Beta-Gamma Time Series Models with Discounting

Abstract

We review the properties and applications of the beta-gamma model, a Markov process whose marginal distribution is a gamma distribution at each time point. For the conjugacy of gamma distributions as the priors for the Gaussian precision and Poisson rate, the beta-gamma model has been used as the state equation of the Gaussian/Poisson state space models, enabling fast,analytical computation of the online and retrospective posterior distributions and predictive distributions. Typical applications include the sequential analysis of volatilities and steaming count-valued data.