Nonparametric Test for Change Point Detection in Time Series

Dmitriy Klyushin (1), Irina Martynenko (2)

1 - Taras Shevchenko National University of Kyiv, prospect Glushkova 4D, Kyiv, 03680, Ukraine
2 -Academy of Labour Social Relations and Tourism, 3-A, Kiltseva doroha, Kyiv, 03187, Ukraine


Abstract
We describe new nonparametric tests for detection change points of the time series, which are the points dividing the time series into segments of random values obeying different distributions. The proposed tests are based on the Dempster–Hill theory and generalizations of the Bernoulli scheme. To recognize the change points, simplified versions of the Klyushin–Petunin homogeneity test are proposed. The significance level of these tests does not exceed 0.05, and the accuracy is comparable to the original version. The tests have high sensitivity and specificity of recognizing the heterogeneity of two random samples with different means and the same variances or equal means but different variances. The described tests can be useful in a wide variety of areas from healthcare (for example, when analyzing time series generated by pulse oximeters) to IoT devices in industry and in everyday life.