On the iterative plug-in algorithm for estimating diurnal patterns of financial trade durations

This paper discusses the detailed performance of an iterative plug-in (IPI) bandwidth selector for estimating the diurnal duration pattern in a recently proposed semiparametric autoregressive conditional duration (SemiACD) model. For this purpose an alternative formula of the asymptotically optimal bandwidth is proposed. A large simulation study was carried out based on this new formula. The effect of different factors, which affect the selected bandwidth is discussed in detail. It is shown that the proposed IPI algorithm works very well in practice and that the SemiACD model in general, is clearly superior to the parametric ACD model, if there is a deterministic trend in the duration data. It is also shown that the quality of the bandwidth selection, the diurnal pattern estimate and the parametric estimation will all be clearly improved, if the sample size is enlarged. Furthermore, according to the goodness-of-fit of the estimated diurnal pattern, a best combination of the above mentioned factors is found.