NON-PARAMETRIC METHOD FOR DETECTING BREAKDOWN OF TIME SERIES USING THE RANDOM WALKS THEORY MECHANISM
Abstract
The task of the on-line detection of a sudden change in the probability properties of a time series is 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 this topic is noted, which is due to the emergence of ever new applied problems where methods and algorithms for breakdown detecting can be successfully used - in particular, when creating monitoring systems in industry, ecology, medicine, etc. Two main varieties of methods for breakdown detecting are discussed: parametric and nonparametric. It is noted that, although nonparametric methods, ceteris paribus, 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 detailed information about the probabilistic properties of the controlled process. This is fundamentally important for building monitoring systems, when detailed information about these properties may either be completely absent and then it is necessary to conduct a rather laborious preliminary study of it, or to be unreliable. An original sequential nonparametric algorithm for detecting discord is proposed based on the implementation of the random walk mechanism or, more specifically, using the theory of success runs. The operating principle of the control algorithm is explained and its description is given. The results of the study of the basic statistical characteristics of the algorithm, including the determination of its effectiveness, and results of comparison with known parametric methods, are given. The area of possible practical 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 monitoring systems for various purposes are noted.
