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.