| Point processes often serve as a natural language to chronicle an event's temporal evolution, and significant changes in the flow, synonymous with non-stationarity, are usually triggered by assignable and frequently preventable causes, often heralding devastating ramifications. Examples include amplified restlessness of a volcano, increased frequencies of airplane crashes, hurricanes, mining mishaps, among others. Guessing these time points of changes, therefore, merits utmost care. Switching the way time traditionally propagates, we posit a new genre of bidirectional tests which, despite a frugal construct, prove to be exceedingly efficient in culling out non-stationarity under a wide spectrum of environments. A journey surveying a lavish class of intensities, ranging from the tralatitious power laws to the deucedly germane rough steps, tracks the established unidirectional forward and backward test's evolution into a p-value induced dual bidirectional test, the best member of the proffered category. Niched within a hospitable Poissonian framework, this dissertation, through a prudent harnessing of the bidirectional category's classification prowess, incites a refreshing alternative to estimating changes plaguing a soporific flow, by conducting a sequence of tests. Validation tools, predominantly graphical, rid the structure of forbidding technicalities, aggrandizing the swath of applicability. Extensive simulations, conducted especially under hostile premises of hard non-stationarity detection, document minimal estimation error and reveal the algorithm's obstinate versatility at its most unerring. |
