for uncertainty in the unobserved threshold level, the observed durations are treated as self-exciting threshold variables. Adopting a Bayesian approach, we develop novel Markov Chain Monte Carlo algorithms to estimate all of the unknown parameters and latent states. To forecast the one-step ahead durations, we employ an auxiliary particle filter where the filter and prediction distributions of the latent states are approximated. The proposed model and the developed MCMC algorithms are illustrated by using both simulated and actual financial transaction data. For model selection, a Bayesian deviance information criterion is calculated to compare our model with other competing models in the literature. Overall, we find that the threshold SCD model performs better than the SCD model when a single positive distribution is assumed for the innovation of the duration equation.