Some developments on seasonal INAR processes with application to influenza data

Area of Science:

• Epidemiology
• Biostatistics
• Time Series Analysis

Background:

• Influenza epidemic data exhibit seasonality and often present challenges such as zero-inflation, zero-deflation, overdispersion, and underdispersion.
• Traditional count data models may not adequately capture these complex features inherent in disease incidence.
• Understanding and modeling these characteristics are crucial for accurate epidemic forecasting and public health interventions.

Purpose of the Study:

• To introduce a flexible statistical model for nonnegative integer-valued time series data with a seasonal autoregressive structure.
• To address and explain the common features observed in influenza case count data, including seasonality and dispersion issues.
• To evaluate the performance of the proposed model against existing methods for analyzing influenza epidemic data.

Main Methods:

• Development of a flexible seasonal integer autoregressive (INAR(p)) model for nonnegative integer-valued time series.
• Discussion of probabilistic properties for the general seasonal INAR(p) model.
• Application of three estimation methods for parameter estimation in the specialized seasonal INAR(1) model.
• Performance evaluation of estimation procedures through simulation studies.
• Analysis of weekly influenza data using the proposed model.

Main Results:

• The proposed seasonal INAR(p) model effectively captures the characteristics of influenza count data, including seasonality and dispersion.
• Simulation studies confirmed the satisfactory performance of the developed estimation methods for the seasonal INAR(1) model.
• Empirical analysis of weekly influenza data from Baden-Württemberg, Germany, demonstrated the model's practical applicability.
• The suggested model outperformed existing models in analyzing the provided influenza dataset.

Conclusions:

• The developed flexible seasonal integer autoregressive model provides a robust framework for analyzing count time series data with seasonal patterns.
• The model's ability to handle zero-inflation and overdispersion makes it a valuable tool for influenza data analysis.
• The proposed model offers improved accuracy and performance over existing methods for understanding and forecasting influenza epidemics.