An autoregressive process for Beta random variables

Abstract

Two stationary first-order autoregressive processes with Beta marginal distributions are presented. They are both linear, additive processes but the coefficients are Beta random variables. Their autocorrelation functions are investigated: One is positive and the other alternates in sign. The usefulness of the models in simulatino is discussed. The Bivariate Beta distributions are two consecutive observations are considered in some detail. Several examples are given, including a Bivariate Uniform process which is also examined in detail. The relationship of these Bivariate Beta distributions to the Dirichelet distribution is discussed.