The time series analysis of compositional data

The analysis of repeated surveys can be approached using model-based inference, utilising the methods of time series analysis. On a long run of repeated surveys it should then be possible to enhance the estimation of a survey parameter. However, many repeated surveys that are suited to this approach consist of variables that are proportions, and hence are bounded between 0 and 1. Furthermore interest is often in a multinomial vector of these proportions, that are sum-constrained to 1, i.e., a composition. A solution to using time series techniques on such data is to apply an additive logistic transformation to the data and then to model the resulting series using vector ARMA models. Here the additive logistic transformation is discussed which requires that one variable be selected as a reference variable. Its application to compositional time series is developed, which includes the result that the choice of’reference variable will not affect any final results in this context. The discussion also includes the production of forecasts and confidence regions for these forecasts. The method is illustrated by application to the Australian Labour Force Survey.