Generalized Pareto distribution change-point detection model and its applications in modeling return period prediction

Generalized Pareto distribution (GPD) changepoint refers to the point where the quantity whose the peak over threshold changes qualitatively, which shows the change of one or more GPD parameters. In this paper, the detection issue of GPD changepoint with three parameters for extreme rainstorm data was expressed as the hypothesis test problem which could be solved by the maximum likelihood ratio test statistic. Although it is impossible to derive an exact distribution of this test statistic, fortunately, we obtained its limiting distribution by proving the limit properties of the GPD changepoint and the asymptotic convergence theorem of the test statistic. Meanwhile, the detection model we developed was used to analyze the monthly maximum precipitation data of Shenzhen with a total number of 55 years. As a result, we found the 1980s is a changepoint of Shenzhen meteorology, which is identical with the narrowest over threshold (NOT) method. In addition, the advantage of GPD changepoint method is that it ensures a consistent analytical framework before and after the detection of changepoint. In this framework, the analysis of GPD changepoint revealed that the extreme value index before that point is negative. Combining the relationship between rainfall and the return period, it might be concluded that the severity of rainstorm in the return period less than 100 years is weaker than before. After that point, the extreme value index is positive, and the degree of rainstorm disaster in the return period more than 100 years is more serious and the phenomenon of extreme rainstorm is more frequent than before. The empirical result showed that the GPD changepoint model is capable to capture the potential rules that the conventional GPD model impotently, which could moderately make up for the deficiency of conventional GPD model in this respect.

Recommended citation: Hu Y, Chen Y*, Wang X, and Liu W. (2021). "Generalized Pareto distribution change-point detection model and its applications in modeling return period prediction." Systems Engineering-Theory & Practice. 41(09): 2379-2391.
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