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

TL;DR

This paper introduces three distribution-free CUSUM-type changepoint detection tests based on record-breaking events, with theoretical validation and practical application to temperature data, implemented in an R package.

Contribution

It proposes novel distribution-free changepoint tests based on record indicators, extending their applicability to series with seasonality and serial correlation.

Findings

Tests are asymptotically Kolmogorov distributed.

Method performs well in size and power in simulations.

Applied successfully to temperature time series in Madrid.

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 $\texttt{RecordTest}$ publicly available on CRAN implements the proposed methods.