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The purpose of this paper is to provide a discussion, with illustratingexamples, on Bayesian forecasting for dynamic generalized linear models(DGLMs). Adopting approximate Bayesian analysis, based on conjugate forms andon Bayes linear estimation, we describe the theoretical framework and then weprovide detailed examples of response distributions, including binomial,Poisson, negative binomial, geometric, normal, log-normal, gamma, exponential,Weibull, Pareto, beta, and inverse Gaussian. We give numerical illustrationsfor all distributions (except for the normal). Putting together all the abovedistributions, we give a unified Bayesian approach to non-Gaussian time seriesanalysis, with applications from finance and medicine to biology and thebehavioural sciences. Throughout the models we discuss Bayesian forecastingand, for each model, we derive the multi-step forecast mean. Finally, wedescribe model assessment using the likelihood function, and Bayesian modelmonitoring.

Dynamic generalized linear models for non-Gaussian time series forecasting