NON-PARAMETRIC METHOD FOR DETECTING BREAKDOWN OF TIME SERIES USING THE RANDOM WALKS THEORY MECHANISM
G. F. Filaretov, Zineddin Bouchaala · Известия Южного федерального университета. Технические науки · 2020
The task of the on-line detection of a sudden change in the probability properties of a time seriesis considered, which is usually interpreted as the detecting task of change point the characteristics(breakdown) in the observed stochastic process. The actuality of the development of research on thistopic is noted, which is due to the emergence of ever new applied problems where methods and algorithmsfor breakdown detecting can be successfully used - in particular, when creating monitoring systemsin industry, ecology, medicine, etc. Two main varieties of methods for breakdown detecting arediscussed: parametric and nonparametric. It is noted that, although nonparametric methods, ceterisparibus, are inferior to parametric methods in terms of efficiency (the speed of breakdown detecting),they also have a number of advantages, without requiring, in particular, for their application detailedinformation about the probabilistic properties of the controlled process. This is fundamentally importantfor building monitoring systems, when detailed information about these properties may either be completelyabsent and then it is necessary to conduct a rather laborious preliminary study of it, or to beunreliable. An original sequential nonparametric algorithm for detecting discord is proposed based onthe implementation of the random walk mechanism or, more specifically, using the theory of successruns. The operating principle of the control algorithm is explained and its description is given. The resultsof the study of the basic statistical characteristics of the algorithm, including the determination ofits effectiveness, and results of comparison with known parametric methods, are given. The area of possiblepractical use of the proposed algorithm is highlighted, where its effectiveness remains quite high.The prospects of using the proposed algorithm as part of the software and algorithmic support of monitoringsystems for various purposes are noted.