Extended Dynamic Generalized Linear Models: the two-parameter exponential family

TL;DR

This paper introduces a Bayesian framework for dynamic modeling of two-parameter exponential family distributions, enabling flexible mean and precision modeling with efficient computation, demonstrated through real-world economic data applications.

Contribution

It extends existing dynamic generalized linear models to incorporate two-parameter exponential families with new link functions and computational methods.

Findings

Effective modeling of unemployment rates in Brazil.

Successful application to UK macroeconomic variables.

Maintains computational efficiency with analytical approximations.

Abstract

We develop a Bayesian framework for estimation and prediction of dynamic models for observations from the two-parameter exponential family. 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. We explore conjugacy and analytical approximations under the class of partial specified models to keep the computation fast. The algorithm of West, Harrison and Migon (1985) is extended to cope with the two-parameter exponential family models. The methodological novelties are illustrated with two applications to real data. The first, considers unemployment rates in Brazil and the second some macroeconomic variables for the United Kingdom.