Sequential Change-point Detection for Binomial Time Series

A binomial time series describes binary behaviors of individuals within a group, which depend on group behaviors in the past. Binomial time series data is widely applied in fields such as infection tracking and behavior analysis. In this paper, we introduce a generalized Binomial AR($p$) model with exogenous variables based on Generalized Linear Model (GLM), prove the statistical properties of the model when $p = 1$, and provide a parameter estimation method. Then, we propose a sequential change-point detection method for the generalized Binomial AR(1) model, facilitate real-time data monitoring and triggering alarms when a change point is detected. We apply the generalized Binomial AR(1) model to weekly pneumonia \& influenza mortality data and successfully identify change points related to the COVID-19 outbreak using the proposed method.