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

Abstract

AbstractThe 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.