Areawise significance tests for windowed recurrence network analysis.

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.