Modelling compositional time series from repeated surveys - ARCHIVED

A compositional time series is defined as a multivariate time series in which each of the series has values bounded between zero and one and the sum of the series equals one at each time point. Data with such characteristics are observed in repeated surveys when a survey variable has a multinomial response but interest lies in the proportion of units classified in each of its categories. In this case, the survey estimates are proportions of a whole subject to a unity-sum constraint. In this paper we employ a state space approach for modelling compositional time series from repeated surveys taking into account the sampling errors. The additive logistic transformation is used in order to guarantee predictions and signal estimates bounded between zero and one which satisfy the unity-sum constraint. The method is applied to compositional data from the Brazilian 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.