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Fractal Fract
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Fractal and Multifractal Analysis in Financial Markets
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Fractal and Multifractal Analysis in Financial Markets

A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "General Mathematics, Analysis".

Deadline for manuscript submissions: closed (31 March 2023) | Viewed by 16109

Special Issue Editor

Dr. Jae Wook Song

E-Mail Website
Guest Editor
Department of Industrial Engineering, Hanyang University, Seoul 04763, Republic of Korea
Interests: business analytics; econophysics; financial engineering; portfolio management; time series
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues

In 1963, Mandelbrot and Fama proposed that the return of financial assets is subject to a fractal process supported by the Pareto–Lévy distribution, which challenges the conventional belief of the Gaussian distribution. Since then, various studies have identified the ubiquitous properties of the fractal perspective, such as fat tails, volatility clustering, and multi-scaling. Such properties indicate a non-linear stochastic process, suggesting a long-term memory in financial time series. Multifractal analysis is an effective instrument that can be used to explore the complex non-linear nature of financial time series.

The distributional characteristics of financial market fluctuations are critical in asset pricing and risk management, since large fluctuations usually cause astounding distress in the economy and financial practices. Multifractal analysis has contributed greatly to the analysis of market risk. In this context, we would like to invite the submission of original research and review articles exploring topics including (but not limited to):

  • Fractional Brownian motion;
  • Fractal dimension of financial networks;
  • Multifractal detrended fluctuation analysis/moving average;
  • Multifractal (partial) cross-correlation;
  • Multifractal volatility;
  • Market efficiency;
  • Applications of multifractal processes in finance.

Dr. Jae Wook Song
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Fractal and Fractional is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2700 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Fractional Brownian motion
  • Fractal dimension of financial networks
  • Multifractal detrended fluctuation analysis/moving average
  • Multifractal (partial) cross-correlation
  • Multifractal volatility
  • Market efficiency
  • Applications of multifractal processes in finance

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Related Special Issue

Published Papers (6 papers)

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Research

23 pages, 7754 KiB  
Article
The Impact of COVID-19 on BRICS and MSCI Emerging Markets Efficiency: Evidence from MF-DFA
by Saba Ameer, Safwan Mohd Nor, Sajid Ali and Nur Haiza Muhammad Zawawi
Fractal Fract. 2023, 7(7), 519; https://doi.org/10.3390/fractalfract7070519 - 30 Jun 2023
Cited by 3 | Viewed by 1782
Abstract
This study examines the response of the BRICS and MSCI emerging stock market indices to the COVID-19 outbreak. For this purpose, this study uses a multifractal detrended fluctuation analysis (MF-DFA) to investigate the market efficiency dynamics of these indices and then ranks them [...] Read more.
This study examines the response of the BRICS and MSCI emerging stock market indices to the COVID-19 outbreak. For this purpose, this study uses a multifractal detrended fluctuation analysis (MF-DFA) to investigate the market efficiency dynamics of these indices and then ranks them based on their market efficiency. Overall, our results indicate that the returns from all the stock indices exhibit long-range correlations, implying that these markets are not weak-form efficient. Specifically, China showed the highest level of multifractality (i.e., inefficiency), which can be attributed to its highly volatile market structure. Using a subsample analysis, we further explore the impact of COVID-19 on these markets’ efficiency by dividing the dataset into pre- and post-COVID periods. The findings indicate that COVID-19 adversely affected the efficiency of all the indices. Surprisingly, improvement in the Chinese market’s inefficiency was witnessed, which can be attributed to the prompt and effective measures (i.e., timely imposition of health-related measures such as lockdowns and resident quarantines to contain COVID-19 and financial packages designed to curtail the economic meltdown) introduced by the Chinese government. The findings of this study may help investors, policymakers and regulators in refining their financial and policy decisions according to the new efficiency levels of these markets. Full article
(This article belongs to the Special Issue Fractal and Multifractal Analysis in Financial Markets)
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17 pages, 5138 KiB  
Article
Uncovering Information Linkages between Bitcoin, Sustainable Finance and the Impact of COVID-19: Fractal and Entropy Analysis
by Kuo-Chen Lu and Kuo-Shing Chen
Fractal Fract. 2023, 7(6), 424; https://doi.org/10.3390/fractalfract7060424 - 24 May 2023
Cited by 4 | Viewed by 1397
Abstract
This study aimed to uncover the impact of COVID-19 on the leading cryptocurrency (Bitcoin) and on sustainable finance with specific attention to their potential long memory properties. In this article, the application of the selected methodologies is based on a fractal and entropy [...] Read more.
This study aimed to uncover the impact of COVID-19 on the leading cryptocurrency (Bitcoin) and on sustainable finance with specific attention to their potential long memory properties. In this article, the application of the selected methodologies is based on a fractal and entropy analysis of the econometric model in the financial market. To detect the regularity/irregularity property of a time series, approximate entropy is introduced to measure deterministic chaos. Using daily data for Bitcoin and sustainable finance, namely DJSW, Green Bond, Carbon, and Clean Energy, we examine long memory behaviour by employing a rescaled range statistic (R/S) methodology. The results of the research present that the returns of Bitcoin, the Dow Jones Sustainability World Index (DJSW), Green Bond, Carbon, and Clean Energy have a significant long memory. Contrastingly, an interdisciplinary approach, namely wavelet analysis, is also used to obtain complementary results. Wavelet analysis can provide warning information about turmoil phenomena and offer insights into co-movements in the time–frequency space. Our findings reveal that approximate entropy shows crisis (turmoil) conditions in the Bitcoin market, despite the nature of the pandemic’s origin. Crucially, compared to Bitcoin assets, sustainable financial assets may play a better safe haven role during a pandemic turmoil period. The policy implications of this study could improve trading strategies for the sake of portfolio managers and investors during crisis and non-crisis periods. Full article
(This article belongs to the Special Issue Fractal and Multifractal Analysis in Financial Markets)
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18 pages, 998 KiB  
Article
The Dynamic Effects of COVID-19 and the March 2020 Crash on the Multifractality of NASDAQ Insurance Stock Markets
by Xing Li and Fang Su
Fractal Fract. 2023, 7(1), 91; https://doi.org/10.3390/fractalfract7010091 - 13 Jan 2023
Cited by 6 | Viewed by 1777
Abstract
Triggered by COVID-19, one of the most dramatic crashes in the stock market in history occurred in March 2020. The sharp reductions in NASDAQ insurance stock indexes were observed after the occurrence of COVID-19 and in March 2020. In this study, the NASDAQ [...] Read more.
Triggered by COVID-19, one of the most dramatic crashes in the stock market in history occurred in March 2020. The sharp reductions in NASDAQ insurance stock indexes were observed after the occurrence of COVID-19 and in March 2020. In this study, the NASDAQ insurance stock markets (including NASDAQ Insurance Index, Developed Markets Insurance Index, and Emerging Markets Insurance Index) and NASDAQ Composite Index are utilized. The “scissors difference” between the NASDAQ Insurance Index and NASDAQ Composite Index is observed. The dynamic effects of the COVID-19 epidemic and the March 2020 crash on the multifractality of four series are explored. Firstly, the apparent and intrinsic multifractality, the components of multifractality, and the dynamic effects of the COVID-19 epidemic on these indexes are analyzed. Secondly, the multifractal cross-correlation between the NASDAQ Insurance Index and NASDAQ Composite Index is investigated. The dynamic influence of the COVID-19 epidemic on the cross-correlation is examined. The multifractal analysis results reveal that four series both before and after the occurrence of COVID-19 have multifractal characteristics. The stronger multifractal characteristics and the greater multifractal degree are obtained after the occurrence of COVID-19. The intrinsic multifractality of the three indexes ascends largely after the occurrence of COVID-19. The multifractal cross-correlation analysis illustrates that the cross-correlation between two indexes before and after the occurrence of COVID-19 is multifractal. The stronger multifractal cross-correlations and greater multifractal degrees are shown. The contribution of the intrinsic multifractal cross-correlation increased after the occurrence of COVID-19. Full article
(This article belongs to the Special Issue Fractal and Multifractal Analysis in Financial Markets)
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13 pages, 3767 KiB  
Article
Analyzing Asymmetric Volatility and Multifractal Behavior in Cryptocurrencies Using Capital Asset Pricing Model Filter
by Minhyuk Lee, Younghwan Cho, Seung Eun Ock and Jae Wook Song
Fractal Fract. 2023, 7(1), 85; https://doi.org/10.3390/fractalfract7010085 - 12 Jan 2023
Cited by 3 | Viewed by 2312
Abstract
This research analyzes asymmetric volatility and multifractality in four representative cryptocurrencies using index-based asymmetric multifractal detrended fluctuation analysis. We suggest investigating an idiosyncratic risk premium, which can be obtained by removing the market influence in the cryptocurrency return series. We call the process [...] Read more.
This research analyzes asymmetric volatility and multifractality in four representative cryptocurrencies using index-based asymmetric multifractal detrended fluctuation analysis. We suggest investigating an idiosyncratic risk premium, which can be obtained by removing the market influence in the cryptocurrency return series. We call the process a capital asset pricing model filter. The analyses on the original return series showed no significant sign of asymmetric volatility. However, the filter revealed a distinct asymmetric volatility, distinguishing the uptrend and downtrend fluctuations. Furthermore, the analyses on the idiosyncratic risk premium detected some cases of asymmetry in the degree and source of multifractality, whereas that on the original return series failed to detect the asymmetry. In conclusion, in a highly volatile market, the capital asset pricing model filter can improve an investigation of the asymmetric multifractality in cryptocurrencies. Full article
(This article belongs to the Special Issue Fractal and Multifractal Analysis in Financial Markets)
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19 pages, 5691 KiB  
Article
Global Collective Dynamics of Financial Market Efficiency Using Attention Entropy with Hierarchical Clustering
by Poongjin Cho and Kyungwon Kim
Fractal Fract. 2022, 6(10), 562; https://doi.org/10.3390/fractalfract6100562 - 3 Oct 2022
Cited by 4 | Viewed by 2280
Abstract
The efficient market hypothesis (EMH) assumes that all available information in an efficient financial market is ideally fully reflected in the price of an asset. However, whether the reality that asset prices are not informational efficient is an opportunity for profit or a [...] Read more.
The efficient market hypothesis (EMH) assumes that all available information in an efficient financial market is ideally fully reflected in the price of an asset. However, whether the reality that asset prices are not informational efficient is an opportunity for profit or a systemic risk of the financial system that needs to be corrected is still a ubiquitous concept, so many economic participants and research scholars have conducted related studies in order to understand the phenomenon of the financial market. This research employed attention entropy of the log-returns of 27 global assets to analyze the time-varying informational efficiency. International markets could be classified hierarchically into groups with similar long-term efficiency trends; however, at the same time, the ranks and clusters were found to remain stable only for a short period of time in terms of short-term efficiency. Therefore, a complex network representation analysis was performed to express whether the short-term efficiency patterns have interacted with each other over time as a coherent picture. It was confirmed that the network of 27 international markets was fully connected, strongly globalized and entangled. In addition, the complex network was composed of two modular structures grouped together with similar efficiency dynamics. As a result, although the informational efficiency of financial markets may be globalized to a high-efficiency state, it shows a collective dynamics pattern in which the global system may fall into risk due to the spread of systemic risk. Full article
(This article belongs to the Special Issue Fractal and Multifractal Analysis in Financial Markets)
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16 pages, 1976 KiB  
Article
Forecasting the Volatility of the Stock Index with Deep Learning Using Asymmetric Hurst Exponents
by Poongjin Cho and Minhyuk Lee
Fractal Fract. 2022, 6(7), 394; https://doi.org/10.3390/fractalfract6070394 - 16 Jul 2022
Cited by 9 | Viewed by 4847
Abstract
The prediction of the stock price index is a challenge even with advanced deep-learning technology. As a result, the analysis of volatility, which has been widely studied in traditional finance, has attracted attention among researchers. This paper presents a new forecasting model that [...] Read more.
The prediction of the stock price index is a challenge even with advanced deep-learning technology. As a result, the analysis of volatility, which has been widely studied in traditional finance, has attracted attention among researchers. This paper presents a new forecasting model that combines asymmetric fractality and deep-learning algorithms to predict a one-day-ahead absolute return series, the proxy index of stock price volatility. Asymmetric Hurst exponents are measured to capture the asymmetric long-range dependence behavior of the S&P500 index, and recurrent neural network groups are applied. The results show that the asymmetric Hurst exponents have predictive power for one-day-ahead absolute return and are more effective in volatile market conditions. In addition, we propose a new two-stage forecasting model that predicts volatility according to the magnitude of volatility. This new model shows the best forecasting performance regardless of volatility. Full article
(This article belongs to the Special Issue Fractal and Multifractal Analysis in Financial Markets)
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