Record tests to detect non-stationarity in the tails with an application to climate change

Abstract

The analysis of trends and other non-stationary behaviours at the extremes of a series is an important problem in global warming. This work proposes and compares several statistical tools to analyse that behaviour, using the properties of the occurrence of records in i.i.d. series. The main difficulty of this problem is the scarcity of information in the tails, so it is important to obtain all the possible evidence from the available data. First, different statistics based on upper records are proposed, and the most powerful is selected. Then, using that statistic, several approaches to join the information of four types of records, upper and lower records of forward and backward series, are suggested. It is found that these joint tests are clearly more powerful. The suggested tests are specifically useful in analysing the effect of global warming in the extremes, for example, of daily temperature. They have a high power to detect weak trends and can be widely applied since they are non-parametric. The proposed statistics join the information of M independent series, which is useful given the necessary split of the series to arrange the data. This arrangement solves the usual problems of climate series (seasonality and serial correlation) and provides more series to find evidence. These tools are used to analyse the effect of global warming on the extremes of daily temperature in Madrid.

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

“…subseries each corresponding to the data of a given day across years and then we select a subset of uncorrelated subseries (Cebrián et al, 2021) on which the procedure of Section 2.3 is applied. The three approaches have series of length T = 80, the first two with M = 1 and the third with M = 58 uncorrelated series out of the 365 dependent subseries.…”

“…An aspect of interest is the study of the evolution of the number of records over time, in particular the identification of changes in their behavior (Cebrián et al, 2021). To analyze this type of change, changepoint detection methods that make use of the record occurrence should be considered.…”

“…Foster and Stuart (1954) proposed two simple statistics based on the number of records to test the hypothesis that T observations have been independently drawn from the same continuous distribution. These tests were later improved by Diersen and Trenkler (1996) and more recently new tests and graphical tools were introduced by Cebrián et al (2021).…”

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

“…Foster and Stuart (1954) proposed two simple statistics based on the number of records to test the hypothesis that T observations have been independently drawn from the same continuous distribution. These tests were later improved by Diersen and Trenkler (1996) and more recently new tests and graphical tools were introduced by Cebrián et al (2022).…”

Spatio-temporal analysis of the extent of an extreme heat event

“…There is strong evidence of global warming due to the increasing concentration of greenhouse gases in the atmosphere (Lai and Dzombak 2019). This global warming suggests more frequent warm days, more frequent and persistent heat waves (Lemonsu et al 2014;Alexander 2016) as well as events that break previous records by much larger margins (Fischer et al 2021;Cebria ´n et al 2021). The analysis of heat waves is particularly important due to the potential for serious anthropogenic, environmental, and economic impacts (Amengual et al 2014;Campbell et al 2018).…”