We congratulate the authors for a remarkable paper, which addresses a problem of fundamental practical importance: parameter estimation in state space models by using sequential Monte Carlo (SMC) algorithms. In Belmonte et al. (2008) we fit duration state space models to high frequency transaction data and we require a computational methodology that can handle efficiently time series of length T =O.104–105/. We have experimented with particle Markov chain Monte Carlo (PMCMC) methods and with the smooth particle filter (SPF) of Pitt (2002). The latter is also based on the use of SMC algorithms to derive maximum likelihood parameter estimates; it is, however, limited to scalar signals. Therefore, in the context of duration modelling this limitation rules out multifactor or multi-dimensional models, and we believe that PMCMC methods can be very useful in such cases.