Bayesian generalizations of the integer-valued autoregressive model

Paulo C Marques F; Helton Graziadei; Hedibert F Lopes

doi:10.1080/02664763.2020.1812544

Bayesian generalizations of the integer-valued autoregressive model

J Appl Stat. 2020 Aug 31;49(2):336-356. doi: 10.1080/02664763.2020.1812544. eCollection 2022.

Authors

Paulo C Marques F¹, Helton Graziadei², Hedibert F Lopes¹

Affiliations

¹ Insper Institute of Education and Research, São Paulo, Brazil.
² Instituto de Matemática e Estatística, Universidade de São Paulo, São Paulo, Brazil.

Abstract

We develop two Bayesian generalizations of the Poisson integer-valued autoregressive model. The AdINAR(1) model accounts for overdispersed data by means of an innovation process whose marginal distributions are finite mixtures, while the DP-INAR(1) model is a hierarchical extension involving a Dirichlet process, which is capable of modeling a latent pattern of heterogeneity in the distribution of the innovations rates. The probabilistic forecasting capabilities of both models are put to test in the analysis of crime data in Pittsburgh, with favorable results.

Grants and funding

Helton Graziadei and Hedibert F. Lopes thank Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) for financial support through grants numbers 2017/10096-6 and 2017/22914-5.