Forecasting compositional time series

Compositional data sets occur in many disciplines and give rise to some interesting statistical considerations. In recent years, the modelling and forecasting of compositional time series has seen some important developments, although this approach does not seem to be widely known. This paper represents a modest step towards rectifying this. After briefly setting out the basic structure of compositional data sets and outlining the implications for forecasting compositional time series, it illustrates the techniques using three examples: modelling and forecasting expenditure shares in the U.K. economy; forecasting trends in obesity in England; and examining shifts in the proportions of English first class cricketers born during particular quarters of the year.