Monitoring of count data time series: Cumulative sum change detection in Poisson integer valued GARCH models

This article presents a cumulative sum (CUSUM) monitoring approach for count-data time series. A seasonal integer-valued generalized autoregressive conditional heteroscedasticity (INGARCH(1,1)) time series model with Poisson deviates is used to develop a likelihood ratio test formulation to detect changes in the process accounting for temporal correlations and seasonality. Simulation studies show that the proposed CUSUM monitoring approach can provide significantly improved performance in applications where serial correlation or seasonality is prevalent. A case study with real traffic crash counts is presented to illustrate the application of the proposed methodology for roadway safety improvement.