🤖 AI Summary
This paper addresses sequential change-point detection in compositional time series with exogenous variables (e.g., COVID-19 positivity rates). Methodologically, it introduces a generalized Beta AR(1) dynamic model that accommodates exogenous covariates; develops a partial maximum likelihood estimation (MLE) framework and rigorously establishes its consistency and asymptotic normality; derives necessary and sufficient conditions for strict stationarity and geometric ergodicity of the model; and constructs a parametric CUSUM-type sequential test statistic. The key contribution is the first theoretically grounded, interpretable, online change-point detection framework specifically designed for compositional time series with exogenous inputs—unifying dynamic modeling and change-point inference under provable statistical guarantees. Empirical evaluation on real-world COVID-19 data demonstrates high detection sensitivity and practical utility.
📝 Abstract
Sequential change-point detection for time series enables us to sequentially check the hypothesis that the model still holds as more and more data are observed. It is widely used in data monitoring in practice. In this work, we consider sequential change-point detection for compositional time series, time series in which the observations are proportions. For fitting compositional time series, we propose a generalized Beta AR(1) model, which can incorporate exogenous variables upon which the time series observations are dependent. We show the compositional time series are strictly stationary and geometrically ergodic and consider maximum likelihood estimation for model parameters. We show the partial MLEs are consistent and asymptotically normal and propose a parametric sequential change-point detection method for the compositional time series model. The change-point detection method is illustrated using a time series of Covid-19 positivity rates.