A Review of Two Decades of Correlations, Hierarchies, Networks and Clustering in Financial Markets

Abstract. Modern utility-scale wind turbines are equipped with a Supervisory Control And Data Acquisition (SCADA) system gathering vast amounts of operational data that can be used for failure analysis and prediction to improve operation and maintenance of turbines. We analyse high freqeuency SCADA-data from the Thanet offshore windpark in the UK and evaluate Pearson correlation matrices for a variety of observables with a moving time window. This renders possible an asessment of non-stationarity in mutual dependcies of different types of data. Drawing from our experience in other complex systems, such as financial markets and traffic, we show this by employing a hierarchichal k-means clustering algorithm on the correlation matrices. The different clusters exhibit distinct typical correlation structures to which we refer as states. Looking first at only one and later at multiple turbines, the main dependence of these states is shown to be on wind speed. In accordance, we identify them as operational states arising from different settings in the turbine control system based on the available wind speed. We model the boundary wind speeds seperating the states based on the clustering solution. This allows the usage of our methodology for failure analysis or prediction by sorting new data based on wind speed and comparing it to the respective operational state, thereby taking the non-stationarity into account.

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“…Such compromises are common when dealing with correlation matrix time series (Marti et al, 2021;Heckens et al, 2020).…”

Section: Correlation Matricesmentioning

confidence: 99%

Non-stationarity in correlation matrices for wind turbine SCADA-data and implications for failure detection

Bette

Jungblut

Guhr

2021

Preprint

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“…Other applications include Sun et al [ 105 , 106 ] and Jiang et al [ 107 ] using the MST to detect insider trading in stock markets, as well as Onnela et al [ 70 , 73 ], Tola et al [ 108 ], and Coelho et al [ 109 ] using the MST for portfolio selection. The popularity of the MST in econophysics should be clear from this quick survey, and interested readers can refer to the reviews [ 110 , 111 ] for even more references.…”

Section: The Minimal Spanning Treementioning

confidence: 99%

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

Yen

Xia

Cheong

2021

Entropy

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In econophysics, the achievements of information filtering methods over the past 20 years, such as the minimal spanning tree (MST) by Mantegna and the planar maximally filtered graph (PMFG) by Tumminello et al., should be celebrated. Here, we show how one can systematically improve upon this paradigm along two separate directions. First, we used topological data analysis (TDA) to extend the notions of nodes and links in networks to faces, tetrahedrons, or k-simplices in simplicial complexes. Second, we used the Ollivier-Ricci curvature (ORC) to acquire geometric information that cannot be provided by simple information filtering. In this sense, MSTs and PMFGs are but first steps to revealing the topological backbones of financial networks. This is something that TDA can elucidate more fully, following which the ORC can help us flesh out the geometry of financial networks. We applied these two approaches to a recent stock market crash in Taiwan and found that, beyond fusions and fissions, other non-fusion/fission processes such as cavitation, annihilation, rupture, healing, and puncture might also be important. We also successfully identified neck regions that emerged during the crash, based on their negative ORCs, and performed a case study on one such neck region.

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“…The methodology of Mantegna is applied with different variations in other contexts (Brida and Risso, 2009;Mizuno et al, 2006;Onnela et al, 2003). Furthermore, Marti et al (2017) propose different alternatives and variants of this methodology.…”

Section: Clustering Financial Datamentioning

confidence: 99%

Analysis of the cryptocurrency market applying different prototype-based clustering techniques

Lorenzo¹,

Arroyo²

2021

Preprint

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Since the appearance of Bitcoin, cryptocurrencies have experienced enormousgrowth not only in terms of capitalization but also in number. As a result, thecryptocurrency market can be an attractive arena for investors as it offers manypossibilities, but a difficult one to understand as well. In this work, we aim tosummarize and segment the whole cryptocurrency market in 2018 with the helpof data analysis tools. We will use three different partitional clustering algorithmseach of them using a different representation for cryptocurrencies, namely: yearlymean and standard deviation of the returns, distribution of returns, and timeseries of returns. Since each representation will provide a different andcomplementary perspective of the market, we will also explore the combination ofthe three clustering results to obtain a fine-grained analysis of the main trends ofthe market. Finally, we will analyse the association of the clustering results withother descriptive features of the cryptocurrencies, including the age, technologicalattributes, and financial ratios derived from them. This will help to enhance theprofiling of the clusters with additional insights. As a result, this work offers adescription of the market and a methodology that can be reproduced by investorsthat want to understand the main trends on the market and that look forcryptocurrencies with different financial performance.

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A Review of Two Decades of Correlations, Hierarchies, Networks and Clustering in Financial Markets

Cited by 75 publications

References 87 publications

Non-stationarity in correlation matrices for wind turbine SCADA-data and implications for failure detection

Non-stationarity in correlation matrices for wind turbine SCADA-data and implications for failure detection

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

Analysis of the cryptocurrency market applying different prototype-based clustering techniques

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