The paper analyses temperature data from 96 selected weather stations world wide, and from reconstructed northern hemisphere temperature data over the last two millennia. Using a non‐parametric test, we find that the stationarity hypothesis is not rejected by the data. Subsequently, we investigate further properties of the data by means of a statistical model known as the fractional Gaussian noise (FGN) model. Under stationarity FGN follows from the fact that the observed data are obtained as temporal aggregates of data generated at a finer (basic) timescale where temporal aggregation is taken over a ‘large’ number of basic units. The FGN process exhibits long‐range dependence. Several tests show that both the reconstructed and most of the observed data are consistent with the FGN model.

中文翻译：

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温度如何随时间变化？：关于温度波动的平稳性和分形性的证据

本文分析了来自全球96个选定气象站的温度数据以及最近两千年来重建的北半球温度数据。使用非参数检验，我们发现平稳假设没有被数据拒绝。随后，我们通过称为分数高斯噪声（FGN）模型的统计模型研究数据的其他属性。在平稳状态下，FGN来自以下事实：观察到的数据是在更精细（基本）的时间尺度上生成的数据的时间聚合而获得的，其中时间聚合是在“大量”的基本单位上进行的。FGN过程表现出长期依赖性。多项测试表明，重建数据和大多数观测数据均与FGN模型一致。