An adaptive cumulative sum method for monitoring integer-valued time-series data

Abstract

In this paper, we propose an adaptive CUSUM monitoring method for detecting step and linear trend changes in count-data time-series. The data is represented using a seasonal INGARCH time series model and an exponential smoother is used to estimate level or trend changes in the data in the cumulative-sum (CUSUM) detector. In a simulation study, the proposed approach is compared to existing CUSUM approaches that are tuned for a specific shift size and the ability of the methods to detect step shifts and linear trends is investigated. The application of the proposed method in public health surveillance is demonstrated using a real infectious disease count data set.