Forecasting the daily balance of the Dutch Giro

This paper is based on a consultancy project for the Dutch Postal Clearing Service, the ‘Giro’. The Giro plays an important part in transactions in the Netherlands. Specifically salary payments to households are important. As most of these take place on rather fixed days each month, and also have yearly patterns, the balance of the giro shows strong calendar variations and seasonality. Apart from that there are clearly trend movements. To develop a model to forecast all these movements was the goal of the project. This succeeded but the resulting model appeared much more complex than expected. Instead of the balance several flows of money going into and out of the system were modelled. Moreover each flow was decomposed into monthly aggregates showing trends and seasonality and the distribution of the aggregates over the days in each month showing all kinds of calendar effects. For all the submodels several possibilities have been tried, evolving from ad hoc solutions based on traditional time-series models to solutions based on the Kalman-filter. Around 1983 we discovered the latter possibilities, mainly due to the work of Harvey (1981). The Kalman-filter has a great appeal as a unified framework. Moreover the certainty that the specified models are optimally estimated — often not possible with ad hoc solutions — is reassuring.