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Multiscale characteristics of the emerging global cryptocurrency market

Marcin Wątorek, Stanisław Drożdż, Jarosław Kwapień, Ludovico Minati, Paweł Oświęcimka, Marek Stanuszek

arXiv:2010.15403v2q-fin.STcs.CEecon.EMstat.CO

TL;DR

The review asks how cryptocurrency markets develop complexity and how their statistical and correlation structures compare with traditional markets. It synthesizes statistical-physics, multifractal, cross-correlation, and network analyses, finding mature-market-like individual time-series characteristics alongside distinct cross-market synchronization and pandemic-era coupling changes.

  • Problem

    The review examines how cryptocurrency-market complexity evolves and how its correlations and structural properties compare with traditional financial markets.

  • Method

    The paper reviews high-frequency cryptocurrency-market studies using statistical-physics, multifractal, cross-correlation, and network methods.

  • Results

    Cryptocurrency time-series complexity approaches mature-market characteristics, while cryptocurrency cross-correlations differ from Forex and changed substantially during the Covid-19 turmoil.

  • Takeaways & Limitations

    Cryptocurrency markets became more complex and cross-correlated over time, with stronger correlations associated with fewer triangular arbitrage opportunities.

  • Takeaways & Limitations

    Bitcoin’s proof-of-work protocol has high energy and computing costs and limited capacity, averaging about five transactions per second.

Abstract

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The review introduces the history of cryptocurrencies, offering a description of the blockchain technology behind them. Differences between cryptocurrencies and the exchanges on which they are traded have been shown. The central part surveys the analysis of cryptocurrency price changes on various platforms. The statistical properties of the fluctuations in the cryptocurrency market have been compared to the traditional markets. With the help of the latest statistical physics methods the non-linear correlations and multiscale characteristics of the cryptocurrency market are analyzed. In the last part the co-evolution of the correlation structure among the 100 cryptocurrencies having the largest capitalization is retraced. The detailed topology of cryptocurrency network on the Binance platform from bitcoin perspective is also considered. Finally, an interesting observation on the Covid-19 pandemic impact on the cryptocurrency market is presented and discussed: recently we have witnessed a "phase transition" of the cryptocurrencies from being a hedge opportunity for the investors fleeing the traditional markets to become a part of the global market that is substantially coupled to the traditional financial instruments like the currencies, stocks, and commodities. The main contribution is an extensive demonstration that structural self-organization in the cryptocurrency markets has caused the same to attain complexity characteristics that are nearly indistinguishable from the Forex market at the level of individual time-series. However, the cross-correlations between the exchange rates on cryptocurrency platforms differ from it. The cryptocurrency market is less synchronized and the information flows more slowly, which results in more frequent arbitrage opportunities. The methodology used in the review allows the latter to be detected, and lead-lag relationships to be discovered.

1. Introduction

Financial markets exhibit complex, self-organized behavior shaped by information flows, heterogeneous participants, and feedback mechanisms. Cryptocurrencies provide an unusually recent market whose development can be studied from its origin, while this review surveys its history, technologies, fluctuations, and statistical structure.

  • Financial markets develop complex phenomena such as speculative bubbles and crashes through rapid information flow, diverse investment horizons, and feedback mechanisms.
  • Cryptocurrencies offer a rare opportunity to observe structural self-organization from market origin through maturation using high-frequency data.
  • The cryptocurrency market expanded from Bitcoin’s introduction into a large multi-platform market with thousands of cryptocurrencies and trading pairs.The first widely recognized BTC-to-fiat exchange platform, Mt. Gox, was founded in February 2011; by October 2020, about 3,600 cryptocurrencies traded across 350 platforms.
  • The review compares cryptocurrency price distributions, autocorrelations, and inter-transaction times with Forex and examines nonlinear correlations, multifractal properties, and cross-platform relationships.It also discusses trading-frequency dependence, triangular arbitrage, and network structure.
  • The paper applies statistical-physics methods, including multifractal analysis and network approaches, to characterize cryptocurrency market complexity and relationships.

2. The emergence and technology of cryptocurrencies

Cryptocurrencies emerged alongside concerns about centralized monetary systems and developed from Bitcoin into a diverse, exchange-based market. Their blockchain architecture enables decentralized record-keeping and consensus, while the expanding market also exhibits major technical and organizational trade-offs.

  • History: Bitcoin emerged around the 2008 financial crisis as a decentralized alternative combining cryptography, distributed databases, and Proof of Work.The review links its emergence to expanded central-bank monetary bases and weakened trust in fiat currencies.
  • The network: Bitcoin’s network uses consensus among distributed users to agree on ownership and currency creation without requiring mutual trust.Proof of Work lets miners validate block candidates, with mining pools using GPU- or ASIC-based computing because validation is computationally costly.
  • Core technology: Blockchain records transactions in linked blocks, making past entries economically difficult to alter while regulating block creation through computational difficulty.Bitcoin blocks are created approximately every 10 minutes, and the maximum block size is 1 MByte.
  • The network: Bitcoin’s security architecture imposes low capacity and high costs: the network handles about 5 transactions per second versus Visa’s roughly 1700.The review identifies computing investment, electricity consumption, and propagation requirements as associated costs and constraints.
  • Applications: Ripple illustrates protocol diversification beyond Bitcoin by replacing Proof of Work and miners with trusted nodes, while Ethereum extended blockchain use toward decentralized applications.Ripple was created in 2012; Ethereum’s platform supports distributed execution of computer code.

3. Statistical properties of fluctuations

The review compares cryptocurrency return statistics, trading pace, and temporal dependence across assets, exchanges, and Forex benchmarks. It finds that increasing trading frequency accompanies more mature fluctuation scaling and stronger, longer volatility structure, while signed-return memory remains absent.

  • Data and measures: The analysis compares fiat- and cryptocurrency-denominated rates, independent exchanges, and EUR/USD using inter-transaction times, return distributions, and autocorrelations.Returns are defined as logarithmic exchange-rate changes over a fixed interval.
  • Trading pace: BTC/USD trading activity rose sharply during bull phases, with higher volume and shorter average inter-transaction times.The 2017 speculative bubble coincided with a substantial volume increase and reduced inter-transaction times.
  • Fluctuation distributions: Power-law scaling ranges do not exceed 1.5 decades and fall below one decade in 2018, so the distributions are safer interpreted as signatures rather than precise power laws.The review also notes that such power-law forms may reflect finite-size effects and be non-universal.
  • Fluctuation distributions: γ increased from 1.7±0.3 in 2012 to 4.5 ± 0.1 in 2018 as average inter-transaction times shortened.The authors relate this relationship to the market’s internal time-flow.
  • Fluctuation distributions: Cryptocurrency return tails generally approach inverse-cubic scaling, but less-liquid rates show thicker tails, poorer scaling, or faster decay across exchanges.On Kraken, most examined rates have γ around 3, while BTC/ETH has γ ≈3.2; Binance tails decay faster than Kraken counterparts.
  • Temporal autocorrelations: Signed-return autocorrelations drop immediately to zero or below zero, whereas volatility autocorrelations decay by power law and persist longer in slower cryptocurrency markets.Volatility clustering spans roughly 10,000 minutes on Kraken versus about 1,000 minutes on Binance; cryptocurrency cluster lengths exceed those of EUR/USD.

4. Multiscale correlations

The review uses nonlinear-correlation and multifractal methods to study multiscale cryptocurrency dynamics and compares correlation behavior across trading platforms. Surrogate tests show that the observed multiscale structure depends on nonlinear correlations rather than return distributions alone.

  • Motivation: Linear measures such as autocorrelation, spectral density, and Pearson correlation do not capture the nonlinear dependencies typical of financial markets.These nonlinear correlations are identified as a primary source of temporal multifractality.
  • Methods: The analysis applies multifractal detrended fluctuation analysis and multifractal cross-correlation analysis to cryptocurrency time series.These methods extend multifractal analysis to cross-correlation cases.

4.1. Detrending based multifractal methodology

The review presents detrending-based multifractal methods for quantifying nonlinear scaling and multiscale cross-correlations in time series. It defines fluctuation functions, generalized Hurst exponents, singularity spectra, and cross-correlation measures while highlighting methodological pitfalls.

  • DFA removes polynomial trends from nonstationary data, but the polynomial degree must balance trend removal against preservation of fluctuation structure.A second-order polynomial is typical for financial time series.
  • MFDFA extends DFA to quantify nonlinear organization in a single time series, while MFCCA extends multifractal analysis to cross-correlations.
  • Absolute-value treatments of cross-correlation fluctuations can create artificial multifractality, motivating MFCCA as a solution to erroneous conclusions.
  • MFCCA evaluates scaling and multiscale detrended cross-correlation, with q emphasizing large fluctuations for positive values and small fluctuations for negative values.For perfect multiscale cross-correlation, d_xy(q) = 0; nonzero values indicate desynchronization.
  • The generalized Hurst exponent h(q) distinguishes monofractal series, where it is constant, from multifractal series, where it depends on q.For q = 2, h(q) corresponds to the standard Hurst exponent.
  • The singularity spectrum f(α) describes the fractal dimensions of points with Hölder exponent α, while its width measures singularity diversity.A limited scaling range can still make spectrum width useful for assessing detrended-correlation heterogeneity.

4.2. Analysis of the Hurst exponent in the cryptocurrency market

The review uses Hurst exponents to track persistence and maturation across cryptocurrency exchange rates and platforms. Results show movement toward H ≈ 0.5 as trading activity increased, with differences between pairs and exchanges.

  • H = 0.5 denotes uncorrelated successive fluctuations, while deviations from 0.5 indicate persistence or antipersistence.Mature financial markets typically have Hurst exponents near 0.5.
  • 2018 marked the year when BTC/USD attained characteristics closest to those typically observed for Forex.
  • From 2018, H approached 0.5 for Kraken pairs involving USD and EUR, while BTC/ETH remained antipersistent until mid-2018.Before this shift, the Kraken exchange rates had H < 0.5 until mid-2017.
  • Higher average H values on Binance than Kraken paralleled Binance’s higher trading frequency in 2018.The comparison covered equivalent exchange rates over the whole year 2018.

4.3. Multiscaling of the exchange rates

The review examines how multiscaling in cryptocurrency exchange rates evolved over time and differed across platforms and from Forex. It finds increasing complexity, but persistent asymmetries and narrower spectra than EUR/USD in several comparisons.

  • 4.3.1. Temporal evolution of the multiscale autocorrelations: From 2012 to 2018, BTC/USD showed progressively improved fluctuation-function scaling, especially for q < 0, alongside shorter inter-transaction times.
  • 4.3.1. Temporal evolution of the multiscale autocorrelations: 2013–2017 BTC/USD spectra were left-asymmetric, whereas 2018 became nearly symmetric with A_α ≈ −0.03 and Δα ≈ 0.41.The widest spectrum occurred in 2017, with Δα ≈ 0.5 and A_α ≈ 0.34.
  • 4.3.1. Temporal evolution of the multiscale autocorrelations: Fourier phase randomization and shuffling removed the observed multiscale effects, indicating that the spectra depended on nonlinear correlations and temporal correlations.
  • 4.3.2. Multiscale characteristics for currencies and cryptocurrencies: Binance displayed better-developed nonlinear organization of small fluctuations than Kraken, attributed to its higher trading frequency.The observed multiscale effects disappeared for both platforms when Fourier and shuffled surrogates were used.
  • 4.3.2. Multiscale characteristics for currencies and cryptocurrencies: For Kraken cryptocurrencies, h(q) depended clearly on q for medium and large returns but not negative q, unlike the symmetric organization of EUR/USD.BTC/USD also had a symmetric f(α) spectrum in 2018.
  • 4.3.2. Multiscale characteristics for currencies and cryptocurrencies: EUR/USD had the widest and most symmetric spectrum, with Δα ≈ 0.75 and A_α ≈ −0.02, while Kraken cryptocurrency spectra were narrower.The BTC/ETH spectrum was widest among Kraken pairs, with Δα ≈ 0.42.
  • 4.3.2. Multiscale characteristics for currencies and cryptocurrencies: Shuffled-data spectra remained narrower than early Bitstamp spectra because Kraken had thinner return-distribution tails.
  • 4.3.2. Multiscale characteristics for currencies and cryptocurrencies: Overall, BTC/USD complexity approached typical Forex levels by 2017 and reached them in 2018, with ETH/USD and BTC/ETH showing similar multiscale properties.

5. Multiscale cross-correlations

Cryptocurrency exchange rates exhibit scale-dependent cross-correlations shaped by liquidity, shared fiat bases, triangle relations, and synchronization across platforms. These correlations strengthen over longer scales, while structural differences create weaker short-scale dependence and arbitrage opportunities.

  • Scaling behavior: Scaling appears for medium and large returns (q > 0), while small returns (q < 0) show no multiscale cross-correlation.The bivariate fluctuation function becomes negative for q < 0.
  • Scaling behavior: Cross-correlation multifractality is reflected by λ(q), with weaker scaling and less-developed multifractality for BTC/ETH–BTC/EUR and BTC/ETH–BTC/USD.These pairs also have the weakest scaling among the ten examined exchange-rate pairs.
  • Intra-platform correlations: Pairs sharing a fiat currency or the same cryptocurrency in EUR and USD reach the strongest correlations, often approaching unity at large scales.For BTC/EUR–BTC/USD, the high correlation is attributed to the lower volatility of traditional currencies relative to cryptocurrencies.
  • Arbitrage and synchronization: Arbitrage opportunities are linked to incomplete short-scale synchronization and become less frequent and smaller when exchange rates synchronize more intensely.The observed decline in arbitrage frequency and size toward the end of 2018 coincided with shorter inter-transaction times and increased short-scale correlation.
  • Platform structure: On Binance, USDT serves as a proxy for USD, and replacing it with a less liquid cryptocurrency reduces short-scale cross-correlations.Binance does not directly list cryptocurrency–fiat exchange rates, limiting direct comparison with some Kraken cases.
  • Intra-platform correlations: Cross-correlations generally increase with scale, but their short-scale strength depends on market synchronization, liquidity, and whether exchange rates form a triangle relation.Non-triangle pairs with different bases have substantially weaker correlations across q and scales, whereas more frequent trading accelerates synchronization.

6. Correlation matrix and network analysis of cross-correlations

The review examines cross-correlations among 100 cryptocurrencies using daily USD quotes from October 2015 to March 2019, alongside their price and capitalization evolution.

  • Data and market evolution: Figure 60 tracks prices for the 100 largest-capitalization cryptocurrencies and compares the capitalization shares of BTC, ETH, XRP, LTC, and the remainder.
  • Data and market evolution: Cryptocurrency capitalization is defined as price multiplied by the number of issued units.
  • Data and market evolution: Market capitalization rose systematically around the turn of 2017–2018 before a bear market continued through 2018.
  • Data and market evolution: BTC’s market share fluctuated sharply, exceeding 80% in March 2017, falling near 40% in May 2017, and returning to 80% in December 2017.

6.1. Correlation matrix

Correlation structure depends strongly on the chosen base currency: BTC produces the least-correlated perspective, whereas peripheral or volatile bases can make the market appear highly collective.

  • Correlation matrices: Correlation matrices compare cryptocurrency exchange-rate returns against a selected fiat or cryptocurrency base currency.Each matrix contains Pearson correlations among exchange-rate pairs sharing that base.
  • Correlation matrix elements: The off-diagonal correlation distribution differs from the random case for every base currency, with BTC showing the smallest deviation and thus the least-correlated perspective.
  • Correlation matrix elements: Peripheral base cryptocurrencies make the market more collective, with a representative distribution mean near 0.9 and many correlations above 0.5.
  • Largest eigenvalue: A volatile fictitious base with σ = 10 produces a largest eigenvalue above 80 because its valuation changes shift all expressed cryptocurrency prices together.
  • Largest eigenvalue: λTEK max is largest for a small-capitalization cryptocurrency, while BTC has the largest capitalization and a lower eigenvalue.
  • Quasi-idempotence: Quasi-idempotence confirms Bitcoin’s centrality, with the lowest ιBTC(∞) values observed when BTC is the base currency.
  • Temporal evolution: The largest eigenvalue increased particularly for USD and low-volatility fictitious bases during the 2017–2018 bull market and crash, then declined after the market calmed.
  • Temporal evolution: ETH temporarily gained importance during ICO-mania, while a 102% XRP/USD increase on 04/02/2017 caused a sharp XRP-based eigenvalue rise.

6.2. Minimal spanning tree representation of the cryptocurrency market

Minimal spanning trees reveal that cryptocurrency-market topology changes with the base currency and over time, shifting between centralized Bitcoin-led and more decentralized structures.

  • MST construction: The network represents exchange rates as nodes and their cross-correlations as weighted edges, transformed into metric distances before MST construction.Prim’s algorithm is then used to construct the minimal spanning tree.
  • Base-currency dependence: For USD as base, the MST is strongly centralized: BTC/USD has degree 51, while all other nodes have degree at most 10.Node degree is interpreted as a centrality measure reflecting relative influence over the remaining cryptocurrencies.
  • Base-currency dependence: The BTC-based MST is much more decentralized and lacks a dominant node, whereas less-important cryptocurrency bases produce even more centralized trees connected mainly to BTC.
  • Degree scaling: Across the whole period, satisfactory degree scaling appears mainly for BTC, while other bases are disrupted by highly centralized MSTs.
  • Degree scaling: An XRP-based window exhibits a scale-free tail with γXRP = 1.43 ± 0.07, while a later USD-based window shows γUSD = 1.5±0.08.
  • Temporal evolution: The market became more decentralized during the final bull-market phase, with γETH, γBTC, and γUSD above 1.8, before BTC dominance returned.
  • Temporal evolution: When BTC dominance returned, the BTC/USD node degree increased fivefold and the MST reverted to a centralized topology.

6.3. The largest eigenvalue vs. MST maximum node degree

The largest eigenvalue and MST maximum degree jointly rank base-currency importance, showing Bitcoin’s persistent dominance except during a temporary ICO-driven shift toward Ethereum.

  • Joint structural indicators: The largest eigenvalue and MST maximum node degree are mutually related indicators of the market’s collective and hierarchical structure.
  • Joint structural indicators: Using a dominant cryptocurrency as base removes part of its own dynamics from the cross-correlations, making the market appear less collective and more decentralized.
  • Temporal comparison: A hierarchical power-law degree structure formed with k(X) max below 40, then disappeared after the bull market ended and BTC dominance returned.
  • Whole-period structure: Over the full interval, k(X) max reached approximately 80 for most base currencies, consistent with a centralized MST dominated by BTC/USD.
  • Whole-period structure: BTC appears to dominate the cryptocurrency market more strongly than USD and is identified as its most natural base currency.

6.4. Cryptocurrency network topology on Binance

The Binance qMST analysis examines cryptocurrency network topology across time scales and return amplitudes, showing increasing decentralization and a scale-dependent transition toward hierarchical structure.

  • Method: qMST extends the minimum spanning tree across time scales s and fluctuation amplitudes selected by q using detrended cross-correlation distances.Only q = 1 and q = 4 are considered, ensuring the distance is a metric.
  • Data: The Binance network contains 94 exchange-rate quotes sampled at 1-minute resolution throughout 2018, predominantly with BTC as the base currency.BTC and ETH were the most frequently traded bases, with 93 and 90 exchange rates respectively.
  • Topology: Mean metric distance decreases with scale and increases with q, whereas binary shortest-path length increases with both scale and q, indicating reduced centralization for large returns.These patterns reflect stronger long-scale cross-correlations and greater network decentralization at q = 4.
  • Degree distributions: The qMST degree distributions show no clear power-law scaling up to approximately 120 minutes because ETH remains dominant at short scales.At longer scales, the tail exponent supports a transition toward organized network topologies.
  • Degree distributions: The hierarchical-network value γ(q, s) ≈1.6 is reached at approximately 7,000 minutes for q = 1 and 1,000 minutes for q = 4.Large returns are globally less correlated, creating more sub-clusters and making standard MST construction less sensitive than qMST.
  • Topology: Cross-correlations increase with time scale because less frequently traded pairs require more time to synchronize, while the MST becomes more diverse and decentralized.The dominant ETH position at short scales disappears as a hierarchical structure develops.

7. Summary and conclusions

The review synthesizes statistical-physics evidence that cryptocurrency markets have matured toward the complexity of traditional markets while retaining distinct cross-correlation structures and unresolved development boundaries.

  • Scope and methods: The review combines high-frequency cryptocurrency data with detrended fluctuation, multifractal, random-matrix, and complex-network methods to study market evolution.Its emphasis is on nonlinear dependencies, cross-correlations, and network structure.
  • Market maturation: Cryptocurrency markets have gradually approached maturity but still differ from Forex in liquidity and transaction numbers.The review identifies financial stylized facts as indicators of market development stage.
  • Individual time-series: BTC/USD and ETH/USD changed from short-term to long-term return memory, while return tails shifted from Lévy-stable behavior toward an inverse cubic law around 2013–2014.The Hurst exponent later rose from approximately 0.4 to approximately 0.5 in 2017.
  • Individual time-series: Large cryptocurrency returns are multiscaling, but smaller returns are monofractal unlike corresponding returns on Forex and other mature markets.The asymmetry of singularity spectra also evolved toward a more mature symmetric form in 2018.
  • Cross-correlations: Cross-correlations are stronger for exchange rates sharing a common base cryptocurrency and form clusters typically linked by triangular relationships.Slower information flow distinguishes these clusters from Forex, where geographic proximity and other factors also correlate currencies.
  • Scope boundary: The review cautions that it remains too early to determine whether the cryptocurrency market will survive substantially or which direction it will take.Liquidity is described as likely to improve, while BTC and ETH can support diversification within the cryptocurrency market.
  • Covid-19 impact: During the Covid-19 turmoil, major cryptocurrency prices became cross-correlated with safe and risky traditional instruments, suggesting a shift from safe-haven status toward global-market integration.The persistence of this coupling beyond the pandemic period remains an open question.

A. Full names and statistical properties of cryptocurrencies from Binance and Kraken

The appendices document cryptocurrency names, exchange-rate distributions, statistical properties, and triangular-arbitrage measures for Binance and Kraken datasets.

  • Cryptocurrency names: Table A.5 lists symbols and full names of cryptocurrencies appearing on both Binance and Kraken.The table provides the naming reference for the two-platform comparison.
  • Return distributions: Figures A.77 and A.78 show cumulative distributions of absolute normalized 1-minute log-returns for Binance and Kraken during 2018.The figures provide platform-specific return-distribution views.
  • Statistical properties: Tables A.6 and A.7 report estimated γ, non-trading-period duration and counts, average USD volume per minute, and Hurst exponents for cryptocurrency pairs listed on Binance in 2018.These tables organize statistical and activity measures for the Binance pairs.
  • Arbitrage: Tables A.8 and A.9 report average and maximum triangular-arbitrage opportunities on Binance and Kraken in 2018.The paired tables enable platform-level comparison of arbitrage measures.

B. List of 100 cryptocurrency names from CoinMarketCap

Table B.10 provides the full names of the 100 cryptocurrencies discussed in Section 6.

  • Cryptocurrency names: Table B.10 lists the full names of the cryptocurrencies used in Section 6.It serves as the naming reference for that section’s 100-cryptocurrency analysis.

C. List of 94 cryptocurrency names from Binance

Table C.11 provides the full names of the cryptocurrencies considered in section 6.4.

  • Table C.11 lists the full names of the cryptocurrencies from section 6.4.
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