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.

中文翻译：

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气候变化的频域证据

本文的目的是寻找针对全球空气表面温度平稳性的确凿证据，这是气候变化最重要的指标之一。为此，在频域中研究可能的远程依赖性。由于有关内存参数的假设的常规检验（其测量长期依赖程度）通常基于渐近论证，因此在中小样本量的情况下实用价值有限，因此我们采用了新的小样本检验以及相关的内存参数估算器。为了防止出现假阳性结果，进行了仿真研究，以检验所采用方法的适用性，并使用半球数据集来检查经验发现对海洋周期引起的低频自然变化的鲁棒性。总体而言，我们的频域分析提供了非平稳性的有力证据，这与先前在时域获得的结果（采用允许随机或确定性趋势的模型）一致。