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.
Highlights
A rich class of natural and artificial phenomenon may be described adequately through the language of point processes - a probabilistic description summarizing their salient features
As a preliminary test to identify which one of the four statistics shown in Table 3 has the highest classification accuracy, we have conducted a power study summarized in Fig. 2 where the immigrant intensity λ0(.) was taken to be time-inhomogeneous and the only change was brought through the offspring kernel ω(.)
We found there is no one statistic that shows the uniformly best power and about the diagonal, there exists an asymmetry in the power surfaces
Summary
A rich class of natural and artificial phenomenon may be described adequately through the language of point processes - a probabilistic description summarizing their salient features. These occurrences may evolve over time, space, their combinations or over more abstract domains and often exhibit complex dependencies. Mathematical tractability often demands simplified constructs - detecting changes only in means or variances, for instance. The purpose of this brief communication is to examine the applicability of some of the techniques proposed recently by the first author to detect more general changes under a deterministic Poissonian framework in a stochastic intensity-driven Hawkes process scenario.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
