Change detection in non-stationary Hawkes processes through sequential testing

Department of Mathematical Sciences, Bentley University, 175 Forest Street, Waltham, Massachusetts, United States of America

^* Corresponding author: mbhaduri@bentley.edu

Abstract

Detecting changes in an incoming data flow is immensely crucial for understanding inherent dependencies, formulating new or adapting existing policies, and anticipating further changes. Distinct modeling constructs have triggered varied ways of detecting such changes, almost every one of which gives in to certain shortcomings. Parametric models based on time series objects, for instance, work well under distributional assumptions or when change detection in specific properties - such as mean, variance, trend, etc. are of interest. Others rely heavily on the “at most one change-point” assumption, and implementing binary segmentation to discover subsequent changes comes at a hefty computational cost. This work offers an alternative that remains both versatile and untethered to such stifling constraints. Detection is done through a sequence of tests with variations to certain trend permuted statistics. We study non-stationary Hawkes patterns which, with an underlying stochastic intensity, imply a natural branching process structure. Our proposals are shown to estimate changes efficiently in both the immigrant and the offspring intensity without sounding too many false positives. Comparisons with established competitors reveal smaller Hausdorff-based estimation errors, desirable inferential properties such as asymptotic consistency and narrower bootstrapped margins. Four real data sets on NASDAQ price movements, crude oil prices, tsunami occurrences, and COVID-19 infections have been analyzed. Forecasting methods are also touched upon.