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 U.S. tax revenues from each of personal tax, corporate tax and social tax. We consider the situation where time series data are available and where interest focuses on theprop(}.rti?~srath7r thaIl.tbe ··actual aIl1ounts. Reasons foranaly:z;ingsul:h •• tiIl1eseries include estimation of the underlying trend, estimation of the effect of covariates and interventions, and forecasting. We develop a state space mode! 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. distribtItion •. OIl. the siIl1ple;<.1'hestate> follows •the Dirichlet-conjugate (DC) distribution which is .introduced here. Thus the model, while based on the Dirichlet distribution, does not have its restrictive independence properties. The state transition distribution, or "state equation ", allows for the ccvariates, trends, seasonality and a model to work to the tax p.v'~"""'T"lI"" forecasting; data; disUL'JUI.LVJ,l. Recersive updating; State Gary K. Grunwald is Lecrurer j Tempcrsry), Department of Statistics. of Melbourne, Parkville, Viaoria 3052, E. Raftery fa Associate of and SociQlogy, WA Professor, of Wuhington, Seattle, WA 98195. The research of Grunwa14 and was supported by National Seienee Foundation Grant no. SES-&615S41. The research of was partially supported by a cooperarrve agreement between the United States Environmental Prctecnon Agency and the Societal Institute for Mad:u:matica1 Sciences, The authors are grateful to Michael Kahn for comments.