Dynamic generalized linear model via product partition model

Abstract

Bayesian methods applied to time series have begun receiving highlighted when the class of dynamic linear models (DLM's) was de ned. The need of working with nonnormal time series have attracted a lot of interest during the years. The class of dynamic generalized linear models (DGLM's) is an atrractive extension of the DLM for observationsin the exponential family and, in turn, corresponds to an extension of generalized linear model allowing the parameters to be time-varying. Recurrently, these time series may be aect by external events that can change the structure of the series, resulting in a change point problem. The product partition model (PPM) appears as an attractive alternative to identify multiple change points. In this work, we proposed to extend theclass of dynamic generalized linear models by using the product partition model in order to accommodate time series in the exponential family within the change point problem. In this fashion, the PPM provides a blocking structure for the data, and the traditional inference of the DGLM is performed, but instead of making inference for each observation,the inference takes place by blocks of observations, implying that observations in the same block will have a common state parameter. The new class proposed is a wider class, since it guarantees all the exibility of the DGLM along with the ability to detect change point problems through the PPM framework. In this work, we analyzed real dataaiming to illustrate the usefulness of the proposed model.