The goal of this paper is to search for conclusive evidence against the stationarity of the global air surface temperature, which is one of the most important indicators of climate change. For this purpose, possible long-range dependencies are investigated in the frequency-domain. Since conventional tests of hypotheses about the memory parameter, which measures the degree of long-range dependence, are typically based on asymptotic arguments and are therefore of limited practical value in case of small or medium sample sizes, we employ a new small-sample test as well as a related estimator for the memory parameter. To safeguard against false positive findings, simulation studies are carried out to examine the suitability of the employed methods and hemispheric datasets are used to check the robustness of the empirical findings against low-frequency natural variability caused by oceanic cycles. Overall, our frequency-domain analysis provides strong evidence of non-stationarity, which is consistent with previous results obtained in the time domain with models allowing for stochastic or deterministic trends.
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