Extended dynamic generalized linear models: The two-parameter exponential family

A Bayesian framework for estimation and prediction of dynamic models for observations from the two-parameter exponential family is developed. Different link functions are introduced to model both the mean and the precision in the exponential family allowing the introduction of covariates and time series components such as trend and seasonality. Conjugacy and analytical approximations are explored under the class of partially specified models to keep the computation fast. Due to the sequential nature of the proposed algorithm, all the advantages of sequential analysis, such as monitoring and intervention, can be applied to cope with the two-parameter exponential family models. The methodological novelties are illustrated with a simulation study and two applications to real data. The first application considers a well known financial time series regarding IBM stock returns modeled as following a gamma distribution. The second considers macroeconomic variables of the United Kingdom modeled as beta distributed data.