Online Change-Point Detection in Categorical Time Series

Abstract

This contribution considers the monitoring of change-points in categorical time series. In its simplest form these can be binomial or beta-binomial time series modeled by logistic regression or generalized additive models for location, scale and shape. The aim of themonitoring is to online detect a structural change in the intercept of the expectationmodel based on a cumulative sum approach known from statistical process control. This is then extended to change-point detection in multicategorical regression models such as multinomial or cumulative logit models. Furthermore, a Markov chain based method is given for the approximate computation of the runlength distribution of the proposed CUSUM detectors. The proposed methods are illustrated using three categorical time series representingmeat inspection at a Danish abattoir,monitoring the age of varicella cases at a pediatrist and an analysis of German Bundesliga teams by a Bradley-Terry model.

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