Product Partition Dynamic Generalized Linear Models

TL;DR

This paper introduces DGLM-PPM, a Bayesian framework combining Dynamic Generalized Linear Models with Product Partition Models for effective change-point detection in time-series data, applicable to exponential family distributions.

Contribution

It extends PPM to DGLM, enabling Bayesian multiple change-point detection in dynamic regression models with exponential family distributions.

Findings

Accurately estimates dynamic parameters.

High change-point detection probability.

Outperforms conventional DGLM in fit measures.

Abstract

Detection and modeling of change-points in time-series can be considerably challenging. In this paper we approach this problem by incorporating the class of Dynamic Generalized Linear Models (DGLM) into the well know class of Product Partition Models (PPM). This new methodology, that we call DGLM-PPM, extends the PPM to distributions within the Exponential Family while also retaining the flexibility of the DGLM class. It also provides a framework for Bayesian multiple change-point detection in dynamic regression models. Inference on the DGLM-PPM follow the steps of evolution and updating of the DGLM class. A Gibbs Sampler scheme with an Adaptive Rejection Metropolis Sampling (ARMS) step appended is used to compute posterior estimates of the relevant quantities. A simulation study shows that the proposed model provides reasonable estimates of the dynamic parameters and also assigns high change-point probabilities to the breaks introduced in the artificial data generated for this work. We also present a real life data example that highlights the superiority of the DGLM-PPM over the conventional DGLM in both in-sample and out-of-sample goodness of fit measures.