Bayesian generalizations of the integer-valued autoregressive model

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.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

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.