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2011.13240#100
|
Blockchain mechanism and distributional characteristics of cryptos
|
It regulates the creation rate of a block and maintains a certain
amount of outputs of a blockchain.
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2011.13240#99
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2011.13240#101
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2011.13240
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2011.13240#101
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Blockchain mechanism and distributional characteristics of cryptos
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Such a mechanism is commonly seen in a PoW framework.
|
2011.13240#100
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2011.13240#102
|
2011.13240
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2011.13240#102
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Blockchain mechanism and distributional characteristics of cryptos
|
An example from Bitcoin is shown in Figure 2 where its diculty adjustment algorithm, known as
DAA, modi es the diculty every 2016 blocks to meet target block time of 10 minutes.
|
2011.13240#101
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2011.13240#103
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2011.13240
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2011.13240#103
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2.2 Time Series Data
The data applied in this paper are collected from Bitinfocharts which is available at https://bitinfocharts.com/.
|
2011.13240#102
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2011.13240#104
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2011.13240
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2011.13240#104
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Blockchain mechanism and distributional characteristics of cryptos
|
These time series are composed of data points observed daily from the genesis date of each crypto.
|
2011.13240#103
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2011.13240#105
|
2011.13240
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2011.13240#105
|
Blockchain mechanism and distributional characteristics of cryptos
|
The lengths of these time series are thus varied coin by coin, but as explained in the section 2.2,
we continue to use the whole time series for each coin.
|
2011.13240#104
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2011.13240#106
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2011.13240
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2011.13240#106
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Blockchain mechanism and distributional characteristics of cryptos
|
Price: Much previous literature has been triggered by the substantial
uctuations in crypto
7
Figure 2: Bitcoin's diculty adjustment toward actual block time.
|
2011.13240#105
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2011.13240#107
|
2011.13240
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2011.13240#107
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Blockchain mechanism and distributional characteristics of cryptos
|
Blockchain mechanism -
plotting
prices.
|
2011.13240#106
|
2011.13240#108
|
2011.13240
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2011.13240#108
|
Blockchain mechanism and distributional characteristics of cryptos
|
In this study we investigate 18 crypto prices in USD on daily time series.
|
2011.13240#107
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2011.13240#109
|
2011.13240
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2011.13240#109
|
Blockchain mechanism and distributional characteristics of cryptos
|
Among these
18 cryptos, Bitcoin has been dominant and Reddcoin has the lowest price on balance as seen in
Figure 3.
|
2011.13240#108
|
2011.13240#110
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2011.13240
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2011.13240#110
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Blockchain mechanism and distributional characteristics of cryptos
|
We characterise these price time series in Table 1.
|
2011.13240#109
|
2011.13240#111
|
2011.13240
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2011.13240#111
|
Blockchain mechanism and distributional characteristics of cryptos
|
Most of these coins (i.e., Bitcoin,
Ethereum, Bitcoin Cash) have high
uctuations in price; while some coins (i.e., XRP, Blackcoin)
tends to be steady.
|
2011.13240#110
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2011.13240#112
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2011.13240
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2011.13240#112
|
Blockchain mechanism and distributional characteristics of cryptos
|
Figure 3: Time series of prices of the 18 cryptos
Blockchain mechanism plotting
8
Actual block time: It is the mean time required in minutes for each day to create the next
block.
|
2011.13240#111
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2011.13240#113
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2011.13240
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2011.13240#113
|
Blockchain mechanism and distributional characteristics of cryptos
|
In other words, it is the average amount of time for the day a user has to wait, after
broadcasting their transaction, to see this transaction appear on the blockchain.
|
2011.13240#112
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2011.13240#114
|
2011.13240
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2011.13240#114
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Blockchain mechanism and distributional characteristics of cryptos
|
Some literature
also refers it as con rmation time.
|
2011.13240#113
|
2011.13240#115
|
2011.13240
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2011.13240#115
|
Blockchain mechanism and distributional characteristics of cryptos
|
It can be considered as a service level indicator for cryptos which
should be maintained by underlying mechanisms.
|
2011.13240#114
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2011.13240#116
|
2011.13240
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2011.13240#116
|
Blockchain mechanism and distributional characteristics of cryptos
|
Most of the coins discussed in this paper tend to
have lower block time compared with Bitcoin as seen in Figure 4.
|
2011.13240#115
|
2011.13240#117
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2011.13240
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2011.13240#117
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Blockchain mechanism and distributional characteristics of cryptos
|
Also, many coins show outliers
in observations and this can indicate that the extreme events appear in the blockchain system.
|
2011.13240#116
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2011.13240#118
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2011.13240
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2011.13240#118
|
Blockchain mechanism and distributional characteristics of cryptos
|
The underlying mechanisms can be ine ective to accommodate the current system demand.
|
2011.13240#117
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2011.13240#119
|
2011.13240
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2011.13240#119
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Blockchain mechanism and distributional characteristics of cryptos
|
The
distributional characteristics for time series of actual block time are presented in Table 2.
|
2011.13240#118
|
2011.13240#120
|
2011.13240
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2011.13240#120
|
Blockchain mechanism and distributional characteristics of cryptos
|
The data
for XRP are missing but its designed block time is around 5 second per transaction.
|
2011.13240#119
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2011.13240#121
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2011.13240
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2011.13240#121
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Blockchain mechanism and distributional characteristics of cryptos
|
Figure 4: Actual block time in minutes.
|
2011.13240#120
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2011.13240#122
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2011.13240
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2011.13240#122
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Blockchain mechanism and distributional characteristics of cryptos
|
Blockchain mechanism plotting
9
Actual block size: It is de ned as the average actual size "usage" of a single block in data
storage for one day.
|
2011.13240#121
|
2011.13240#123
|
2011.13240
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2011.13240#123
|
Blockchain mechanism and distributional characteristics of cryptos
|
Since a block is is comprised of transaction data, it can represent the status
of how a cryptocurrency mechanism allocates transactions to a block.
|
2011.13240#122
|
2011.13240#124
|
2011.13240
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2011.13240#124
|
Blockchain mechanism and distributional characteristics of cryptos
|
In this study, as introduced
in Section 1, we consider it as an indicator for the stableness of scalability of a crypto.
|
2011.13240#123
|
2011.13240#125
|
2011.13240
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2011.13240#125
|
Blockchain mechanism and distributional characteristics of cryptos
|
In Figure 5
shows that most of the cryptos under study have smaller block size usage than Bitcoin, except
Bitcoin SV.
|
2011.13240#124
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2011.13240#126
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2011.13240
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2011.13240#126
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Blockchain mechanism and distributional characteristics of cryptos
|
The plot also depicts that almost all the coins have outliers.
|
2011.13240#125
|
2011.13240#127
|
2011.13240
|
2011.13240#127
|
Blockchain mechanism and distributional characteristics of cryptos
|
These outliers can lead
to the imbalance in transaction fee and reward which can in
uence the ecosystem of a crypto.
|
2011.13240#126
|
2011.13240#128
|
2011.13240
|
2011.13240#128
|
Blockchain mechanism and distributional characteristics of cryptos
|
The
characteristics for block size time series are shown in Table 3.
|
2011.13240#127
|
2011.13240#129
|
2011.13240
|
2011.13240#129
|
Blockchain mechanism and distributional characteristics of cryptos
|
XRP does not have typical blockchain
structure, hence, there is no block size data in the study.
|
2011.13240#128
|
2011.13240#130
|
2011.13240
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2011.13240#130
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Blockchain mechanism and distributional characteristics of cryptos
|
The data for Peercoin are missing.
|
2011.13240#129
|
2011.13240#131
|
2011.13240
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2011.13240#131
|
Blockchain mechanism and distributional characteristics of cryptos
|
Figure 5: Actual block size in megabytes.
|
2011.13240#130
|
2011.13240#132
|
2011.13240
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2011.13240#132
|
Blockchain mechanism and distributional characteristics of cryptos
|
Blockchain mechanism plotting
10
3 Methodology
In order to investigate the relationship between underlying blockchain mechanism of cryptocur-
rencies and the distributional characteristics of cryptos as a proxy of behaviour, we aim to group
them into number of clusters and scrutinise the compositions of features in each group.
|
2011.13240#131
|
2011.13240#133
|
2011.13240
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2011.13240#133
|
Blockchain mechanism and distributional characteristics of cryptos
|
These
blockchain-based features manifest the underlying mechanism of how the cryptos operate trans-
actions on their chains, and subsequently govern the price, actual block size and block time.
|
2011.13240#132
|
2011.13240#134
|
2011.13240
|
2011.13240#134
|
Blockchain mechanism and distributional characteristics of cryptos
|
As
described in the previous section, we use the time series data of 18 di erent cryptos with a range
of di erent mechanisms.
|
2011.13240#133
|
2011.13240#135
|
2011.13240
|
2011.13240#135
|
Blockchain mechanism and distributional characteristics of cryptos
|
The time series data available for the cryptos is subject to numerous limitations.
|
2011.13240#134
|
2011.13240#136
|
2011.13240
|
2011.13240#136
|
Blockchain mechanism and distributional characteristics of cryptos
|
The most
important one of them is that di erent coins were introduced at di erent time points, therefore,
the data available for each coin has di erent lengths.
|
2011.13240#135
|
2011.13240#137
|
2011.13240
|
2011.13240#137
|
Blockchain mechanism and distributional characteristics of cryptos
|
For the clustering problems (Aghabozorgi
et al., 2015), de ning the distance metric between points in time series with various lengths is not
conventional.
|
2011.13240#136
|
2011.13240#138
|
2011.13240
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2011.13240#138
|
Blockchain mechanism and distributional characteristics of cryptos
|
For many analytical problems, this issue is easily tackled by truncating the time series
to the shared sample period.
|
2011.13240#137
|
2011.13240#139
|
2011.13240
|
2011.13240#139
|
Blockchain mechanism and distributional characteristics of cryptos
|
We refrain from doing so because, in the analysis of cryptocurrency
prices, the evolution of the data in time is highly crucial for an investigation in the short term
and long term dynamics and therefore, truncating the time series would lead to loss of important
information.
|
2011.13240#138
|
2011.13240#140
|
2011.13240
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2011.13240#140
|
Blockchain mechanism and distributional characteristics of cryptos
|
Hence, we deal with the time series data of cryptos with di erent lengths and do not
directly impose a distance metric on the input data points.
|
2011.13240#139
|
2011.13240#141
|
2011.13240
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2011.13240#141
|
Blockchain mechanism and distributional characteristics of cryptos
|
Furthermore, characterising the behaviour of a time series in terms of a single quantitative
attribute (such as range based volatility) has its own limitations.
|
2011.13240#140
|
2011.13240#142
|
2011.13240
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2011.13240#142
|
Blockchain mechanism and distributional characteristics of cryptos
|
The chosen attribute usually
captures the dynamics of time series in one particular aspect, which may not be sucient to
encompass an entire behaviour or introduces a biased assessment.
|
2011.13240#141
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2011.13240#143
|
2011.13240
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2011.13240#143
|
Blockchain mechanism and distributional characteristics of cryptos
|
This becomes particularly true
in the problems of crypto classi cation and clustering where these attributes, used as a similarity
measure, are very diverse, resulting in weak robustness in the results.
|
2011.13240#142
|
2011.13240#144
|
2011.13240
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2011.13240#144
|
Blockchain mechanism and distributional characteristics of cryptos
|
To cope with these limitations, we resort to the characteristic based clustering method proposed
by Wang et al.
|
2011.13240#143
|
2011.13240#145
|
2011.13240
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2011.13240#145
|
Blockchain mechanism and distributional characteristics of cryptos
|
(2005).
|
2011.13240#144
|
2011.13240#146
|
2011.13240
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2011.13240#146
|
Blockchain mechanism and distributional characteristics of cryptos
|
It was recently applied by Pele et al.
|
2011.13240#145
|
2011.13240#147
|
2011.13240
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2011.13240#147
|
Blockchain mechanism and distributional characteristics of cryptos
|
(2020) for classifying cryptos in order to
11
distinguish them from traditional assets.
|
2011.13240#146
|
2011.13240#148
|
2011.13240
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2011.13240#148
|
Blockchain mechanism and distributional characteristics of cryptos
|
This methods recommends to incorporate various global
measures describing the structural characteristics of a time series for a clustering problem.
|
2011.13240#147
|
2011.13240#149
|
2011.13240
|
2011.13240#149
|
Blockchain mechanism and distributional characteristics of cryptos
|
These
global measures are obtained by applying statistical operations that best represent the underlying
characteristics.
|
2011.13240#148
|
2011.13240#150
|
2011.13240
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2011.13240#150
|
Blockchain mechanism and distributional characteristics of cryptos
|
Also, by extracting a set of measures from the original time series we simply bypass
the issue of de ning a distance metric.
|
2011.13240#149
|
2011.13240#151
|
2011.13240
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2011.13240#151
|
Blockchain mechanism and distributional characteristics of cryptos
|
It's understood that the global measures are domain-
speci c.
|
2011.13240#150
|
2011.13240#152
|
2011.13240
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2011.13240#152
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Blockchain mechanism and distributional characteristics of cryptos
|
Employing a greedy search algorithm, Wang et al.
|
2011.13240#151
|
2011.13240#153
|
2011.13240
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2011.13240#153
|
Blockchain mechanism and distributional characteristics of cryptos
|
(2005) selects the pivotal features in
the clustering tasks.
|
2011.13240#152
|
2011.13240#154
|
2011.13240
|
2011.13240#154
|
Blockchain mechanism and distributional characteristics of cryptos
|
In our case, we import the experts' discretion on the choice of features as
distributional characteristics which best represent the dynamics of cryptocurrencies.
|
2011.13240#153
|
2011.13240#155
|
2011.13240
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2011.13240#155
|
Blockchain mechanism and distributional characteristics of cryptos
|
We choose a variety of measures for our analysis.
|
2011.13240#154
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2011.13240#156
|
2011.13240
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2011.13240#156
|
Blockchain mechanism and distributional characteristics of cryptos
|
Starting from the rst four moments and
quantiles that characterises the distribution and symmetry of the data, we include the statistics
for concluding the global structure such as global optimum, as well as the measures for long term
dependencies, risk and noise.
|
2011.13240#155
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2011.13240#157
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2011.13240
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2011.13240#157
|
Blockchain mechanism and distributional characteristics of cryptos
|
The selected features are mean, standard deviation, skewness, kur-
tosis, maximum, minimum, rst quartile, median, third quartile, 1% and 5% extreme quantiles
as a measure of downside risk, linear trend, intercept, autocorrelation for long term dependency,
self-similarity using Hurst exponent and chaos using Lyaponav's exponents.
|
2011.13240#156
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2011.13240#158
|
2011.13240
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2011.13240#158
|
Blockchain mechanism and distributional characteristics of cryptos
|
We further extend the methodology by including the power spectrum of time series as an addi-
tional measure.
|
2011.13240#157
|
2011.13240#159
|
2011.13240
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2011.13240#159
|
Blockchain mechanism and distributional characteristics of cryptos
|
The power spectrum is obtained in this work using Fast Fourier Transform (FFT).
|
2011.13240#158
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2011.13240#160
|
2011.13240
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2011.13240#160
|
Blockchain mechanism and distributional characteristics of cryptos
|
For computational ease, discrete fourier transform (DFT) has been formalised as a linear operator
that maps the data points in a discrete input signal Xfx1;x2;;xngto the frequency domain
f=ff1;f2;fng.
|
2011.13240#159
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2011.13240#161
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2011.13240
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2011.13240#161
|
Blockchain mechanism and distributional characteristics of cryptos
|
For a given time series Xofntime points, sine and cosine functions are used to get the
coecients !n=e 2i=and the frequencies are calculated using the matrix multiplication:
12
2
666666666664f1
f2
f3
...
|
2011.13240#160
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2011.13240#162
|
2011.13240
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2011.13240#162
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Blockchain mechanism and distributional characteristics of cryptos
|
fn3
777777777775=2
6666666666641 1 1 1
1!n!2
n!n 1
n
1!2
n!4
n!2(n 1)
n
...............
|
2011.13240#161
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2011.13240#163
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2011.13240
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2011.13240#163
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Blockchain mechanism and distributional characteristics of cryptos
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1!n 1
n!2(n 1)
n!(n 1)2
n3
7777777777752
666666666664x1
x2
x3
...
|
2011.13240#162
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2011.13240#164
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2011.13240
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2011.13240#164
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Blockchain mechanism and distributional characteristics of cryptos
|
xn3
777777777775(1)
This matrix multiplication involves O(n2) and makes DFT computationally expensive.
|
2011.13240#163
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2011.13240#165
|
2011.13240
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2011.13240#165
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Blockchain mechanism and distributional characteristics of cryptos
|
FFT is
a fast algorithm to compute DFT using only O(nlogn) operations (Brunton and Kutz, 2019).
|
2011.13240#164
|
2011.13240#166
|
2011.13240
|
2011.13240#166
|
Blockchain mechanism and distributional characteristics of cryptos
|
A
simple tcommand in python computes the FFT of the given time signal.
|
2011.13240#165
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2011.13240#167
|
2011.13240
|
2011.13240#167
|
Blockchain mechanism and distributional characteristics of cryptos
|
The power spectrum of
this signal is the normalised squared magnitude of the fand it indicates how much variance of the
initial space each frequency explains (Brunton and Kutz, 2019).
|
2011.13240#166
|
2011.13240#168
|
2011.13240
|
2011.13240#168
|
Blockchain mechanism and distributional characteristics of cryptos
|
Including the power spectrum as
a feature for characteristic based clustering allows capturing the variability in the time signal that
is not explained by any other measure.
|
2011.13240#167
|
2011.13240#169
|
2011.13240
|
2011.13240#169
|
Blockchain mechanism and distributional characteristics of cryptos
|
Accumulating all the aforementioned features in a vector gives in a reduced dimensional rep-
resentation of time series of each crypto.
|
2011.13240#168
|
2011.13240#170
|
2011.13240
|
2011.13240#170
|
Blockchain mechanism and distributional characteristics of cryptos
|
These vectors are then used to cluster the cryptos into
groups using spectral clustering.
|
2011.13240#169
|
2011.13240#171
|
2011.13240
|
2011.13240#171
|
Blockchain mechanism and distributional characteristics of cryptos
|
Spectral clustering exploits the eigenvalues of similarity matrix
to cluster and results in more balanced clusters than other techniques that were employed during
the process.
|
2011.13240#170
|
2011.13240#172
|
2011.13240
|
2011.13240#172
|
Blockchain mechanism and distributional characteristics of cryptos
|
For details related to spectral clustering, the readers are recommended to follow the
tutorial on spectral clustering by von Luxburg (2006).
|
2011.13240#171
|
2011.13240#173
|
2011.13240
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2011.13240#173
|
Blockchain mechanism and distributional characteristics of cryptos
|
The results of the above methodology are
discussed in detail in the next section.
|
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2011.13240#174
|
2011.13240
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2011.13240#174
|
Blockchain mechanism and distributional characteristics of cryptos
|
4 Empirical Evidence
In this section, we showcase the result from the characteristic based clustering individually on the
crypto price and operational features{which are constructed with price, block size "scalability" and
block time "service level" time series.
|
2011.13240#173
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2011.13240#175
|
2011.13240
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2011.13240#175
|
Blockchain mechanism and distributional characteristics of cryptos
|
We explore the clustering results and classify them with the
underlying mechanisms of the investigated 18 cryptos.
|
2011.13240#174
|
2011.13240#176
|
2011.13240
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2011.13240#176
|
Blockchain mechanism and distributional characteristics of cryptos
|
The 18 cryptos are: Bitcoin, Bitcoin Cash,
Bitcoin Gold, Bitcoin SV, Blackcoin , Dash, Dogecoin, Ethereum, Ethereum Classic, Feathercoin,
13
Litecoin, Monero, Novacoin, Peercoin, Reddcoin, Vertcoin, XRP, and Zcash.
|
2011.13240#175
|
2011.13240#177
|
2011.13240
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2011.13240#177
|
Blockchain mechanism and distributional characteristics of cryptos
|
We calculate the characteristics for each of these cryptos for prices, block size and block time
separately.
|
2011.13240#176
|
2011.13240#178
|
2011.13240
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2011.13240#178
|
Blockchain mechanism and distributional characteristics of cryptos
|
The results of all other attributes except the FFT are summarised in Tables 1, 2, 3
correspondingly in Appendix.
|
2011.13240#177
|
2011.13240#179
|
2011.13240
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2011.13240#179
|
Blockchain mechanism and distributional characteristics of cryptos
|
Note that the data for XRP are not available for the block size and
block time, and for Peercoin block size is missing as described before in Section 3.
|
2011.13240#178
|
2011.13240#180
|
2011.13240
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2011.13240#180
|
Blockchain mechanism and distributional characteristics of cryptos
|
After calculating the attributes and FFT power spectrum described in section 2.2, the feature
space is 216 dimensional (200 dimensional vector of power spectrum and 16 characteristics), vi-
sualisation of which is not possible.
|
2011.13240#179
|
2011.13240#181
|
2011.13240
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2011.13240#181
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Blockchain mechanism and distributional characteristics of cryptos
|
We project the feature space into a three dimensional space
using principle component analysis (PCA), and the results of which are exhibited for an intuitive
understanding.
|
2011.13240#180
|
2011.13240#182
|
2011.13240
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2011.13240#182
|
Blockchain mechanism and distributional characteristics of cryptos
|
We discuss each of the clustering in detail below.
|
2011.13240#181
|
2011.13240#183
|
2011.13240
|
2011.13240#183
|
Blockchain mechanism and distributional characteristics of cryptos
|
Moreover, in order to avoid a
monopoly outcome and sustain a certain level of interpretability, we impose the maximum number
of the clusters to avoid a single coin case in each cluster.
|
2011.13240#182
|
2011.13240#184
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2011.13240
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2011.13240#184
|
Blockchain mechanism and distributional characteristics of cryptos
|
4.1 Clustering with crypto prices
Table 1 shows that as expected, Bitcoin has the highest average price and highest standard deviation,
due to high magnitude of its prices.
|
2011.13240#183
|
2011.13240#185
|
2011.13240
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2011.13240#185
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Blockchain mechanism and distributional characteristics of cryptos
|
The VaR99 and VaR95 for Bitcoin are, however, very low,
showing a low downside risk of Bitcoin.
|
2011.13240#184
|
2011.13240#186
|
2011.13240
|
2011.13240#186
|
Blockchain mechanism and distributional characteristics of cryptos
|
On the contrary, Bitcoin Cash, Bitcoin SV, Bitcoin Gold and
Zcash all show high value at risk.
|
2011.13240#185
|
2011.13240#187
|
2011.13240
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2011.13240#187
|
Blockchain mechanism and distributional characteristics of cryptos
|
This could be due to low persistence of risk shocks (de Souza,
2019; Katsiampa et al., 2019).
|
2011.13240#186
|
2011.13240#188
|
2011.13240
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2011.13240#188
|
Blockchain mechanism and distributional characteristics of cryptos
|
The high positive coecients of self similarity for all the coins
show high dependency on the previous time values.
|
2011.13240#187
|
2011.13240#189
|
2011.13240
|
2011.13240#189
|
Blockchain mechanism and distributional characteristics of cryptos
|
The high autocorrelation further con rms the
presence of long term dependencies of the time series.
|
2011.13240#188
|
2011.13240#190
|
2011.13240
|
2011.13240#190
|
Blockchain mechanism and distributional characteristics of cryptos
|
The Lyaponov exponent as a measure of
chaos is greater than 0 for all the time series which shows unstable dynamics throughout the prices
of cryptos.
|
2011.13240#189
|
2011.13240#191
|
2011.13240
|
2011.13240#191
|
Blockchain mechanism and distributional characteristics of cryptos
|
The characteristics of Dogecoin in Table 1 assume very low values, unlike any other coin, because
the prices of Dogecoin are very low, despite it being a popular coin.
|
2011.13240#190
|
2011.13240#192
|
2011.13240
|
2011.13240#192
|
Blockchain mechanism and distributional characteristics of cryptos
|
This can be due to high supply
of the coin with no limit on the total number of coins created.
|
2011.13240#191
|
2011.13240#193
|
2011.13240
|
2011.13240#193
|
Blockchain mechanism and distributional characteristics of cryptos
|
The coin also has no technical
innovations, which is considered as one of the reasons why the coin has such small price.
|
2011.13240#192
|
2011.13240#194
|
2011.13240
|
2011.13240#194
|
Blockchain mechanism and distributional characteristics of cryptos
|
Hence,
14
the uncontrolled underlying mechanism of the coin has signi cant impact on the prices, despite the
high trading volumes of the coin.
|
2011.13240#193
|
2011.13240#195
|
2011.13240
|
2011.13240#195
|
Blockchain mechanism and distributional characteristics of cryptos
|
Same can be concluded for XRP and Reddcoin, which also have
a very high maximum supply that is re
ected in their very low prices.
|
2011.13240#194
|
2011.13240#196
|
2011.13240
|
2011.13240#196
|
Blockchain mechanism and distributional characteristics of cryptos
|
Using characteristic based clustering on price time series, we have the result with 5 clusters as
below:
0.
|
2011.13240#195
|
2011.13240#197
|
2011.13240
|
2011.13240#197
|
Blockchain mechanism and distributional characteristics of cryptos
|
Bitcoin, Dash
1.
|
2011.13240#196
|
2011.13240#198
|
2011.13240
|
2011.13240#198
|
Blockchain mechanism and distributional characteristics of cryptos
|
Bitcoin SV, Zcash
2.
|
2011.13240#197
|
2011.13240#199
|
2011.13240
|
2011.13240#199
|
Blockchain mechanism and distributional characteristics of cryptos
|
Bitcoin Cash, Bitcoin Gold
3.
|
2011.13240#198
|
2011.13240#200
|
2011.13240
|
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