An integer GARCH model for a Poisson process with time-varying zero-inflation

Area of Science:

• Statistics
• Biostatistics
• Epidemiology

Background:

• Count data time series, such as infectious disease outbreaks, often exhibit excess zeros and temporal dependence.
• Existing models may not adequately capture the dynamic nature of zero-inflation and count intensity over time.

Purpose of the Study:

• To propose a novel serially dependent Poisson process model with time-varying zero-inflation.
• To investigate the performance of expectation maximization (EM) and maximum likelihood estimation (MLE) for parameter estimation.
• To evaluate the model's fit against existing methods using real-world infant mortality data.

Main Methods:

• Development of an integer-valued generalized autoregressive conditional heteroscedastic (INGARCH) model with a time-varying zero-inflation parameter.
• Implementation of both EM and MLE for parameter estimation.
• Application and comparison with existing zero-inflated INGARCH models on infant death data.

Main Results:

• Simulation studies demonstrated that both EM and MLE provide accurate parameter estimates.
• The proposed INGARCH model showed a superior fit to infant mortality data compared to existing zero-inflated INGARCH models.
• An extended non-linear INGARCH model with zero-inflation and exogenous input showed comparable performance on some criteria.

Conclusions:

• The proposed time-varying zero-inflated INGARCH model is effective for analyzing infectious disease count data.
• This model offers improved flexibility and fit over existing methods for count time series with dynamic excess zeros.
• Further research can explore extensions and applications in various epidemiological contexts.