Relationship between Entropy and Dimension of Financial Correlation-Based Network

Nie, Chun-Xiao; Song, Fu-Tie

doi:10.3390/e20030177

Cited by 15 publications

(8 citation statements)

References 66 publications

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“…PMFG is a network drawn in a plane, such that there are no intersecting links [17,38]. If N is total number of stocks, then it contains 3(N − 2) links.…”

Section: Planar Maximally Filtered Graphmentioning

confidence: 99%

A Perspective on Correlation-Based Financial Networks and Entropy Measures

et al. 2020

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In this mini-review, we critically examine the recent work done on correlation-based networks in financial systems. The structure of empirical correlation matrices constructed from the financial market data changes as the individual stock prices fluctuate with time, showing interesting evolutionary patterns, especially during critical events such as market crashes, bubbles, etc. We show that the study of correlation-based networks and their evolution with time is useful for extracting important information of the underlying market dynamics. Also, we present our perspective on the use of recently-developed entropy measures, such as structural entropy and eigen-entropy, for continuous monitoring of correlation-based networks.

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“…PMFG is a network drawn in a plane, such that there are no intersecting links [17,38]. If N is total number of stocks, then it contains 3(N − 2) links.…”

Section: Planar Maximally Filtered Graphmentioning

confidence: 99%

A Perspective on Correlation-Based Financial Networks and Entropy Measures

et al. 2020

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“…Using MST and a hierarchical tree, Yang et al [ 28 ] mentioned the core nodes that should be monitored to maintain the stability and a slight increase in the clustering degree during a financial crisis for China’s stock market. Recently, Nie and Song [ 29 ] exhibited the integration of entropy and the dimension of financial correlation-based networks among stock markets of three countries: China, the UK, and the US. It is worth noticing that there are a lot of local stock markets that need to be explored via complex network methods, as past research is targeted at a few stock markets of the world.…”

Section: Introductionmentioning

confidence: 99%

Structural Change and Dynamics of Pakistan Stock Market during Crisis: A Complex Network Perspective

Memon

Yao

2019

Entropy

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We studied the cross-correlations in the daily closing prices of 181 stocks listed on the Pakistan stock exchange (PSX) covering a time period of 2007–2017 to compute the threshold networks and minimum spanning trees. In addition to the full sample analysis, our study uses three subsamples to examine the structural change and topological evolution before, during, and after the global financial crisis of 2008. We also apply Shannon entropy on the overall sample to measure the volatility of individual stocks. Our results find substantial clustering and a crisis-like less stable overall market structure, given the external and internal events of terrorism, political, financial, and economic crisis for Pakistan. The subsample results further reveal hierarchal scale-free structures and a reconfigured metastable market structure during a postcrisis period. In addition, time varying topological measures confirm the evidence of the presence of several star-like structures, the shrinkage of tree length due to crisis-related shocks, and an expansion in the recovery phase. Finally, changes of the central node of minimum spanning trees (MSTs), the volatile stock recognition using Shannon entropy, and the topology of threshold networks will help local and international investors of Pakistan Stock Exchange limited (PSX) to manage their portfolios or regulators to monitor the important nodes to achieve stability and to predict an upcoming crisis.

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“…Besides, it can be noticed that various network entropies are defined, to describe the degree of network heterogeneity with different metrics. Li et al [ 55 ] found Shannon, Renyi, and Tsallis stock network entropy, evolving similarly over time. Xu [ 54 ] also discovered that network entropies constructed with node degree, clustering coefficient, and the shortest path length evolved with the same trend.…”

Section: Resultsmentioning

confidence: 99%

“…Among the rare examples are Li et al [ 53 ] who considered three types of network entropies to analyze the financial market. Nie and Song [ 55 ] introduced a standardized Rényi entropy to capture the structural differences of financial correlation-based networks. Caraiani [ 56 ] employed singular-value decomposition entropy to study comovement among various financial networks.…”

Section: Net Entropy Of a Stock Marketmentioning

confidence: 99%

Stock Net Entropy: Evidence from the Chinese Growth Enterprise Market

Han

Wan

et al. 2018

Entropy

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By introducing net entropy into a stock network, this paper focuses on investigating the impact of network entropy on market returns and trading in the Chinese Growth Enterprise Market (GEM). In this paper, indices of Wu structure entropy (WSE) and SD structure entropy (SDSE) are considered as indicators of network heterogeneity to present market diversification. A series of dynamic financial networks consisting of 1066 daily nets is constructed by applying the dynamic conditional correlation multivariate GARCH (DCC-MV-GARCH) model with a threshold adjustment. Then, we evaluate the quantitative relationships between network entropy indices and market trading-variables and their bilateral information spillover effects by applying the bivariate EGARCH model. There are two main findings in the paper. Firstly, the evidence significantly ensures that both market returns and trading volumes associate negatively with the network entropy indices, which indicates that stock heterogeneity, which is negative with the value of network entropy indices by definition, can help to improve market returns and increase market trading volumes. Secondly, results show significant information transmission between the indicators of network entropy and stock market trading variables.

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Relationship between Entropy and Dimension of Financial Correlation-Based Network

Cited by 15 publications

References 66 publications

A Perspective on Correlation-Based Financial Networks and Entropy Measures

A Perspective on Correlation-Based Financial Networks and Entropy Measures

Structural Change and Dynamics of Pakistan Stock Market during Crisis: A Complex Network Perspective

Stock Net Entropy: Evidence from the Chinese Growth Enterprise Market

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