Time Series of Continuous Proportions

Gary K. Grunwald, Adrian E. Raftery, Peter Guttorp

Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 1993 · Volume 55 · Issue 1

DOI: 10.1111/j.2517-6161.1993.tb01470.x

Abstract

A vector of continuous proportions consists of the proportions of some total accounted for by its constituent components. An example is the proportions of world motor vehicle production by Japan, the USA and all other countries. We consider the situation where time series data are available and where interest focuses on the proportions rather than the actual amounts. Reasons for analysing such times series include estimation of the underlying trend, estimation of the effect of covariates and interventions, and forecasting. We develop a state space model for time series of continuous proportions. Conditionally on the unobserved state, the observations are assumed to follow the Dirichlet distribution, often considered to be the most natural distribution on the simplex. The state follows the Dirichlet conjugate distribution which is introduced here. Thus the model, although based on the Dirichlet distribution, does not have its restrictive independence properties. Covariates, trends, seasonality and interventions may be incorporated in a natural way. The model has worked well when applied to several examples, and we illustrate with components of world motor vehicle production.

Keywords

bayesian forecasting, compositional data, dirichlet distribution, recursive updating, state space model

Enable JavaScript for citation tools and additional paper interactions.