Detecting Abrupt Changes in High-Dimensional Self-Exciting Poisson Processes

Spectra of some self - exciting and mutually exciting point processes

In recent years methods of data analysis for point processes have received some attention, for example, by Cox & Lewis (1966) and Lewis (1964). In particular Bartlett (1963a, b) has introduced methods of analysis based on the point spectrum. Theoretical models are relatively sparse. In this paper the theoretical properties of a class of processes with particular reference to the point spectrum ...

Detecting Abrupt Changes by Wavelet Methods

The objective of this paper is to contribute to the methodology available for dealing with the detection and the estimation of the location of discontinuities in one dimensional piecewise smooth regression functions observed in white Gaussian noise over an interval. Our approach is nonparametric in nature because the unknown function is not assumed to have any speciic form. Our method relies up...

On Detecting Abrupt Changes in Network Entropy Time Series

In recent years, much research focused on entropy as a metric describing the “chaos” inherent to network traffic. In particular, network entropy time series turned out to be a scalable technique to detect unexpected behavior in network traffic. In this paper, we propose an algorithm capable of detecting abrupt changes in network entropy time series. Abrupt changes indicate that the underlying f...

Self-exciting point processes with applications in finance and medicine

The Marginalized Likelihood Ratio Test for Detecting Abrupt Changes

The generalized likelihood ratio (GLR) test is a widely used method for detecting abrupt changes in linear systems and signals. In this paper the marginalized likelihood ratio (MLR) test is introduced for eliminating three shortcomings of GLR, while preserving its applicability and generality. Firstly, the need for a user-chosen threshold is eliminated in MLR. Secondly, the noise levels need no...