Change point analysis in the generalized Pareto distribution

Abstract

The general goal of data statistical analysis is to find a near perfect translation to reality such that minimal information is lost in the approximating model. In this paper change point problem is viewed as a model selection problem where the point in time that model parameters change is estimated. This paper develops a change point estimator of the shape parameter of the generalized Pareto distribution which is shown to be consistent through simulations. The likelihood ratio test statistic based on the Kullback-Leibler divergence is used to detect a change point under the assumption that the model is correctly specified. The maximum likelihood estimation method is used to estimate the change point. The estimator is then used to detect a change point within extreme events with a climatic application in mind.