. Introduction
When Satoshi Nakamoto proposed the cryptocurrency Bitcoin (BTC) based on peer-to-peer
network and encryption techniques [1] in 2008, the blockchain technology was born. The idea behind
this was providing, for the first time in human history, a tool thanks to which people anywhere could
entrust each other and transact within an extensive network not requiring centralized management.
The methods on which the Bitcoin is based, as regards information storage, encryption technologies,
and consensus protocols, were already established beforehand [2]. Nevertheless, as is often the case,
for innovation to take place someone needs to combine existing technology in a new way and this must
land on fertile ground, which was provided in 2009 by the aftermath of the financial crisis and resulted
in the Bitcoin network as a distributed secure database. At that time, the Bitcoin quickly started getting
wider recognition, not only within communities of tech geeks but also within the broader financial
industry and, due to the anonymity of the transactions, even in the “underworld” of traders involved in
dubious, when not outright illegal, businesses. The first fiat-to-bitcoin exchange, Mt. Gox, was launched
in July 2010 and soon afterwards in February 2011 the first rules-free decentralized marketplace,
called Silk Road, where one could buy nearly any conceivable good using BTC, was launched.
These events resulted in a drastically increased demand, leading to the first BTC bubble [3], which burst
Future Internet 2019, 11, 154; doi:10.3390/fi11070154 www.mdpi.com/journal/futureinternet
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in the beginning of 2014 after the closure of Silk Road in October 2013 and the Mt. Gox trading
suspension in February 2014.
As the public awareness recognition of the Bitcoin increased, and more players developed an
interest in the blockchain technology, it became apparent that the distributed ledger could be used not
only as a basis for digital currencies but also for passing information and executing computer code on
the blockchain. The idea of a globally-distributed cloud computing network, Ethereum, was proposed
in late 2013 and then launched in July 2015. It allows anyone to create decentralized applications and
own tokens by using smart contracts on the network. This capability provided the ground for the
Initial Coin Offer (ICO) mania in 2017, which led to bubble engulfing the entire cryptocurrency market
and eventually bursting in January 2018.
The current state of the blockchain technology could be compared to the dot-com bubble,
which unfolded at the turn of the last century. At that time, nearly everyone saw generic potential in
internet technology, but it was not precisely known towards which direction the same would develop.
In those times of euphoria, even rumors that a company started dealing with web technology would
cause an increase in share price. Predictably, after the bubble burst, only a fraction of the leading
companies survived.
Financial markets, especially the Forex market, due to their huge transactions volume, widely
diversified participants and high speed of information processing, possess many of the emergent
features that hallmark complex systems . A multitude of studies have analyzed the properties of
the Forex market in terms of the returns distribution and volatility clustering, persistence,
multifractality and cross-correlations. Recently, largely owing to its drastically higher
volatility, the cryptocurrency market also gained research attention. The studies published to
date encompass market efficiency analysis, multifractal analysis. and cross-correlations
analysis;  see Ref.  for additional references. However, mainly data with a temporal
granularity (resolution) of one day have as yet been considered: evidently, this is inadequate given
the high, and ever increasing, speed of information transmission. Here, the Forex market and the
cryptocurrency market are compared, the latter represented at a more appropriate fine granularity of
10 s, as supported by the Kraken exchange data.
At the time of writing (May 2019), there are some 2200 active cryptocurrencies and tokens.
New blockchain-related projects and initiatives materialize at a remarkable rate, (as exemplified by
the Facebook coin (Libra) ; applications in the energy sector related to the smart energy grid,
aggregating multiple energy resources, and more broadly in the Internet of Things (IoT) receive
increasing attention. There is a clear (over)proliferation and fragmentation of cryptocurrencies,
crypto-exchanges, and trading platforms. Here, a speculation is put forward that the future may
bring their closer integration, leading to the emergence of a marketplace more closely resembling, in
terms of its statistical features, the established currency Forex market.
2. Data Specification and Properties
The data set used in the present study consists of the exchange rates reflecting the actual
trade involving the Bitcoin (BTC), Ethereum (ETH), Euro (EUR) and US dollar (USD). On this
basis, the following six exchange rates are defined: BTC/USD, BTC/EUR, ETH/USD, ETH/EUR,
BTC/ETH, together with the EUR/USD, herein taken as a standard benchmark. Since 1 July 2016,
all cryptocurrency transactions are tracked at a frequency of ∆t = 10 s, with the resulting time-series
being recorded by Kraken, which is the world’s largest Euro-to-Bitcoin exchange. Operating
since September 2013 as one of the longest-trading, continuously-running Bitcoin exchanges, it has
branches in Canada, the EU, and the US. Supported fiat pairs include the CAD, EUR, and USD. Notable
supported cryptocurrencies encompass the BTC, ETH, LTC, BCH, XRP, XMR, DASH, XLM, DOGE, EOS,
ICN, GNO, MLN, REP, USDT, ZEC, ADA and QTUM, allowing both fiat-to-crypto and crypto-to-crypto
trades. In the present study, the four most liquid pairs, namely BTC/EUR, BTC/USD, ETH/EUR,
Future Internet 2019, 
ETH/USD, and the most liquid crypto-to-crypto pair, BTC/ETH, are considered. The Kraken API
allowed seamless access to tick-by-tick data.
The data were collected until 31 December 2018. The EUR/USD exchange rate is considered at
the same ∆t = 10 s frequency, and within the same period of time but, due to Forex market trading
specifications, without weekends (the Forex does not operate between Friday 10 p.m. UTC and Sunday
10 p.m. UTC), as recorded by the Swiss forex bank Dukascopy [28]. Charts illustrating the time
variation of these six exchange rates over the time-span under consideration are shown in Figure 1.
Exchange rate logarithm
BTC/EUR
BTC/USD
ETH/EUR
ETH/USD
BTC/ETH
EUR/USD
Figure 1. (Color online) Logarithm of the exchange rates BTC/EUR, BTC/USD, ETH/EUR, ETH/USD,
BTC/ETH and EUR/USD over the period between 1 July 2016 and 31 December 2018. For improved
visibility, the EUR/USD exchange rate was magnified by a factor of 100.
In the corresponding logarithmic returns, one has r∆t = log(p(t + ∆t)) − log(p(t)), where ∆t
stands for the returns’ time-lag gaps, and where and the time intervals during which some instruments
were not traded have been removed (7 May 2017 22.30–23.45—DDoS attack on ETH/USD, 6.40 11
January 2018–14.30 13 January 2018 Kraken maintenance shutdown). Thus, the series of returns from
Kraken comprise approximately N = 7.6 million observations for each of the considered time-series
involving the BTC and ETH. For EUR/USD, there are about 5.6 million observations.
Volatility clustering, a phenomenon reflecting the fact that large fluctuations tend to be followed by
large fluctuations, of either sign, and small fluctuations tend to be followed by small fluctuations [29],
is considered to be among the most characteristic financial stylized facts [5]. Such an effect is clearly
seen in Figure 2, which shows the time-variation of the moduli of logarithmic returns for all six
exchange rates under consideration. Remarkably, however, as demonstrated by the consecutive
magnifications in the EUR/USD panel, the average time-span of the corresponding clusters in all
the cases involving either the BTC or the ETH is about one order of magnitude longer than for the
EUR/USD rate. In the former case, one can recognize about three high-low volatility cycles within
the corresponding monthly insets of Figure 2, whereas in the latter case, five such