Ordered Avalanches on the Bethe Lattice

Krawczyk, Małgorzata J.; Oświęcimka, Paweł; Kułakowski, K.; Dróżdż, S.

doi:10.3390/e21100968

Cited by 3 publications

(3 citation statements)

References 52 publications

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“…Multifractal analysis is one of the most promising methods of studying empirical data representing natural and social systems as it is able to quantify complexity of such systems and express it in a relatively simple way with a small set of associated quantities. It has already been applied in many works to univariate and multivariate data sets from a number of different systems: Physics [ 54 ], biology [ 55 ], chemistry [ 56 ], geophysics [ 57 ], hydrology [ 58 ], atmospheric physics [ 59 ], quantitative linguistics [ 60 ], behavioral sciences [ 61 ], cognitive structures [ 62 ], music [ 63 ], songbird rhythms [ 64 ], physiology [ 65 ], human behaviour [ 66 ], social psychology [ 67 ] and even ecological sciences [ 68 ], but especially financial markets [ 69 , 70 , 71 , 72 , 73 , 74 , 75 , 76 , 77 ].…”

Section: Methods and Resultsmentioning

confidence: 99%

Complexity in Economic and Social Systems: Cryptocurrency Market at around COVID-19

Dróżdż

Kwapień

Oświęcimka

et al. 2020

Entropy

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Social systems are characterized by an enormous network of connections and factors that can influence the structure and dynamics of these systems. Among them the whole economical sphere of human activity seems to be the most interrelated and complex. All financial markets, including the youngest one, the cryptocurrency market, belong to this sphere. The complexity of the cryptocurrency market can be studied from different perspectives. First, the dynamics of the cryptocurrency exchange rates to other cryptocurrencies and fiat currencies can be studied and quantified by means of multifractal formalism. Second, coupling and decoupling of the cryptocurrencies and the conventional assets can be investigated with the advanced cross-correlation analyses based on fractal analysis. Third, an internal structure of the cryptocurrency market can also be a subject of analysis that exploits, for example, a network representation of the market. In this work, we approach the subject from all three perspectives based on data from a recent time interval between January 2019 and June 2020. This period includes the peculiar time of the Covid-19 pandemic; therefore, we pay particular attention to this event and investigate how strong its impact on the structure and dynamics of the market was. Besides, the studied data covers a few other significant events like double bull and bear phases in 2019. We show that, throughout the considered interval, the exchange rate returns were multifractal with intermittent signatures of bifractality that can be associated with the most volatile periods of the market dynamics like a bull market onset in April 2019 and the Covid-19 outburst in March 2020. The topology of a minimal spanning tree representation of the market also used to alter during these events from a distributed type without any dominant node to a highly centralized type with a dominating hub of USDT. However, the MST topology during the pandemic differs in some details from other volatile periods.

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Section: Methods and Resultsmentioning

confidence: 99%

Complexity in Economic and Social Systems: Cryptocurrency Market at around COVID-19

Dróżdż

Kwapień

Oświęcimka

et al. 2020

Entropy

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“…is mechanism seems to us the most reliable, since it is based on the hierarchically subordinate distribution of information in the form of retweets on Twitter. In addition, there is some strong evidence that the dissemination of information in hierarchical structures is avalanche-like (see the papers [61][62][63][64][65][66]).…”

Section: First Debatementioning

confidence: 99%

Identification of Self‐Organized Critical State on Twitter Based on the Retweets’ Time Series Analysis

Dmitriev

2021

Complexity

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There is a number of studies, in which it is established that the observed flows of microposts generated by microblogging social networks (e.g., Twitter) are characterized by avalanche-like behavior. Time series of microposts depicting such streams are the time series with a power-law distribution, with 1/f noise and long memory. Despite this, there are no studies devoted to the detection and analysis of self-organized critical state, subcritical phase, and supercritical phase. The presented paper is devoted to the detection and investigation of such critical states and phases. An algorithm is proposed that allowed to detect of critical phases and critical conditions on Twitter, based on the analysis of retweets time series corresponding to the three debates of the 2016 United States Presidential Election, as the most popular debate in the history of America, collecting 84 million live views.

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“…The distribution of the fluctuation functions already suggests a bi-fractal organization (Fig. 8b) [68]. However, the multifractal spectra estimated through the MFDFA and WL algorithms resemble typical multifractal characteristics, with a strong left-sided asymmetry (Fig.…”

Section: Artefactual Multifractality In the Rössler Systemmentioning

confidence: 81%

Wavelet-based discrimination of isolated singularities masquerading as multifractals in detrended fluctuation analyses

et al. 2020

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The robustness of two widespread multifractal analysis methods, one based on detrended fluctuation analysis and one on wavelet leaders, is discussed in the context of time-series containing non-uniform structures with only isolated singularities. Signals generated by simulated and experimentallyrealized chaos generators, together with synthetic data addressing particular aspects, are taken into consideration. The results reveal essential limitations affecting the ability of both methods to correctly infer the non-multifractal nature of signals devoid of a cascade-like hierarchy of singularities. Namely, signals harboring only isolated singularities are found to artefactually give rise to broad multifractal spectra, resembling those expected in the presence of a well-developed underlying multifractal structure. Hence, there is a real risk of incorrectly inferring multifractality due to isolated singularities. The careful consideration of local scaling properties and the distribution of Hölder exponent obtained, for example, through wavelet analysis, is indispensable for rigorously assessing the presence or absence of multifractality.

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Ordered Avalanches on the Bethe Lattice

Cited by 3 publications

References 52 publications

Complexity in Economic and Social Systems: Cryptocurrency Market at around COVID-19

Complexity in Economic and Social Systems: Cryptocurrency Market at around COVID-19

Identification of Self‐Organized Critical State on Twitter Based on the Retweets’ Time Series Analysis

Wavelet-based discrimination of isolated singularities masquerading as multifractals in detrended fluctuation analyses

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