Nonparametric Sequential Change-point Detection on High Order Compositional Time Series Models with Exogenous Variables

Sequential change-point detection for time series is widely used in data monitoring in practice. In this work, we focus on sequential change-point detection on high-order compositional time series models. Under the regularity conditions, we prove that a process following the generalized Beta AR(p) model with exogenous variables is stationary and ergodic. We develop a nonparametric sequential change-point detection method for the generalized Beta AR(p) model, which does not rely on any strong assumptions about the sources of the change points. We show that the power of the test converges to one given that the amount of initial observations is large enough. We apply the nonparametric method to a rate of automobile crashes with alcohol involved, which is recorded monthly from January 2010 to December 2020; the exogenous variable is the price level of alcoholic beverages, which has a change point around August 2019. We fit a generalized Beta AR(p) model to the crash rate sequence, and we use the nonparametric sequential change-point detection method to successfully detect the change point.