Time Series Analysis of Compositional Data Using a Dynamic Linear Model Approach

Compositional time series data comprises of multivariate observations that at each time point are essentially proportions of a whole quantity. This kind of data occurs frequently in many disciplines such as economics, geology and ecology. Usual multivariate statistical procedures available in the literature are not applicable for the analysis of such data since they ignore the inherent constrained nature of these observations as parts of a whole. This article describes new techniques for modeling compositional time series data in a hierarchical Bayesian framework. Modified dynamic linear models are fit to compositional data via Markov chain Monte Carlo techniques. The distribution of the underlying errors is assumed to be a scale mixture of multivariate normals of which the multivariate normal, multivariate t, multivariate logistic, etc., are special cases. In particular, multivariate normal and Student-t error structures are considered and compared through predictive distributions. The approach is illustrated on a data set.