Lekscha Jaqueline, Donner Reik V
Potsdam Institute for Climate Impact Research (PIK) - Member of the Leibniz Association, 14473 Potsdam, Germany.
Department of Physics, Humboldt University, 12489 Berlin, Germany.
Proc Math Phys Eng Sci. 2019 Aug;475(2228):20190161. doi: 10.1098/rspa.2019.0161. Epub 2019 Aug 14.
Many time-series analysis techniques use sliding window approaches or are repeatedly applied over a continuous range of parameters. When combined with a significance test, intrinsic correlations among the pointwise analysis results can make falsely positive significant points appear as continuous patches rather than as isolated points. To account for this effect, we present an areawise significance test that identifies such false-positive patches. For this purpose, we numerically estimate the decorrelation length of the statistic of interest by calculating correlation functions between the analysis results and require an areawise significant point to belong to a patch of pointwise significant points that is larger than this decorrelation length. We apply our areawise test to results from windowed traditional and scale-specific recurrence network analysis in order to identify dynamical anomalies in time series of a non-stationary Rössler system and tree ring width index values from Eastern Canada. Especially, in the palaeoclimate context, the areawise testing approach markedly reduces the number of points that are identified as significant and therefore highlights only the most relevant features in the data. This provides a crucial step towards further establishing recurrence networks as a tool for palaeoclimate data analysis.
许多时间序列分析技术采用滑动窗口方法，或者在连续的参数范围内反复应用。当与显著性检验相结合时，逐点分析结果之间的内在相关性会使误报的显著点呈现为连续的斑块，而不是孤立的点。为了解决这一问题，我们提出了一种区域显著性检验方法，用于识别此类误报斑块。为此，我们通过计算分析结果之间的相关函数，对感兴趣的统计量的去相关长度进行数值估计，并要求区域显著点属于一个逐点显著点的斑块，且该斑块大于此去相关长度。我们将区域检验应用于窗口化传统分析和特定尺度递归网络分析的结果，以识别非平稳罗塞尔系统时间序列和加拿大东部树木年轮宽度指数值中的动态异常。特别是在古气候背景下，区域检验方法显著减少了被识别为显著的点数，因此仅突出了数据中最相关的特征。这为进一步确立递归网络作为古气候数据分析工具迈出了关键一步。
