Advances in Count Time Series: Addressing Zero Inflation and Structural Breaks in INAR Models

I. Pereira, M. Monteiro

Integer-valued autoregressive (INAR) models have become a cornerstone for analyzing count time series, using thinning operators to emulate autoregressive processes while handling discrete data. They can accommodate both equidispersion and overdispersion, features commonly observed in count data.
This work reviews INAR models, detailing their structure and thinning operators in generating stationary count time series. It then explores zero-inflated INAR models for datasets with excess zeros. We further examine INAR models with structural breaks, focusing on detecting and estimating parameter shifts over time—critical for dynamic processes like epidemics or policy changes. Both equidispersed and overdispersed innovations are considered. Parameter estimation is discussed using classical and Bayesian methods, comparing frequentist and Bayesian approaches in identifying change points. A real-world health application demonstrates these models’ ability to capture complex count dynamics.

Keywords: INAR model, MCMC, structural break, zero inflation

FENStatS-SEIO: Statistics and Data Science
June 11, 2025  10:30 AM
Auditorio 1. Ricard Vinyes

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