Modelling compositional time series from repeated surveys

A compositional time series is defined as multivariate time series in which each of the series has values bounded betweenzero and one and the sum of the series equals one at each time point. Data with such characteristics are observed in repeatedsurveys when a survey variable has a multinomial response but interest lies in the proportion of units classified in each of itscategories. In this case, the survey estimates are proportions of a whole subject to a unitysum constraint. In this paper we employ a state space approach for modelling compositional time series from repeated surveys taking into account thesampling errors. The additive logistic transformation is used in order to guarantee predictions and signal estimates boundedbetween zero and one which satisfy the unitysumconstraint. The method is applied to compositional data from theBrazilian Labour Force Survey. Estimates of the vector of proportions and the unemployment rate are obtained. In addition,the structural components of the signal vector, such as the seasonals and the trends, are produced.