Time Series of Proportions: A Compositional Approach

Taking account of the compositional nature of proportions, the logistic function is the natural transformation to apply when analyzing and modelling time series of continuous proportions. From the metric structure on the simplex, an isomorphic structure is defined on the set of continuous proportions. This structure permits the translation of the standard analysis of univariate time series to the compositional analysis of proportions in which the logistic transformation arises naturally and not as a mere alternative to the transformation of the data.