A Non-Parametric Approach for Change-Point Detection of Multi-Parameters in Time-Series Data

Abstract

Change-point analysis of time-series data plays a vital role in various fields of earth sciences under changing environments. Most of the analysis approaches were usually designed to detect the change-point in the level of time-series mean. In this study, we aimed to propose a non-parametric approach to detect the change-point of different parameters of time-series data. In this approach, the Boot- strap method, coupling with Kernel density estimation, was first used to estimate the probability distribution function (pdf) of a parameter before and after any potential change-points. Second, the Ar-index based on the uncross area of the two pdfs was designed to quantify the difference of the parameter before and after each potential change-point. Finally, the potential change-point owning the largest Ar-index value was determined as the locations of the change-point of the parameter. The hydrological extreme series from four stations in the Hanjiang basin were used to demonstrate this approach. The Pettitt test method commonly used in hydrology was employed as a comparison to indirectly analyze the reliability of the proposed approach. The results show that change-point detected by the proposed approach in the four stations are identified with those detected by the Pettitt approach in the level of time-series mean. But in comparison with the Pettitt test, the proposed approach can provide more detection information for other parameters, such as coefficient of variation (Cv) and coefficient of skewness (Cs) of the series. The results also show that the degree of change in the series mean is greater than its Cv and Cs, while the degree of change in series Cv is greater than its Cs.

Keywords: time-series data, change-point analysis, multi-parameters, bootstrap method, kernel density estimation