Multiscale characteristics of the emerging global cryptocurrency market

Background

• Financial markets exhibit complex-system features because heterogeneous participants and nonlinear feedback generate emergent phenomena, including speculative bubbles and flash crashes.Participants operate across horizons ranging from years to milliseconds, while economic, political, and social information influences market behavior.Source: §1 · p. 5

Motivation

• Cryptocurrency markets uniquely allow researchers to observe structural self-organization from market origin to maturity and test whether their complexity resembles traditional markets, especially Forex.Established markets cannot be observed from their origins, whereas cryptocurrencies provide this opportunity during rapid development.Source: §1 · p. 5

Background

• The cryptocurrency market developed rapidly after Bitcoin’s 2008 proposal, reaching thousands of cryptocurrencies, hundreds of platforms, and substantial capitalization while remaining decentralized and lacking a single reference price.The passage reports approximately 3,600 cryptocurrencies, 350 platforms, nearly 30,000 pairs, and about 350 billion USD capitalization in October 2020.Source: §1 · pp. 5–6

Scope of the review

• The review compares cryptocurrency return distributions, autocorrelations, inter-transaction times, nonlinear correlations, multifractal properties, and cross-market dependencies with Forex and traditional financial markets.It also examines frequency dependence, correlations within and across platforms, triangle arbitrage, and the Covid-19 impact on cryptocurrency–traditional-market relationships.Source: §1 · p. 6
• The review concludes its introductory roadmap with a network analysis in which Bitcoin is identified as a natural base cryptocurrency for other cryptocurrencies.The network approach is presented as the final part of the review.Source: §1 · p. 6

2.1. History: from barter through the blockchain

• Bitcoin emerged after 2008 by combining asymmetric cryptography, a distributed database, and Proof of Work into a decentralized blockchain register.Cryptocurrencies aim to avoid institutional control, enable near-zero-latency transfers, combine cash-like anonymity with electronic convenience, and impose built-in supply limits.Source: §2.1 · p. 7
• The technology’s diffusion produced speculative cycles and platform competition: the 2017 ICO boom doubled cryptocurrencies from 700 to 1,400 and lifted total capitalization to USD 800 billion before the bubble burst in January 2018.Ethereum’s smart contracts enabled ICO fundraising, while EOS raised 4.2 billion USD in its year-long offering, trading higher scalability for reduced security.Source: §2.1 · pp. 8–9, §2.3 · p. 18

2.2. Core technology

• The blockchain solves double spending by making transactions public and independently verifiable through peer-to-peer networking, cryptography, and chained blocks.Bitcoin’s register is decentralized, copied across participants, and designed to prevent corruption of transaction history.Source: §2.2 · pp. 9–10, §2.2.1 · p. 10

2.2.1. The network

• Proof of Work lets miners validate transactions and reach network-wide ownership consensus without a centralized manager, but requires specialized hardware, substantial electricity, and computationally costly hashing.Miners search for a nonce producing a hash with a prescribed number of leading zeros; economically unprofitable forks and rejected invalid blocks support consensus.Source: §2.2.1 · pp. 11–13
• Bitcoin’s security mechanisms also impose limits: it creates a block about every 10 minutes, caps supply at 21 million Bitcoins, averages about 5 TPS versus Visa’s 1700 TPS, and remains vulnerable to 51% attacks.Proof of Work consumes electricity at a scale comparable to entire countries, while SegWit and the proposed Lightning Network seek greater capacity with trade-offs in security.Source: §2.2.1 · pp. 14–15

2.2.2. Methods for attaining network-wide consensus

• Proof of Stake replaces competitive hashing with stake-based validator selection, improving efficiency and speed but retaining vulnerability to 51% attacks; delegated Proof of Stake adds voting and greater scalability.PoS validators risk losing their stake for fraudulent transactions, while DPoS delegates are elected by users and can be removed for poor performance.Source: §2.2.2 · pp. 15–16

2.3. Cryptoassets and diversified applications of the blockchain technology

• Blockchain applications expanded beyond payment cryptocurrencies into cryptoassets, including cryptocommodities that fuel decentralized applications and tokens enabled by smart contracts.Ethereum exemplifies this expansion as an open-source platform for programmable contracts and decentralized applications, while Ripple and private coins pursue alternative transfer and anonymity models.Source: §2.3 · pp. 16–18
• Cryptoassets comprise tokens, stablecoins, and DeFi applications alongside blockchain-based cryptocommodities, extending blockchain use beyond cryptocurrency transactions.Tokens commonly support dApps or ICOs; stablecoins track fiat currencies such as USDT’s one-to-one link with the US dollar, while DeFi uses smart contracts for borrowing, lending, and banking services [52].Source: §2.3 · pp. 19–20

2.4. Cryptocurrency trading

• Cryptocurrency trading is decentralized across approximately 350 exchanges, operates continuously, is dominated by individual investors, and lacks a common reference price unlike Forex.Only bitcoin has a futures contract quoted on the CME Group.Source: §2.4 · p. 20
• Exchange fragmentation creates valuation differences and arbitrage opportunities, including triangular arbitrage and decentralized-exchange trading through smart contracts without a central server [59].The same cryptocurrency pairs trade on multiple exchanges and can be transferred almost immediately worldwide.Source: §2.4 · p. 20
• The market includes approximately 3600 cryptocurrencies and nearly 30,000 exchange rates, with capitalization around 350 billion USD after rapid growth and a speculative bubble phase.Actively traded cryptocurrencies increased sharply in 2017, while ICO offers continued rising systematically.Source: §2.4 · p. 21

3.1. Data

• The datasets cover BTC, ETH, less-liquid cryptocurrencies, crypto–fiat and crypto–crypto rates, and Binance, Kraken, Bitstamp, and Forex benchmarks, with returns defined as logarithmic exchange-rate changes.The EUR/USD benchmark excludes weekends and holidays, unlike continuously recorded cryptocurrency data.Source: §3.1 · p. 22

3.2. Average inter-transaction time

• BTC/USD trading accelerated from 2012 to the 2017–2018 bubble, when inter-transaction times reached about one second; after the bear market, they remained below 10 seconds.Volume increased as inter-transaction times decreased, while the subsequent bear market reduced volume but left it above the pre-crash 2017 level.Source: §3.2 · p. 23, Figure 11 · p. 23

3.3. Fluctuation distributions

• At 10-second sampling, BTC/USD tail exponents rose from γ2012 = 1.7±0.3 to γ2018 = 4.5 ± 0.1 as inter-transaction times shortened, approaching inverse-cubic behavior at higher trading frequency.The observed scaling ranges are limited, so the distributions show signatures rather than precise power laws; BTC/USD reached γ ≈3.5 in 2014 and γ ≈4.5 in 2018.Source: §3.3 · pp. 27, 29
• Across platforms, both return distributions have γ ≈3, but Binance’s higher trading frequency produces faster-decaying tails than Kraken’s less-liquid rates.Binance has shorter non-trading intervals and fewer non-trading periods, whereas Kraken’s slower internal time yields thicker tails and poorer scaling.Source: §3.3 · pp. 28–29, Table 1 · p. 29

3.4. Temporal autocorrelations

• BTC/USD volatility memory strengthened over time: it was short-range in 2012, but a power-law decay emerged from 2013 and extended beyond 10^4 minutes by 2018.The increase in volatility autocorrelation time is attributed to the growing number of transactions per unit time.Source: §3.4 · pp. 30–31
• Cryptocurrency volatility autocorrelations decay as power laws, extending to about a week versus about one day for EUR/USD, while signed-return autocorrelations drop immediately to zero or below.For Binance and Kraken, the volatility-decay cutoff is about 1,000 and 10,000 minutes, respectively.Source: §3.4 · pp. 31–32

Motivation

• Nonlinear correlations are a primary source of multifractality in financial markets, while fat-tailed probability distributions provide an additional reinforcing factor.Linear measures such as autocorrelation, spectral density, and Pearson correlation capture only linear interdependencies.Source: §4 · p. 33

Methodological basis

• Power-law decay in absolute-log-return autocorrelations indicates nonlinear correlations and motivates expecting multiscaling in cryptocurrency-market data.The anticipated multiscaling is examined using multifractal detrended fluctuation analysis, multifractal cross-correlation analysis, and the q-dependent detrended cross-correlation coefficient ρ(q, s).Source: §4 · p. 33

Methods

• The cryptocurrency time-series analyses apply multifractal methods to quantitatively characterize nonlinear correlations and cross-correlations.The methods include MFDFA, its cross-correlation generalization MFCCA, and ρ(q, s).Source: §4 · pp. 33–34

4.1. Detrending based multifractal methodology

• DFA removes polynomial trends from nonstationary data, but detrending degree is critical, while multifractal indications may be limited by finite samples, fat tails, outliers, or narrow scaling ranges.A second-order polynomial is commonly used for financial data; multifractal methods provide quantitative descriptions of temporal organization but do not always establish genuine multifractality.Source: §4.1 · pp. 34–35
• MFCCA extends MFDFA and DCCA to quantify scaling properties and multiscale detrended cross-correlations, while avoiding artifacts caused by taking absolute cross-correlation fluctuations.MF-DXA is an earlier extension of MFDFA, whereas MFCCA was proposed to address erroneous conclusions and artificial multifractality in cross-correlations.Source: §4.1 · p. 35, §4.1.1 · p. 35

4.1.1. MFCCA as a generalization of MFDFA and DCCA

• MFCCA detrends profiles segmentwise, estimates q-dependent scaling exponents, and identifies multifractality when λ(q) or h(q) depends on q rather than remaining constant.Positive q emphasizes large fluctuations, negative q emphasizes small fluctuations, and the singularity spectrum characterizes the diversity and asymmetry of singularities.Source: §4.1.1 · pp. 36–37

4.1.2. Detrended cross-correlation coefficient

• The q-dependent detrended correlation coefficient ρ(q, s) decomposes cross-correlations by fluctuation magnitude and scale, including nonstationary signals that need not be fractal.For q > 0, ρ(q, s) ranges from −1 to 1 and has the Pearson-correlation interpretation; q < 0 emphasizes small fluctuations, while q > 0 emphasizes large ones.Source: §4.1.2 · p. 38

4.1.3. Relationship between λ(q) and ρ(q, s)

• The relationship between λ(q) and ρ(q, s) determines scale dependence: ρ(q, s) increases, decreases, or remains constant with s when dxy(q) is positive, negative, or zero, respectively.This result assumes finite-length time series; as s approaches infinity, only λ(q) ≤ hxy(q) is allowed.Source: §4.1.3 · pp. 38–39

Interpretation and method

• The Hurst exponent quantifies persistence: H = 0.5 means no autocorrelation, H > 0.5 indicates positive persistence, and H < 0.5 indicates antipersistence.The study calculates H using MFDFA with q = 2; convergence toward 0.5 is treated as market maturation, while short-term declines below 0.5 may precede trend changes.Source: §4.2 · p. 39

BTC/USD evolution

• By 2018, BTC/USD from Bitstamp had approached H = 0.5 after being antipersistent by late 2016, paralleling characteristics closest to Forex.Monthly Hurst estimates used 10-second log-returns and approximately 260,000 observations per window; H < 0.5 indicates antipersistence, whereas H = 0.5 indicates uncorrelated fluctuations.Source: §4.2 · p. 39, Figure 22 · p. 40

Cross-rate evolution

• From 2018, Kraken pairs involving USD or EUR reached H = 0.5, while BTC/ETH remained antipersistent until mid-2018.These shifts coincided with shortened inter-transaction times beginning in April 2017; EUR/USD is shown for comparison.Source: §4.2 · p. 39, Figure 22 · p. 40

Platform comparison

• Binance cryptocurrency pairs had larger 2018 Hurst exponents, closer to 0.5, than equivalent Kraken pairs, consistent with Binance’s higher trading frequency.The comparison uses one-minute returns over the full year 2018 from both platforms.Source: §4.2 · pp. 40–41, Table 2 · p. 41
• ETC/ETH had the smallest Hurst exponent on both platforms, while BCH/BTC, XMR/BTC, and DASH/BTC were also antipersistent on Kraken.These pairs were characterized by low trading frequency, with H < 0.5 reported for the three Kraken pairs.Source: §4.2 · p. 41

4.3. Multiscaling of the exchange rates

• Cryptocurrency multiscaling is quantified with generalized Hurst exponents h(q) and singularity-spectrum width, which measures time-series complexity or internal structural diversity.MFDFA calculates h(q), while the admissible q range depends on return-distribution tails and available moments.Source: §4.3 · p. 41

4.3.1. Temporal evolution of the multiscale autocorrelations

• By 2018, BTC/USD developed symmetric multifractal organization, with Δα ≈0.41 and Aα ≈−0.03, after earlier dominance of large-return fluctuations.The 2017 spectrum was widest at Δα ≈0.5 with Aα ≈0.34, whereas 2012 was effectively monofractal or nonfractal because long-range nonlinear correlations were absent.Source: §4.3.1 · p. 43, Figure 24 · p. 44
• Binance exchange rates show wider, more symmetric singularity spectra than Kraken rates, indicating that higher trading frequency better develops nonlinear organization in small fluctuations.For both platforms, multiscale effects disappear in Fourier and shuffled surrogates; other low-frequency Kraken rates are generally monofractal.Source: §4.3.1 · pp. 43–44, Figure 25 · p. 45

4.3.2. Multiscale characteristics for currencies and cryptocurrencies

• Across 2016–2018, cryptocurrency rates exhibit heterogeneous organization mainly for medium and large returns, whereas EUR/USD shows multiscale organization across all fluctuation magnitudes.By 2017–2018, BTC/USD approached Forex-like complexity; ETH/USD and BTC/ETH also showed similar multiscale properties, with Binance closer to Forex than Kraken.Source: §4.3.2 · pp. 45–46, Figure 27 · p. 47
• Compared with cryptocurrency rates, EUR/USD has the widest and most symmetric spectrum, with Δα ≈0.75 and Aα ≈−0.02; crypto-crypto BTC/ETH reaches Δα ≈0.42.Other cryptocurrency/fiat rates have Aα ∈[0.7, 0.9] and Δα ≈0.35, so their small returns behave more like monofractal noise.Source: §4.3.2 · p. 45, Figure 28 · p. 47

5.1. Multiscale cross-correlations for the BTC and ETH

• Cross-correlations are strongest for BTC and ETH expressed in the same fiat currencies, while BTC/ETH–BTC/EUR and BTC/ETH–BTC/USD show the weakest scaling and multifractality.Scaling appears for medium and large returns (q > 0), but not for small returns (q < 0); for most pairs, ρ(q, s) increases with s, especially at q = 1.Source: §5.1 · pp. 48–50
• During 2018, short-scale BTC–ETH correlations increased, while triangular-arbitrage opportunities decreased in frequency and size as trading synchronization intensified.Before 2018, correlations near the smallest scales remained close to zero; after the January 2018 crash, BTC/ETH correlations with BTC/EUR and BTC/USD weakened because ETH declined faster than BTC.Source: §5.1 · pp. 50, 51, 53

5.2. Multiscale cross-correlations on the different trading platforms

• On Kraken and Binance, exchange rates sharing a common fiat or proxy base show the strongest cross-correlations, whereas unrelated-base rates remain substantially weaker, especially at short scales.Kraken reaches ρ(q, s) ≈0.8 for BTC/ETH expressed in the same fiat currency at s > 200 min; on Binance, USDT-based pairs are strongest, while liquidity raises maximum correlation.Source: §5.2.1 · pp. 54–57

5.2.1. Intra-platform multiscale cross-correlations

• Cross-correlation hierarchies are shaped primarily by fiat-currency involvement, liquidity, and return magnitude; distances increase with q and are typically larger on Binance than Kraken.On Kraken, the most liquid cryptocurrencies cluster most closely when expressed in fiat currencies, while same-cryptocurrency EUR/USD pairs form additional clusters reflecting correlated currency movements.Source: §5.2.1 · pp. 56, 57, 59, 61
• Within Binance, liquid cryptocurrencies form strongly correlated common-base clusters, whereas less liquid assets remain more independent, especially at q = 4.Large base-cryptocurrency fluctuations can correlate assets expressed in that base, analogous to volatility episodes in Forex.Source: §5.2.1 · pp. 61–62, Figure 41 · p. 62

5.2.2. Inter-platform multiscale cross-correlations

• On Binance and Kraken, triangle-related rates are more strongly correlated, Binance is stronger at short scales, and correlations converge by s ≈300 min.For ETH/USD∗–XRP/BTC, Kraken correlations can approach zero near s = 10 min, whereas longer-scale correlation levels converge across platforms.Source: §5.2.2 · p. 63, Figure 43 · p. 65
• Binance leads Kraken by 1–2 min for BTC/ETH and generally leads the remaining cross-platform pairs, while Bitstamp synchronizes with Kraken but lags Binance.The lead is strongest for more liquid rates; less liquid rates may require longer lags to synchronize large returns.Source: §5.2.2 · pp. 65–67, Figure 45 · p. 67, Figure 46 · p. 68

5.2.3. Arbitrage on the cryptocurrency market

• Cryptocurrency triangular arbitrage is larger on Kraken, lower on Binance, concentrated in less liquid rates, and rare for the most liquid rates at Δt = 1 min.The largest opportunities occurred during the volatile cryptocurrency crash period at the beginning of 2018; slower information diffusion and lower liquidity sustain these opportunities.Source: §5.2.3 · pp. 69–71, Table 4 · p. 70

5.3. Multiscale cross-correlations and triangular arbitrage on Forex

• Forex triangle-related rates synchronize more strongly than unrelated rates, while Forex correlations depend less on scale and remain much higher for unrelated pairs than in cryptocurrencies.For large returns, Forex cross-correlations are substantially weaker than for cryptocurrencies, with stronger q-dependence and pronounced triangle-related clustering.Source: §5.3 · pp. 72–74, Figure 52 · p. 74
• Forex triangular arbitrage is rare because high liquidity and trading frequency produce faster synchronization, appearing mainly during exceptional volatility such as the Swiss National Bank intervention and Brexit referendum.When turmoil periods are removed, the observed arbitrage opportunities disappear and cross-correlation strength increases.Source: §5.3 · pp. 74, 76, 77, Figure 55 · p. 77

5.4. COVID-19 impact on multiscale cross-correlations between the cryptocurrency market and traditional markets

• Covid-19 triggered four periods of significant cryptocurrency–traditional-market cross-correlations in 2020, unlike the insignificant relationships observed during 2018–2019.The correlations appeared during the January outbreak, March panic, June second wave, and late-August recovery period.Source: §5.4 · pp. 79, 81, Figure 58 · p. 80, Figure 59 · p. 81
• During the initial January 2020 outbreak, BTC negatively correlated with S&P500 at q = 4 and s = 360 min while positively correlating with JPY, CHF, and gold, whereas ETH remained insignificant.BTC therefore retained a hedge-like relationship to risky assets during this phase.Source: §5.4 · pp. 79–80, Figure 58 · p. 80, Figure 59 · p. 81
• During the March 2020 panic, BTC and ETH became positively correlated with traditional assets, with stronger BTC correlations at s = 360 min than s = 10 min.For q = 4, BTC was mainly linked to S&P500; for q = 1, it also correlated with copper, crude oil, gold, and CAD, while remaining negative with JPY.Source: §5.4 · pp. 80–81, Figure 58 · p. 80, Figure 59 · p. 81
• In June and from late August 2020, BTC and ETH showed increasingly broad positive correlations, eventually including JPY across all tested scales, possibly reflecting USD weakness.EUR became especially strongly correlated with both cryptocurrencies at s = 360 min, unlike before.Source: Figure 58 · p. 80, §5.4 · pp. 81–82, Figure 59 · p. 81
• The pandemic appears to have transformed cryptocurrencies from a market island into a connected part of global finance, though whether this change is transient or stable remains open.Correlations persisted during both sharp declines and the subsequent recovery phase.Source: §5.4 · pp. 81–82

Data and methodology

• The analysis covers N = 100 cryptocurrency daily USD quotes over 10/2015–03/2019, with T = 1278 observations aggregated from 273 trading platforms by transaction volume.The sample represents 95% of total cryptocurrency market capitalization.Source: §6 · pp. 82–83

Market evolution

• By the turn of 2017–2018, total cryptocurrency market capitalization rose systematically before entering a bear market throughout 2018.Figure 60 presents the price evolution and total market-capitalization shares for the largest cryptocurrencies.Source: Figure 60 · p. 82, §6 · p. 83

Market-share dynamics

• BTC’s market share fluctuated from over 80% in March 2017 to around 40% in May and back to 80% in December, while ETH and XRP moved oppositely.ETH’s increased valuation in early 2017 was associated with ICO activity on the Ethereum platform; ETH peaked in January 2018, nearly a month after BTC.Source: §6 · p. 83

6.1. Correlation matrix

• Correlation matrices are constructed from normalized logarithmic returns for each base currency, with Pearson coefficients, eigenvalues, eigenvectors, and eigensignals compared against the Wishart ensemble.The Marchenko-Pastur distribution provides the random-matrix reference for distinguishing noise-dominated eigenvalues from collective market structure.Source: §6.1 · pp. 83–84

6.1.1. Correlation matrix elements

• TEK-based exchange-rate correlations are strongest, with all pairs exceeding 0.5 and mean near 0.9, whereas BTC provides the least-correlated market perspective.Increasing fictitious-currency volatility shifts correlations rightward; σ = 10 produces behavior similar to TEK.Source: §6.1.1 · p. 84

6.1.2. Correlation matrix eigenvalues

• λmax ≈19 for USD versus λmax ≈9.7 for BTC, while λTEKmax accounts for more than 90% of the trace and squeezes other eigenvalues near zero.After removing the largest market factor, most residual eigenvalues fall within the Marchenko-Pastur limits and eigenvector components become approximately normal.Source: §6.1.2 · p. 86, Figure 62 · p. 87

6.1.3. The largest eigenvalue for various base currencies

• λmax varies systematically by base currency: it is largest for low-capitalization TEK and exceeds 80 for fict(σ = 10), reflecting valuation-dragging by volatile bases.BTC has the largest capitalization and relatively low λmax, while base-currency changes can make the entire market appear strongly synchronous or weakly correlated.Source: §6.1.3 · pp. 89, 91, Figure 65 · p. 90

6.1.4. Quasi-idempotence

• Bitcoin has the lowest quasi-idempotence values when used as the base, showing that the market’s non-random collective dynamics largely stem from Bitcoin’s influence.The measure assesses how closely a correlation matrix approaches its infinitely squared form, with anticorrelations clipped to zero because of convergence issues.Source: §6.1.4 · p. 91, Figure 66 · p. 92

6.1.5. Evolution of the market cross-correlation structure

• During the 2017–2018 bull market and crash, λmax rose sharply for USD and fict(σ = 1), then declined after market stabilization but remained above 2017 levels.ETH temporarily overtook BTC’s dominant role during the ICO period, while a 102% XRP/USD increase caused a corresponding spike in λXRPmax.Source: §6.1.5 · pp. 93–94

Construction

• MST edges are constructed by transforming correlation weights into metric distances in [0, 2] and applying Prim’s algorithm.The network represents exchange rates as nodes and cross-correlations as weighted edges.Source: §6.2 · p. 94

USD-based MST

• BTC/USD has degree 51 while every other node has degree at most 10, demonstrating a strongly centralized USD-based market MST.Node degree measures a cryptocurrency’s relative importance, and BTC’s dominance agrees with the largest-eigenvalue analysis.Source: §6.2 · p. 94, Figure 68 · p. 95

Base-currency dependence

• The BTC-based MST is much more decentralized with no dominant node, while less-important base cryptocurrencies produce even more centralized trees connected mostly to BTC.The topology therefore changes substantially with the base currency choice.Source: §6.2 · pp. 94–95, Figure 69 · p. 96

Degree-distribution scaling

• Only BTC shows whole-period scaling traces, while BTC’s exponent oscillates around 2 in some intervals and XRP reaches γXRP = 1.43 ± 0.07 with a scale-free tail.Scaling improves during 10/2017–03/2018; USD reaches γUSD = 1.5±0.08 in 04/2018–09/2018.Source: §6.2 · p. 95, Figure 70 · p. 96

Temporal evolution

• During the bull market, ETH temporarily became dominant and the market decentralized, but returning BTC dominance restored a centralized MST and eliminated scale-free CDF tails.Between 11/2017 and 03/2018, γETH exceeded 2; during 05/2018–07/2018, γETH, γBTC, and γUSD exceeded 1.8, while γXRP was about 1.6.Source: §6.2 · pp. 96–98

6.3. The largest eigenvalue vs. MST maximum node degree

• Base-currency choice changes the market’s apparent organization: dominant cryptocurrencies show weak collectivity and decentralization, whereas self-dynamic bases produce strong collectivity and centralization.The comparison uses the largest eigenvalue and MST maximum node degree across semi-annual windows and the full 10/2015–03/2019 interval.Source: §6.3 · p. 98, Figure 72 · p. 98
• BTC holds a dominant hierarchical position in every period except 10/2017–3/2018, when it shared the lowest λ(X) max value with another market configuration.A base cryptocurrency in the plot’s bottom-left region is interpreted as hierarchically dominant.Source: §6.3 · p. 98
• During 10/2017–2/2018, k(X) max = 40 supported a hierarchical power-law node-degree structure that disappeared after the bull market ended in 1/2018.BTC’s dominance subsequently returned.Source: §6.3 · pp. 98–99
• Across 10/2015–03/2019, k(X) max ≈80 for most base cryptocurrencies, reflecting an MST centralized around BTC/USD; BTC dominates more than USD.Most nodes connect to BTC/USD with unit degree, making BTC the market’s most natural base.Source: §6.3 · p. 99

Method

• The analysis uses qMST distances derived from detrended cross-correlations, evaluated for q = 1 and q = 4 across multiple time scales.Positive q values ensure that the distance is a metric.Source: §6.4 · p. 99

Data

• The study analyzes 94 Binance cryptocurrency exchange-rate quotes with 1-minute returns covering 2018, restricting the network to BTC-based pairs to avoid distortion from BTC’s own evolution.There were 93 BTC-based exchange rates; ETH was the most frequently traded alternative, appearing in 90 exchange rates.Source: §6.4 · p. 99

Network topology

• At scales above roughly 120 minutes, the ETH hub loses centrality and the Binance qMST progressively decentralizes, with maximum degree falling below 20 at two weeks.At shorter scales, q = 1 is nearly centralized with ⟨L(q, s)⟩≈2 and kmax(q, s)≈90, while q = 4 is significantly centralized with ⟨L(q, s)⟩≈3 and kmax(q, s)≈60.Source: §6.4 · p. 99, Figure 73 · p. 100

Scaling structure

• For s ≳500 minutes, node-degree CDFs develop scaling tails, and γ(q, s) exceeds 1.8 at one week, indicating decentralized networks.Before roughly 120 minutes, large error bars prevent clear power-law scaling because of ETH’s dominance.Source: §6.4 · p. 100, Figure 76 · p. 103

Sensitivity to fluctuation amplitude

• The hierarchical-network regime γ(q, s)≈1.6 appears at about 1,000 minutes for q = 4 but only about 7,000 minutes for q = 1, showing greater sensitivity for large returns.Large returns are globally less correlated, allowing q = 4 to form sub-clusters earlier; standard MST is therefore less sensitive than qMST.Source: §6.4 · p. 100

Interpretation

• Increasing time scales strengthen cross-correlations because less frequently traded pairs need time to synchronize, producing more diverse and decentralized MST structures; this occurs sooner for large returns.The short-scale ETH dominance disappears as a hierarchical structure develops.Source: §6.4 · p. 103

Methods

• Statistical-physics methods applied to high-frequency exchange data reveal nonlinear dependencies, multifractal behavior, cross-correlations, and network structure in cryptocurrency markets.The review emphasizes detrended fluctuation analysis, multifractal extensions, random-matrix cross-correlation analysis, and complex network theory.Source: §7 · pp. 103–104

Market maturity

• Cryptocurrency markets have moved from immature toward mature stages, driven primarily by rising trading volume and frequency, with BTC, ETH, XRP, and LTC among the most mature assets.Stylized facts include leptokurtic returns, long volatility memory, antipersistent returns, and multiscale auto- and cross-correlations; maturity remains below Forex overall because liquidity and transaction counts differ.Source: §7 · p. 104
• BTC/USD and ETH/USD developed mature-market dynamics around 2013–2014 and 2017–2018, including inverse-cubic tails, neutral Hurst behavior, and more symmetric multifractal spectra.Return autocorrelation shifted from short- to long-memory behavior; the Hurst exponent rose from approximately 0.4 to 0.5, while small returns remained monofractal unlike Forex.Source: §7 · p. 104

Cross-correlations and arbitrage

• Cross-correlations strengthen with scale, over time, and especially between rates sharing a base cryptocurrency, forming triangle-linked clusters unlike the weaker and differently structured Forex dependence.Stronger cross-correlations reduce triangular arbitrage opportunities; slower information flow prevents clusters from incorporating rates without triangle relationships, while decentralized platforms exhibit different maturity stages.Source: §7 · pp. 104–105

Outlook

• The review leaves the market’s long-term survival and evolution open, while expecting liquidity to improve and identifying BTC and ETH as mature, liquid assets supporting diversification.Despite high volatility, cryptocurrency offers investment and portfolio-diversification opportunities; using BTC or ETH as exchange-rate bases can further diversify the cryptocurrency portfolio.Source: §7 · p. 105

Covid-19 impact

• During the 2020 Covid-19 turmoil, major cryptocurrencies shifted from being uncorrelated with traditional instruments to becoming positively cross-correlated with safe and risky assets across panic and recovery phases.Correlations first appeared with the Japanese yen and later with the S&P 500, currencies, and commodities, suggesting a possible transition from safe-haven status into the global market network.Source: §7 · pp. 105–106

• The section lists the symbols and full names of cryptocurrencies traded on both Binance and Kraken.Source: Table A.5 · p. 107
• Cumulative distributions of absolute normalized 1-minute log-returns are presented separately for Binance and Kraken in 2018.Source: Figure A.77 · p. 108, Figure A.78 · p. 110
• For cryptocurrency pairs on Binance in 2018, the reported measures include the estimated γ exponent, zero-return-period length and count, average USD volume per minute, and Hurst exponent.Source: Table A.6 · p. 109
• The same statistical measures are tabulated for cryptocurrency pairs listed on Kraken in 2018.Source: Table A.7 · p. 111
• Average and maximum triangular-arbitrage opportunities are reported separately for Binance and Kraken in 2018.Source: Table A.8 · p. 112, Table A.9 · p. 113

B. List of 100 cryptocurrency names from CoinMarketCap

• The table provides the full names of the cryptocurrencies included in section 6.Source: Table B.10 · p. 114

• Table C.11 lists the full names of the 94 cryptocurrencies from Binance discussed in section 6.4.Source: Table C.11 · p. 115