Time Series of Continuous Proportions

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 wher...

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Bibliographic Details
Published in:Journal of the Royal Statistical Society. Series B, Methodological Methodological, 1993-01, Vol.55 (1), p.103-116
Main Authors: Grunwald, Gary K., Raftery, Adrian E., Guttorp, Peter
Format: Article
Language:English
Subjects:
Approximation
bayesian forecasting
compositional data
dirichlet distribution
Exact sciences and technology
Forecasting models
Gross national product
Inference from stochastic processes
time series analysis
Mathematical independent variables
Mathematical vectors
Mathematics
Motor vehicles
Probability and statistics
recursive updating
Sciences and techniques of general use
state space model
Statistical forecasts
Statistics
Time series
Time series forecasting
Time series models
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Summary: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.
ISSN:0035-9246
1369-7412
2517-6161
1467-9868
DOI:10.1111/j.2517-6161.1993.tb01470.x