Retrospective change detection for binary time series models

• Retrospective, or off-line change detection procedures are proposed for autocorrelated binary time series.
• The test statistic is based on the standardized multidimensional partial efficient score process.
• Logistic regression describes the relationship between the parameters and the binary responses.
• Examples on surgeon performance and IBM transactions data demonstrate the easy applicability.
• Monte Carlo experiments show excellent control over the type I error and the power properties.

Detection of changes in health care performance, financial markets, and industrial processes have recently gained momentum due to the increased availability of complex data in real-time. As a consequence, there has been a growing demand in developing statistically rigorous methodologies for change-point detection in various types of data. In many practical situations, the data being monitored for the purpose of detecting changes are autocorrelated binary time series. We propose a new statistical procedure based on the partial likelihood score process for the retrospective detection of change in the coefficients of a logistic regression model with AR(p)-type autocorrelations. We carry out some Monte Carlo experiments to evaluate the power of the detection procedure as well as its probability of false alarm (type I error). We illustrate the utility using data on 30-day mortality rates after cardiac surgery and to data on IBM share transactions.