In this paper we model financial durations by discrete and continuous-time point processes in state-space form (SSF). We illustrate our analysis on a duration dataset analysed in Engle(00). For estimation of intensity and static parameters, we resort to particle filters. We compare estimates delivered by simulation-based filters, with methodology suggested in Engle(00) and Bauwens and Veredas(04).
We conclude that the smooth particle filter (SPF) of Pitt(02) is an efficient method for off-line parameter estimation and on-line filtering of univariate SSF duration models. We have applied the particle MCMC of Andrieu et. al. (10) to univariate models and offer a comparison with estimates from the SPF.