Nonlinear correlations in multifractals: Visibility graphs of magnitude and sign series

Abstract

Correlations in multifractal series have been investigated, extensively. Almost all approaches try to find scaling features of a given time series. However, the analysis of such scaling properties has some difficulties such as finding a proper scaling region. On the other hand, such correlation detection methods may be affected by the probability distribution function of the series. In this article, we apply the horizontal visibility graph algorithm to map stochastic time series into networks. By investigating the magnitude and sign of a multifractal time series, we show that one can detect linear as well as nonlinear correlations, even for situations that have been considered as uncorrelated noises by typical approaches like MFDFA. In this respect, we introduce a topological parameter that can well measure the strength of nonlinear correlations. This parameter is independent of the probability distribution function and calculated without the need to find any scaling region.Our findings may provide new insights about the multifractal analysis of time series in a variety of complex systems. * manshour@pgu.ac.ir

A mixed multifractal analysis for quasi Ahlfors vector-valued measures

“…Mixed multifractal analysis has been emerged in such a field to model the nonlinear correlation in time series and/or their volatility to understand better the dependence between markets' indices. See [12,14,38,44].…”

Multiple serial correlations in global air temperature anomaly time series

“…This type of correlation is generally driven by larger-scale processes such as climate change, natural cycles, and anthropogenic emissions [ 10 , 18 – 20 ]. Nonlinear correlation (NC) reflects the nonlinearity and complexity of stochastic climate time series [ 21 ]. Time series of air temperature anomalies reflect the complex dynamics of climate system on different scales; thus, it is actually a mixture of white noise (uncorrelated), STC, LTC and NC [ 22 – 24 ].…”

“…Furthermore, the nonlinearity of the original time series can be assessed by applying DFA or MFDFA to the decomposed series of magnitude and sign derived from the original time series [ 24 , 33 – 35 ]. However, some studies have indicated that the presence of correlation in the magnitude series alone is not a definitive indicator of nonlinearity in the original time series [ 21 ]. Additionally, the successful application of DFA and MFDFA is influenced by factors such as the polynomial order, the scaling region, and the probability distribution function (PDF) of the series [ 21 ].…”

“…However, some studies have indicated that the presence of correlation in the magnitude series alone is not a definitive indicator of nonlinearity in the original time series [ 21 ]. Additionally, the successful application of DFA and MFDFA is influenced by factors such as the polynomial order, the scaling region, and the probability distribution function (PDF) of the series [ 21 ]. In this study, nonlinearity is treated as a proxy for multifractality and estimated using a novel method based on complex network analysis.…”

“…Nevertheless, it has been verified that the HVG method can still be applied to detect NC by eliminating linear correlations and calculating a newly proposed topological parameter, Δ σ . This detection method is robust and unaffected by the probability distribution of the time series [ 21 ].…”