Change-point analysis using two-sample empirical likelihood method with applications to climatology

The change-point detection in time series analysis is the problem of discovering time points at which the properties of data change. In this paper, we deal with detecting shifts in mean values for weakly dependent data. This covers a broad range of real-world problems since the real data may have a dependence structure that violates the assumptions of some popular statistical tests. For the change-point detection, we establish and propose to use the two-sample blockwise empirical likelihood for the difference of two-sample means. We recommend to produce the adjusted p-value graphs showing not only the statistical significance, but allowing also to detect the location of the change-point graphically and numerically. We compare the two-sample empirical likelihood method by the simulation study with some classical methods for the change-point detection and show the advantages of the method for weakly dependent observations. Using the historical wind speed observations in Latvia, we demonstrate the applicability of the proposed method to the real data. The method has been implemented using the R-package EL, which deals with different two-sample problems.