A Time-Varying Zero-Inflated Generalized Poisson INGARCH Model

Thomas M. Menino Convention & Exhibition Center 

Count time series arising in public health, epidemiology, and finance often exhibit serial dependence, excess zeros, and time-varying dispersion features that are inadequately captured by standard Poisson models. We propose a time-varying zero-inflated generalized Poisson INGARCH (TV-ZIGP-INGARCH) framework that simultaneously accommodates serial dependence, dynamic zero inflation, and evolving dispersion. In the proposed model, the conditional mean (intensity) follows an INGARCH-type evolution, while both the zero-inflation probability and the dispersion parameter are allowed to vary over time as functions of past observations and exogenous covariates. This structure enables the model to capture evolving structural zeros, periods of under- and over-dispersion, and nonstationary behavior within a unified count time-series framework. Parameter estimation is conducted using both maximum likelihood and expectation maximization approaches. Applications to real-world count time series show substantial gains in goodness-of-fit and predictive accuracy, particularly during periods characterized by changing zero-inflation intensity and dispersion.

Count time series

Zero-inflated models

Generalized Poisson distribution

INGARCH models

Time-varying parameters. 

Section on Statistics in Epidemiology