Areawise significance tests for recurrence network analysis.

Significance testing is arguably one of the most important concepts of time series analysis.Still, in many applications that include a windowed approach or a repeated analysis over acontinuous range of parameters, results are often tested for every point separately. This givesrise to the requirement of multiple testing corrections and neglects possible intrinsiccorrelations within the analysis results that may make false positive significant points ratherappear as continuous patches than as isolated points. To detect such false positive patches, wehere introduce a general concept for an areawise significance test similar to the one presentedby Maraun et al. [1] for the wavelet spectrum. There, the wavelet reproducing kernel isused to assess the scale of decay of intrinsic correlations which then determinesthe areawise test. Our test is more general and can in principle be applied to anyanalysis method but requires a numerical estimation of the scale of decay of theintrinsic correlations. This estimation can be achieved by choosing a null modeland then calculating correlation functions of the analysis results of surrogate datafollowing the null model for overlapping time windows or for the varying analysisparameters. We here apply the areawise test to windowed and multiscale windowed recurrencenetwork analysis in order to identify dynamical anomalies in palaeoclimate archives such as,for example, tree rings. In this context, recurrence based methods have already proven to bevaluable tools but significance tests have so far only be restricted to pointwise tests. To applythe areawise test, we consider three null models, (i) Gaussian white noise, (ii) anAR(1) process and (iii) a data-adaptive model using iAAFT surrogates. For each nullmodel, we create corresponding sets of surrogate data and then estimate the scale ofdecay of the intrinsic correlations of the measure of interest in the time and windowwidth domains for windowed recurrence network analysis, and in the time andscale domains for multiscale windowed recurrence network analysis. To test ourapproach, we first study a non-stationary Rössler system and then apply the proposedanalysis procedure to a paleoclimate time series of tree ring width indices fromEast Canada. We find dynamical anomalies in times following major explosivevolcanic eruptions depending on the chosen embedding delay, possibly reflecting thatdifferent volcanic eruptions cause dynamical responses on different time scales. Still,to draw reliable conclusions about this effect, more proxy time series need to beanalysed. [1] D. Maraun, J. Kurths, and M. Holschneider. Nonstationary gaussian processes inwavelet domain: Synthesis, estimation, and significance testing. Phys. Rev. E, 75:016707,2007. [ABSTRACT FROM AUTHOR]