Research Of Dynamical Characteristics Of Time Series Based On Weighted Network

There is transformation relation between nonlinear time series and networkstructures so it is possible from the perspective of the network to examine time series,which becomes a hot topic in the realm of time series analysis in recent years. Thispaper aims to study time series with diverse typical dynamics by means of theapproaches of complex networks. We obtain different topological structures to identifydynamical characteristics of the given time series.Firstly, we select the transformation threshold to confirm the equivalenttransformation from time series to its network structure. We, thereby, transform timeseries to the network with variant transformation threshold, and then inverse thenetworks to reproduce the time series. We can estimate the relationship between thevarious thresholds and the correlation coefficient of these two time series so as todetermine the optimal threshold. Such preprocessing guarantees not only theequivalence of the transformation between the weighted networks and time series butalso the suitable threshold.Secondly, we describe different methods of transforming time series intonetworks. We divide the degree of the transformed network into output degree andinput degree (i.e. the link with the positive weight is regarded as the output degreewhile the link with the negative weight is an input degree). The recurrence plot methodis used to transform the time series to the corresponding directed weighted network.We choose the time delay lag, absolute time delay lag, amplitude delay lag, absoluteamplitude delay lag as the edge weights of the network respectively. We calculate thestatistical point weight, unit weight, the relation of degree and average weight for eachtransformation strategy. Our results demonstrate that when the weight adopts theamplitude difference, the statistical relation of degree and average weight candifferentiate time series with different dynamics. Inspired by this finding, we presentthe new statics (degree slope) to identify different time series. We also study therobustness of our method. Given the same time series contaminated with noise (signalto noise ratio=25dB), we find that the robustness of the networks is good.Finally, we study the transformed network with time information of the originaltime series. That is, we employ the time lag of data points as the edge weighs of thenetwork. We then repeat the previous statistics but they fail to differentiate time serieswith typical dynamics. We, therefore, propose another popular statistic (the clusteringcoefficient) to differentiate them. To further ensure the transformed network containtime information, we employ the surrogate data method to validate whether thenetwork transformed from the surrogate data is consistent with the network from the original none. We notice that the network with time weights can reflect the dynamicalstructures of the time series. We also add noise to the periodic and chaotic data, and theresult indicates that such transformed networks are robust against noise disturbance.When we try longer time series, the results holds similarly.