Time Series Modelling of Daily Tax Revenues

We provide a detailed discussion of the time series modelling of daily tax revenues. The mainfeature of daily tax revenue series is the pattern within calendar months. Standard seasonal timeseries techniques cannot be used since the number of banking days per calendar month varies andbecause there are two levels of seasonality: between months and within months.We start the analysis with a periodic regression model with time varying parameters.This modelis then extended with a component for intra-month seasonality, which is specified as a stochasticcubic spline. State space techniques are used for recursive estimation and evaluation as they allowfor irregular spacing of the time series.The model is recently made operational and used for daily forecasting at the Dutch Ministry ofFinance. For this purpose a front-end for model configuration and data input is implemented withVisual C++, while statistical tools and graphical diagnostics are built around Ox and SsfPack. Wepresent the current model and forecasting results up to December 1999. The model and itsforecasts are evaluated.