A change-point model for the r-largest order statistics with applications to environmental and financial data.

• A new change-point model for the r -largest order statistics is proposed. • The proposed model can be used for any application that involves an extreme time series with a structural break. • A Bayesian adaptation for the estimation of the optimal number of order statistics is proposed. • Simulations and real data sets shows the good performance of this new model. • The application in three examples verifies the performance of the new model is better than that the usual model. This study makes a new contribution to extreme value theory by proposing a change-point model of the distribution of the r -larger order statistics. In some situations, using only the maxima of grouped data results in a small sample size that may require a larger dataset. In this sense, using the joint distribution of the r -largest order statistics provides more information and, consequently, better estimators. We perform a comprehensive simulation to show the advantage of this method over other competitive models that approach the change-point model in extremes. Finally, the proposed model is fitted to river quota data (environmental data) and NASDAQ daily returns data (financial data) to demonstrate its potential for practical application. [ABSTRACT FROM AUTHOR]