Distribution-free changepoint detection tests based on the breaking of records

Abstract

The analysis of record-breaking events is of interest in fields such as climatology, hydrology or anthropology. In connection with the record occurrence, we propose three distribution-free statistics for the changepoint detection problem. They are CUSUM-type statistics based on the upper and/or lower record indicators observed in a series. Using a version of the functional central limit theorem, we show that the CUSUM-type statistics are asymptotically Kolmogorov distributed. The main results under the null hypothesis are based on series of independent and identically distributed random variables, but a statistic to deal with series with seasonal component and serial correlation is also proposed. A Monte Carlo study of size, power and changepoint estimate has been performed. Finally, the methods are illustrated by analyzing the time series of temperatures at Madrid, Spain. The R package publicly available on CRAN implements the proposed methods.

Bayesian Variable Selection in Generalized Extreme Value Regression: Modeling Annual Maximum Temperature

“…The Bayesian hierarchical model can be used to simulate series of annual maximum temperature. This simulation tool could be used, e.g., to study and make inference on different types of features of these series such as the occurrence and magnitude of its record events [38,39], in the observed period and future climate scenarios, using the ESM projections of the covariates.…”

RecordTest: An R Package to Analyze Non-Stationarity in the Extremes Based on Record-Breaking Events

“…In particular, the fact that the distribution of the record occurrence under the CRM does not depend on the underlying distribution of the X t 's allows the use of distribution-free statistics and Monte Carlo methods. RecordTest includes the tests of this type proposed by Foster and Stuart (1954), Diersen and Trenkler (1996), Benestad (2003Benestad ( , 2004, Cebrián, Castillo-Mateo, and Asín (2022), Castillo-Mateo (2022a), and some extensions thereof proposed in this paper. The package also includes useful graphical tools based on the behavior of the record occurrence under the CRM.…”