Сomparative analysis of algorithms for change points detection in regression models of time series
Keywords:time series, anomalies, change points detection, change detection predictive algorithms, regression models
Changes detection in the behavior of the object is one of the main goals оf any real-world objects’ monitoring. The behavior of an object can change over time due to its reaction to external events, as well as under the influence of the internal development laws of the object. Problems occur in cases when internal changes couldn't be observed directly. In such cases, it is possible to obtain information about the internal changes only through analysis of the time series observed parameters, the measurement of which could be performed technically and/or organizationally. Several changes detection algorithms in time series, which are based on the linear regression models are discussed. It is assumed that if the event of changes occurs, the time series before and the time series after the change point are described by models which cannot be considered identical. Some known algorithms for analyzing the identity of models and algorithms that have not previously been deposited in the literature are considered. In particular, an algorithm for change points detection based on changes in the values of the regression models coefficients; based on analyzing the confidence interval of the predicted values of the series; based on analyzing regression residuals based on the use of Höffding's inequality; Chow algorithms for comparing variances of residuals; an algorithm for comparing the distributions of residuals using the Kolmogorov-Smirnov's two-samples test. The variety of objects in the real world, types of changes in their behavior, which are based on the unpredictability of the reasons that caused them, do not allow choosing a single change points detection method and makes a comparative assessment of various algorithms an urgent engineering problem. The paper proposes an algorithms’ analysis depending on the types of changes that are most typical for parameters time series in various domains. The effectiveness of the algorithms is assessed by the method of the statistical experiment by their ability to detect a change, as well as by comparing the number of false detection errors and skipping real changes. The obtained results can be used for further research of algorithms, in particular, in the case of constructing an ensemble of algorithms for identifying change points of the behavior of monitored objects.
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