Understanding Changes in the Topology and Geometry of Financial Market Correlations during a Market Crash

Yen, T. W.; Xia, Kelin; Cheong, Siew Ann

doi:10.3390/e23091211

Cited by 14 publications

(6 citation statements)

References 212 publications

(269 reference statements)

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“…From a complex system perspective, given the recent introduction of TPTs [27], the meaning of those transitions is not fully known and depends on the specificity of the complex system itself. It can range from identifying crashes in financial networks [118], to characterizing image quality perception in EEG [82]. The connection between TPTs and other topics on high-order interactions in complex systems is also relevant.…”

Section: Discussionmentioning

confidence: 99%

The Euler characteristic and topological phase transitions in complex systems

Amorim¹,

Moreira²,

Santos³

2022

J. Phys. Complex.

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In this work, we use methods and concepts of applied algebraic topology to comprehensively explore the recent idea of topological phase transitions (TPT) in complex systems. TPTs are characterized by the emergence of nontrivial homology groups as a function of a threshold parameter. Under certain conditions, one can identify TPT's via the zeros of the Euler characteristic or by singularities of the Euler entropy. Recent works provide strong evidence that TPTs can be interpreted as a complex network's intrinsic fingerprint. This work illustrates this possibility by investigating some classic network and empirical protein interaction networks under a topological perspective. We first investigate TPT in protein-protein interaction networks (PPIN) using methods of topological data analysis for two variants of the Duplication-Divergence model, namely, the totally asymmetric model and the heterodimerization model. We compare our theoretical and computational results to experimental data freely available for gene co-expression networks (GCN) of Saccharomyces cerevisiae, also known as baker's yeast, as well as of the nematode Caenorhabditis elegans. Supporting our theoretical expectations, we can detect topological phase transitions in both networks obtained according to different similarity measures. Later, we perform numerical simulations of TPTs in four classical network models: the Erdos-Renyi, the Watts-Strogatz model, the Random Geometric Graph, and the Barabasi-Albert. Finally, we discuss some perspectives and insights on the topic. Given the universality and wide use of those models across disciplines, our work indicates that TPT permeates a wide range of theoretical and empirical networks.

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Section: Discussionmentioning

confidence: 99%

The Euler characteristic and topological phase transitions in complex systems

Amorim¹,

Moreira²,

Santos³

2022

J. Phys. Complex.

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“…Guo et al [30] also used topological features of complex networks that were extracted using PH to find critical dates for financial crises. In addition, dynamics of financial market correlations based on topology and geometry are examined using PH in Yen et al [31]. Moreover, Yen and Cheong [32]also tested PH to analyze Singapore and Taiwan markets.…”

Section: Literature Reviewmentioning

confidence: 99%

Early Warning Signals of Financial Crises Using Persistent Homology and Critical Slowing Down: Evidence From Different Correlation Tests

Ismail

Noorani²,

Ismail³

et al. 2022

Front. Appl. Math. Stat.

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In this study, a new market representation from persistence homology, known as the L1-norm time series, is used and applied independently with three critical slowing down indicators [autocorrelation function at lag 1, variance, and mean for power spectrum (MPS)] to examine two historical financial crises (Dotcom crash and Lehman Brothers bankruptcy) in the US market. The captured signal is the rising trend in the indicator time series, which can be determined by Kendall's tau correlation test. Furthermore, we examined Pearson's and Spearman's rho correlation tests as potential substitutes for Kendall's tau correlation. After that, we determined a correlation threshold and predicted the whole available date. The point of comparison between these correlation tests is to determine which test is significant and consistent in classifying the rising trend. The results of such a comparison will suggest the best test that can classify the observed rising trend and detect early warning signals (EWSs) of impending financial crises. Our outcome shows that the L1-norm time series is more likely to increase before the two financial crises. Kendall's tau, Pearson's, and Spearman's rho correlation tests consistently indicate a significant rising trend in the MPS time series before the two financial crises. Based on the two evaluation scores (the probability of successful anticipation and probability of erroneous anticipation), by using the L1-norm time series with MPS, our result in the whole prediction demonstrated that Spearman's rho correlation (46.15 and 53.85%) obtains the best score as compared to Kendall's tau (42.31 and 57.69%) and Pearson's (40 and 60%) correlations. Therefore, by using Spearman's rho correlation test, L1-norm time series with MPS is shown to be a better way to detect EWSs of US financial crises.

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“…In this study, we used a subgraph representation of the network to encode both its local and global characteristics, rather than the whole network itself. The minimum spanning tree (MST) has been widely utilized by studies focused on financial networks [58][59][60][61][62][63][64][65][66] due to its efficacy in modeling and evaluating network structure. According to the definition, the MST is a network subgraph with all nodes and the lowest number of feasible edges connecting them.…”

Section: Directed Correlation Networkmentioning

confidence: 99%

Network-Induced Soft Sets and Stock Market Applications

2022

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The intricacy of the financial systems reflected in bilateral ties has piqued the interest of many specialists. In this research, we introduce network-induced soft sets, a novel mathematical model for studying the dynamics of a financial stock market with several orders of interaction. To achieve its intelligent parameterization, this model relies on the bilateral connections between economic actors, who are agents in a financial network, rather than relying on any other single feature of the network itself. Our study also introduces recently developed statistical measures for network-induced soft sets and provides an analysis of their application to the study of financial markets. Findings validate the efficacy of this novel method in assessing the effects of various economic stress periods registered in Borsa Istanbul.

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Understanding Changes in the Topology and Geometry of Financial Market Correlations during a Market Crash

Cited by 14 publications

References 212 publications

The Euler characteristic and topological phase transitions in complex systems

The Euler characteristic and topological phase transitions in complex systems

Early Warning Signals of Financial Crises Using Persistent Homology and Critical Slowing Down: Evidence From Different Correlation Tests

Network-Induced Soft Sets and Stock Market Applications

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