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Abstract Financial networks can be constructed to model the intertemporal price dependencies within an asset market, giving rise to a causal network. These networks are traditionally inferred through multivariate predictive modelling. However, the application of these techniques to financial data is highly challenged. The interplay of social and economic factors produces unstable price behaviour that violates most conventional modelling assumptions, limiting the informational content of networks derived from standard inference tools. Despite these limitations, it remains unclear whether the improved accuracy of robustly estimated networks translates into qualitatively unique insight. This study provides an extended analysis of our recently introduced Rank-Vector-Autoregression model, demonstrating its capacity to identify properties that are undetected with standard methodology. We initially validate the superior accuracy of Rank-VAR through a simulation study on processes that contain adversarial abnormalities. When applied to a dataset of 261 cryptocurrencies, our rank network uniquely displays capitalisation-dependent hierarchical ordering, with outgoing influence being positively, and incoming influence negatively correlated to total coin valuation. Applying our method to the squared deviations verifies that even under robust estimation, volatility networks display fundamentally differing dynamics to raw returns, with more connections, clustering, and causal cycles. Our results demonstrate the use of Rank-VAR to identify and verify unique properties in the causal structures of cryptocurrency markets.

This study aims to employ a causal network model based on transfer entropy for the early warning of systemic risk in commodity markets. We analyzed the dynamic causal relationships of prices for 25 commodities related to China (including futures and spot prices of energy, industrial metals, precious metals, and agricultural products), validating the effect of the causal network structure among commodity markets on systemic risk. Our research results identified commodities and categories playing significant roles, revealing that industry and precious metal markets possess stronger market information transmission capabilities, with price fluctuations impacting a broader range and with greater force on other commodity markets. Under the influence of different types of crisis events, such as economic crises and the Russia–Ukraine conflict, the causal network structure among commodity markets exhibited distinct characteristics. The results of the effect of external shocks to the causal network structure of commodity markets on the entropy of systemic risk suggest that network structure indicators can warn of systemic risk. This article can assist investors and policymakers in managing systemic risk to avoid unexpected losses. [ABSTRACT FROM AUTHOR]

Emerging or diminishing nonlinear interactions in the evolution of a complex system may signal a possible structural change in its underlying mechanism. This type of structural break may exist in many applications, such as in climate and finance, and standard methods for change-point detection may not be sensitive to it. In this article, we present a novel scheme for detecting structural breaks through the occurrence or vanishing of nonlinear causal relationships in a complex system. A significance resampling test was developed for the null hypothesis (H0) of no nonlinear causal relationships using (a) an appropriate Gaussian instantaneous transform and vector autoregressive (VAR) process to generate the resampled multivariate time series consistent with H0; (b) the modelfree Granger causality measure of partial mutual information from mixed embedding (PMIME) to estimate all causal relationships; and (c) a characteristic of the network formed by PMIME as test statistic. The significance test was applied to sliding windows on the observed multivariate time series, and the change from rejection to no-rejection of H0, or the opposite, signaled a non-trivial change of the underlying dynamics of the observed complex system. Different network indices that capture different characteristics of the PMIME networks were used as test statistics. The test was evaluated on multiple synthetic complex and chaotic systems, as well as on linear and nonlinear stochastic systems, demonstrating that the proposed methodology is capable of detecting nonlinear causality. Furthermore, the scheme was applied to different records of financial indices regarding the global financial crisis of 2008, the two commodity crises of 2014 and 2020, the Brexit referendum of 2016, and the outbreak of COVID-19, accurately identifying the structural breaks at the identified times. [ABSTRACT FROM AUTHOR]

Many methods of Granger causality, or broadly termed connectivity, have been developed to assess the causal relationships between the system variables based only on the information extracted from the time series. The power of these methods to capture the true underlying connectivity structure has been assessed using simulated dynamical systems where the ground truth is known. Here, we consider the presence of an unobserved variable that acts as a hidden source for the observed high-dimensional dynamical system and study the effect of the hidden source on the estimation of the connectivity structure. In particular, the focus is on estimating the direct causality effects in high-dimensional time series (not including the hidden source) of relatively short length. We examine the performance of a linear and a nonlinear connectivity measure using dimension reduction and compare them to a linear measure designed for latent variables. For the simulations, four systems are considered, the coupled Hénon maps system, the coupled Mackey–Glass system, the neural mass model and the vector autoregressive (VAR) process, each comprising 25 subsystems (variables for VAR) at close chain coupling structure and another subsystem (variable for VAR) driving all others acting as the hidden source. The results show that the direct causality measures estimate, in general terms, correctly the existing connectivity in the absence of the source when its driving is zero or weak, yet fail to detect the actual relationships when the driving is strong, with the nonlinear measure of dimension reduction performing best. An example from finance including and excluding the USA index in the global market indices highlights the different performance of the connectivity measures in the presence of hidden source.

The occurrence of epileptiform discharges (ED) in electroencephalographic (EEG) recordings of patients with epilepsy signifies a change in brain dynamics and particularly brain connectivity. Transcranial magnetic stimulation (TMS) has been recently acknowledged as a non-invasive brain stimulation technique that can be used in focal epilepsy for therapeutic purposes. In this case study, it is investigated whether simple time-domain connectivity measures, namely cross-correlation and partial cross-correlation, can detect alterations in the connectivity structure estimated from selected EEG channels before and during ED, as well as how this changes with the application of TMS. The correlation for each channel pair is computed on non-overlapping windows of 1 s duration forming weighted networks. Further, binary networks are derived by thresholding or statistical significance tests (parametric and randomization tests). The information for the binary networks is summarized by statistical network measures, such as the average degree and the average path length. Alterations of brain connectivity before, during and after ED with or without TMS are identified by statistical analysis of the network measures at each state.

Granger causality and variants of this concept allow the study of complex dynamical systems as networks constructed from multivariate time series. In this work, a large number of Granger causality measures used to form causality networks from multivariate time series are assessed. These measures are in the time domain, such as model-based and information measures, the frequency domain, and the phase domain. The study aims also to compare bivariate and multivariate measures, linear and nonlinear measures, as well as the use of dimension reduction in linear model-based measures and information measures. The latter is particular relevant in the study of high-dimensional time series. For the performance of the multivariate causality measures, low and high dimensional coupled dynamical systems are considered in discrete and continuous time, as well as deterministic and stochastic. The measures are evaluated and ranked according to their ability to provide causality networks that match the original coupling structure. The simulation study concludes that the Granger causality measures using dimension reduction are superior and should be preferred particularly in studies involving many observed variables, such as multi-channel electroencephalograms and financial markets.

Studying systemically important financial institutions (SIFIs) becomes the research hotspots in risk management of financial markets. In this paper, we study China's SIFIs based on the complex network modeling method on multi-time scales. First, we use complete empirical mode decomposition based on adaptive noise (CEEMDAN) and partial cross mapping (PCM) to construct multi-time scale causality networks based on the normalized daily returns of 30 institutions during 2011–2020.​ Then, the SIFIs is investigated from the perspective of connectedness (information transmission and node centrality) on multi-time scales. Finally, using the technique for order preference by similarity to an ideal solution with entropy weight method (EW-TOPSIS) to comprehensively evaluate SIFIs, and deliver a sensitivity analysis. We find that: (i) interconnectedness primarily concentrates on the inter-institution in the long-term; (ii) the evaluations of SIFIs measurement from perspective of connectedness on multi-time scale are different; (iii) the scores of SIFIs measured by multi-attribute EW-TOPSIS clarify that banks and insurers represent the SIFIs in each economic circle, and SIFIs can be evaluated according to preference for attributes. • We propose using CEEMDAN and PCM to constract multi-time scale causality networks. • The evaluations of SIFIs measurement from perspective of connectedness on multi-time scale are different. • We make use of EW-TOPSIS which combined connectedness with scale to establish a comprehensive evaluation of SIFIs. • The banks and insurers are evaluated as the SIFIs based on equal-weighted attributes in each economic period. [ABSTRACT FROM AUTHOR]

The occurrence of epileptiform discharges (ED) in electroencephalographic (EEG) recordings of patients with epilepsy signifies a change in brain dynamics and particularly brain connectivity. Transcranial magnetic stimulation (TMS) has been recently acknowledged as a non-invasive brain stimulation technique that can be used in focal epilepsy for therapeutic purposes. In this case study, it is investigated whether simple time-domain connectivity measures, namely cross-correlation and partial cross-correlation, can detect alterations in the connectivity structure estimated from selected EEG channels before and during ED, as well as how this changes with the application of TMS. The correlation for each channel pair is computed on non-overlapping windows of 1 s duration forming weighted networks. Further, binary networks are derived by thresholding or statistical significance tests (parametric and randomization tests). The information for the binary networks is summarized by statistical network measures, such as the average degree and the average path length. Alterations of brain connectivity before, during and after ED with or without TMS are identified by statistical analysis of the network measures at each state. [ABSTRACT FROM AUTHOR]

Abstract: We present a model for the dynamic spreading of failures in networked systems. The model combines network nodes as active, bistable elements and delayed interactions along directed links. By means of simulations, we explore the time-dependent spreading and cascade failures in different network topologies. The results of these simulations point towards a phase transition in the spreading dynamics that depends on node parameters and network topology. In particular, we observe a critical threshold for node recovery. Below this threshold, any disturbance propagates only through a small fraction of the network. The size of this perturbed fraction is determined numerically. Furthermore, we discuss the robustness of networks challenged by coinciding internal failures. Our model may be used to improve disaster preparedness and anticipative disaster response management. [Copyright &y& Elsevier]

Many methods of Granger causality, or broadly termed connectivity, have been developed to assess the causal relationships between the system variables based only on the information extracted from the time series. The power of these methods to capture the true underlying connectivity structure has been assessed using simulated dynamical systems where the ground truth is known. Here, we consider the presence of an unobserved variable that acts as a hidden source for the observed high-dimensional dynamical system and study the effect of the hidden source on the estimation of the connectivity structure. In particular, the focus is on estimating the direct causality effects in high-dimensional time series (not including the hidden source) of relatively short length. We examine the performance of a linear and a nonlinear connectivity measure using dimension reduction and compare them to a linear measure designed for latent variables. For the simulations, four systems are considered, the coupled Hénon maps system, the coupled Mackey–Glass system, the neural mass model and the vector autoregressive (VAR) process, each comprising 25 subsystems (variables for VAR) at close chain coupling structure and another subsystem (variable for VAR) driving all others acting as the hidden source. The results show that the direct causality measures estimate, in general terms, correctly the existing connectivity in the absence of the source when its driving is zero or weak, yet fail to detect the actual relationships when the driving is strong, with the nonlinear measure of dimension reduction performing best. An example from finance including and excluding the USA index in the global market indices highlights the different performance of the connectivity measures in the presence of hidden source. [ABSTRACT FROM AUTHOR]

Granger causality and variants of this concept allow the study of complex dynamical systems as networks constructed from multivariate time series. In this work, a large number of Granger causality measures used to form causality networks from multivariate time series are assessed. These measures are in the time domain, such as model-based and information measures, the frequency domain, and the phase domain. The study aims also to compare bivariate and multivariate measures, linear and nonlinear measures, as well as the use of dimension reduction in linear model-based measures and information measures. The latter is particular relevant in the study of high-dimensional time series. For the performance of the multivariate causality measures, low and high dimensional coupled dynamical systems are considered in discrete and continuous time, as well as deterministic and stochastic. The measures are evaluated and ranked according to their ability to provide causality networks that match the original coupling structure. The simulation study concludes that the Granger causality measures using dimension reduction are superior and should be preferred particularly in studies involving many observed variables, such as multi-channel electroencephalograms and financial markets. [ABSTRACT FROM AUTHOR]