Areawise significance tests for windowed recurrence network analysis.

Area of Science:

• Time-series analysis
• Dynamical systems
• Palaeoclimatology

Background:

• Time-series analysis often uses sliding windows, leading to correlated results.
• Pointwise significance tests can produce false-positive patches due to these correlations.
• Recurrence networks are emerging tools for time-series analysis, especially in palaeoclimatology.

Purpose of the Study:

• To develop a novel areawise significance test to correct for false-positive patches in time-series analysis.
• To improve the identification of dynamical anomalies in non-stationary time series.
• To enhance the utility of recurrence networks for palaeoclimate data analysis.

Main Methods:

• Numerically estimating the decorrelation length of the statistic of interest.
• Calculating correlation functions between analysis results.
• Requiring significant patches to exceed the estimated decorrelation length.

Main Results:

• The areawise significance test effectively identifies false-positive patches.
• Application to Rössler system and tree ring data revealed significant dynamical anomalies.
• The approach markedly reduced spurious significant points in palaeoclimate data.

Conclusions:

• The areawise significance test is a crucial step for robust anomaly detection in time series.
• This method enhances the reliability of findings from recurrence network analysis.
• The developed test is particularly valuable for palaeoclimate studies, highlighting key features.