Record Tests to Detect Non Stationarity in the Tails With an Application to Climate Change

Abstract

The analysis of non stationary behaviours and trends in the extremes of a series is an important problem in global warming. This work develops 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 that it is important to obtain all the possible evidences from the data available. To that end, 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 than these joint tests are clearly more powerful. The suggested tests are specifically useful in the analysis of the effect of global warming in the extremes, for example of daily temperature. They have a high power to detect weak trends and they can be widely applied, since they are non parametric. The proposed statistics join the information of M independent series, what is useful given the necessary split of the series to arrange the data. This arrangement solves usual problems of climate series (seasonality and serial correlation) and provides more series to find evidences. These tools are used to analyse the effect of global warming in the extremes of daily temperature in Madrid.