Modelling Intra-day Seasonality and Forecasting Densities in Financial Duration Data

In this paper we model intra-daily seasonality in the shape of the residual distribution of the standard ACD model, which is estimated using diurnally (seasonally) adjusted duration data. Specifically, for two of the three companies in our sample, the shapes of the residual distribution for periods corresponding to the mornings and afternoons in a trading day are virtually identical, and are different from the shape of the residual distribution corresponding to the lunch time period. As a next step, we investigate whether the observed seasonality can explain the bias in density and interval ACD model forecasts, which are popular tools for econometric model evaluation and comparison.