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Abstract:
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Point processes, often of the Poisson type, offer a framework to model random events evolving in continuous time, and the self-exciting subclass tackles cases where the occurrence of one inflates or deflates the occurrence probability of another in an immediate neighborhood. Examples include an earthquake and its aftershocks, a sequence of landslides, a tweet and its re-tweets, and several others. There exist combinations of underlying intensities, especially close similarities between the pre- and post-change flow that make the detection and estimation of changes in the first or second generation sub-process quite hard. Through extensive simulations and real applications, this work examines how a newly developed statistic, formed through switching the usual flow of time, aids the detection exercise. Improvements over established competitors have been quantified, optimal intensity classes have been characterized, and generalizations have been described.
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