The Time Series Analysis of Compositional Data Teresa M. Brunsdon and T.M.F. Smith Abstract: The analysis of repeated surveys can be approached using modelbased 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 sumconstrained 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. Keywords: Repeated surveys; additive logistic transformation; VARMA; dependence; labour force survey.
