Fractal structure in the S&amp;P500: A correlation-based threshold network approach

Ku, Seungmo; Lee, Changju; Chang, Woojin; Song, Jae Wook

doi:10.1016/j.chaos.2020.109848

Cited by 9 publications

(6 citation statements)

References 41 publications

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“…Here, we're considering the previous discussion on the potential applicability of the triangle of machine learning, fractional calculus, and renormalization group on financial data. Again, we found evidence for fractal statistics present in economic data, i.e., the S&P 500 index, [100]. Thus we recommend future research for analyzing stock market data to employ ideas from fractional calculus, machine learning, and the renormalization group and subsequently to analyze the fractal behavior of these data sets.…”

Section: Renormalization Groupmentioning

confidence: 60%

“…And finally, we also didn't find an application of fractal statistics or fractals. However, given the numerous evidence for fractal behavior and statistics in various fields, e.g., in hydrology [98], rock mechanics [99] or finance, [100], we still aim to provide a link. Here, we're considering the previous discussion on the potential applicability of the triangle of machine learning, fractional calculus, and renormalization group on financial data.…”

Section: Renormalization Groupmentioning

confidence: 99%

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Combining Fractional Derivatives and Supervised Machine Learning: A Review

Raubitzek¹,

Mallinger²,

Neubauer³

2022

Preprint

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Fractional calculus gained a lot of attention in the last couple of years. Researchers discovered that processes in various fields follow rather fractional dynamics than ordinary integer-ordered dynamics, meaning the corresponding differential equations feature non-integer valued derivatives. There are several arguments for why this is the case, one of them being that fractional derivatives’ inherit spatiotemporal memory and/or the ability to express complex naturally occurring phenomena. Another popular topic nowadays is machine learning, i.e., learning behavior and patterns from historical data. In our ever-changing world with ever-increasing amounts of data, machine learning is a powerful tool for data analysis, problem-solving, modeling, and prediction. It further provides many insights and discoveries in various scientific disciplines. As these two modern-day topics provide a lot of potential for combined approaches to describe complex dynamics, this article reviews combined approaches of fractional derivatives and machine learning from the past, puts them into context, and thus provides a list of possible combined approaches and the corresponding techniques. Note, however, that this article does not deal with neural networks, as there already is profound literature on neural networks and fractional calculus. We sorted past combined approaches from the literature into three categories, i.e., preprocessing, machine learning &amp; fractional dynamics, and optimization. The contributions of fractional derivatives to machine learning are manifold as they provide powerful preprocessing and feature augmentation techniques, can improve physically informed machine learning, and are capable of improving hyperparameter optimization. Thus, this article serves to motivate researchers dealing with data-based problems, to be specific machine learning practitioners, to adopt new tools and enhance their existing approaches.

show abstract

Section: Renormalization Groupmentioning

confidence: 60%

Section: Renormalization Groupmentioning

confidence: 99%

Combining Fractional Derivatives and Supervised Machine Learning: A Review

Raubitzek¹,

Mallinger²,

Neubauer³

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…In the literature on financial networks, alternative estimation techniques have been used, including partial correlation [ 31 , 32 ], correlation threshold networks [ 33 ], and cross-correlation function (CCF)-based Granger causality to test spillover effects [ 20 , 34 ]. Different network inference methods can be combined with network filtering procedures such as the minimum spanning tree or the planar maximally filtered graph (PMFG) method [ 35 , 36 , 37 ], among others (for an extensive review of the inference methods on financial networks, see [ 38 ]).…”

Section: Methodsmentioning

confidence: 99%

Structure of Investor Networks and Financial Crises

Baltakys

Viet

Kanniainen

2021

Entropy

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In this paper, we ask whether the structure of investor networks, estimated using shareholder registration data, is abnormal during a financial crises. We answer this question by analyzing the structure of investor networks through several most prominent global network features. The networks are estimated from data on marketplace transactions of all publicly traded securities executed in the Helsinki Stock Exchange by Finnish stock shareholders between 1995 and 2016. We observe that most of the feature distributions were abnormal during the 2008–2009 financial crisis, with statistical significance. This paper provides evidence that the financial crisis was associated with a structural change in investors’ trade time synchronization. This indicates that the way how investors use their private information channels changes depending on the market conditions.

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“…Furthermore, finally, we also did not find an application of fractal statistics or fractals. However, given the numerous evidence for fractal behavior and statistics in various fields, e.g., in hydrology [99], rock mechanics [100] or finance [101], we still aim to provide a link. Here, we consider the previous discussion on the potential applicability of the triangle of machine learning, fractional calculus, and renormalization group on financial data.…”

Section: Renormalization Groupmentioning

confidence: 99%

Combining Fractional Derivatives and Machine Learning: A Review

Raubitzek

Mallinger²,

Neubauer³

2022

Entropy

View full text Add to dashboard Cite

Fractional calculus has gained a lot of attention in the last couple of years. Researchers have discovered that processes in various fields follow fractional dynamics rather than ordinary integer-ordered dynamics, meaning that the corresponding differential equations feature non-integer valued derivatives. There are several arguments for why this is the case, one of which is that fractional derivatives inherit spatiotemporal memory and/or the ability to express complex naturally occurring phenomena. Another popular topic nowadays is machine learning, i.e., learning behavior and patterns from historical data. In our ever-changing world with ever-increasing amounts of data, machine learning is a powerful tool for data analysis, problem-solving, modeling, and prediction. It has provided many further insights and discoveries in various scientific disciplines. As these two modern-day topics hold a lot of potential for combined approaches in terms of describing complex dynamics, this article review combines approaches from fractional derivatives and machine learning from the past, puts them into context, and thus provides a list of possible combined approaches and the corresponding techniques. Note, however, that this article does not deal with neural networks, as there is already extensive literature on neural networks and fractional calculus. We sorted past combined approaches from the literature into three categories, i.e., preprocessing, machine learning and fractional dynamics, and optimization. The contributions of fractional derivatives to machine learning are manifold as they provide powerful preprocessing and feature augmentation techniques, can improve physically informed machine learning, and are capable of improving hyperparameter optimization. Thus, this article serves to motivate researchers dealing with data-based problems, to be specific machine learning practitioners, to adopt new tools, and enhance their existing approaches.

show abstract

Fractal structure in the S&P500: A correlation-based threshold network approach

Cited by 9 publications

References 41 publications

Combining Fractional Derivatives and Supervised Machine Learning: A Review

Combining Fractional Derivatives and Supervised Machine Learning: A Review

Structure of Investor Networks and Financial Crises

Combining Fractional Derivatives and Machine Learning: A Review

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