Signatures of the Crypto-Currency Market Decoupling from the Forex
<p>(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.</p> "> Figure 2
<p>(Color online) Time-variation of the moduli of <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mi>t</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math> s logarithimic returns corresponding to the exchange rates of BTC/EUR, BTC/USD, ETH/EUR, ETH/USD, BTC/ETH and EUR/USD over the period between 1 July 2016 and 31 December 2018. The insets provide magnifications of the time-spans indicated.</p> "> Figure 3
<p>(Color online) Volatility autocorrelation functions <math display="inline"><semantics> <mrow> <mi>C</mi> <mo>(</mo> <mi>τ</mi> <mo>)</mo> </mrow> </semantics></math> for to the BTC/EUR, BTC/USD, ETH/EUR, ETH/USD, BTC/ETH and EUR/USD exchange rates over the period between 1 July 2016 and 31 December 2018. The daily trend was removed according to an established procedure [<a href="#B5-futureinternet-11-00154" class="html-bibr">5</a>].</p> "> Figure 4
<p>(Color online) Log-log plot of the cumulative distributions of the normalized absolute returns <math display="inline"><semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>r</mi> <mrow> <mo>Δ</mo> <mi>t</mi> </mrow> </msub> <mrow> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>|</mo> </mrow> </mrow> </semantics></math> for BTC/EUR, BTC/USD, BTC/ETH, ETH/EUR, ETH/USD over the period between 1 July 2016 and 31 December 2018. The dashed line represents the expected inverse cubic power-law.</p> "> Figure 5
<p>Family of the <span class="html-italic">q</span>th-order fluctuation functions <math display="inline"><semantics> <mrow> <msub> <mi>F</mi> <mi>q</mi> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> for different values of <math display="inline"><semantics> <mrow> <mi>q</mi> <mo>∈</mo> <mo>[</mo> <mo>−</mo> <mn>4</mn> <mo>,</mo> <mn>4</mn> <mo>]</mo> </mrow> </semantics></math> in steps of 0.2 (the upper-most one represents <math display="inline"><semantics> <mrow> <mi>q</mi> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math>), calculated for the six exchange rates BTC/EUR, BTC/USD, ETH/EUR, ETH/USD, BTC/ETH and EUR/USD. Vertical dotted lines indicate the range of scales used in determining the generalized Hurst exponents <math display="inline"><semantics> <mrow> <mi>h</mi> <mo>(</mo> <mi>q</mi> <mo>)</mo> </mrow> </semantics></math>. Insets show the corresponding dependence of <math display="inline"><semantics> <mrow> <mi>h</mi> <mo>(</mo> <mi>q</mi> <mo>)</mo> </mrow> </semantics></math> on <span class="html-italic">q</span>.</p> "> Figure 6
<p>(Color online) Singularity spectra <math display="inline"><semantics> <mrow> <mi>f</mi> <mo>(</mo> <mi>α</mi> <mo>)</mo> </mrow> </semantics></math> calculated for all six considered time-series of BTC/EUR, BTC/USD, ETH/EUR, ETH/USD, BTC/ETH and EUR/USD returns, setting <math display="inline"><semantics> <mrow> <mi>q</mi> <mo>∈</mo> <mo>[</mo> <mo>−</mo> <mn>4</mn> <mo>,</mo> <mn>4</mn> <mo>]</mo> </mrow> </semantics></math>. Insets show the <span class="html-italic">q</span>-dependence of the corresponding generalized Hurst exponents <math display="inline"><semantics> <mrow> <mi>h</mi> <mo>(</mo> <mi>q</mi> <mo>)</mo> </mrow> </semantics></math>.</p> "> Figure 7
<p>Hurst exponent <span class="html-italic">H</span> calculated over 30-days window for the BTC/EUR, BTC/USD, ETH/EUR, ETH/USD, BTC/ETH and EUR/USD exchange rates from 1 July 2016 to 31 December 2018. Error bars reflect the standard error of the regression slope.</p> "> Figure 8
<p>Family of the <span class="html-italic">q</span>th-order fluctuation cross-covariance functions <math display="inline"><semantics> <mrow> <msub> <mi>F</mi> <mrow> <mi>X</mi> <mi>Y</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>q</mi> <mo>,</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>, for different values of <span class="html-italic">q</span> in steps of 0.2, and calculated for the cross-correlations among the BTC/EUR, BTC/USD, ETH/EUR, ETH/USD, BTC/ETH and EUR/USD exchange rates. The upper-most lines correspond to <math display="inline"><semantics> <mrow> <mi>q</mi> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math>, whereas the bottom ones to those for which <math display="inline"><semantics> <mrow> <msub> <mi>F</mi> <mrow> <mi>X</mi> <mi>Y</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>q</mi> <mo>,</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> are still positive. Insets illustrate the resulting <span class="html-italic">q</span>-dependence of <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>(</mo> <mi>q</mi> <mo>)</mo> </mrow> </semantics></math> versus the average of the generalized Hurst exponents <math display="inline"><semantics> <mrow> <msub> <mi>h</mi> <mrow> <mi>x</mi> <mi>y</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>q</mi> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <msub> <mi>h</mi> <mi>x</mi> </msub> <mrow> <mo>(</mo> <mi>q</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>h</mi> <mi>y</mi> </msub> <mrow> <mo>(</mo> <mi>q</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mo>/</mo> <mn>2</mn> </mrow> </semantics></math> of the two series <math display="inline"><semantics> <mrow> <mi>x</mi> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>y</mi> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </semantics></math> under study.</p> "> Figure 9
<p>(Color online) Differences between multifractal cross-correlation scaling exponents <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>(</mo> <mi>q</mi> <mo>)</mo> </mrow> </semantics></math> and the average generalized Hurst exponents <math display="inline"><semantics> <mrow> <msub> <mi>h</mi> <mrow> <mi>x</mi> <mi>y</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>q</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> estimated for <math display="inline"><semantics> <mrow> <mi>q</mi> <mo>∈</mo> <mo>[</mo> <mn>1</mn> <mo>,</mo> <mn>4</mn> <mo>]</mo> </mrow> </semantics></math> corresponding to the cases considered in <a href="#futureinternet-11-00154-f008" class="html-fig">Figure 8</a>.</p> "> Figure 10
<p>(Color online) <span class="html-italic">q</span>-dependent detrended cross-correlation coefficients <math display="inline"><semantics> <mrow> <msub> <mi>ρ</mi> <mi>q</mi> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> for the same ensemble of exchange rates as in <a href="#futureinternet-11-00154-f008" class="html-fig">Figure 8</a>, shown as functions of the temporal scale <span class="html-italic">s</span> for <math display="inline"><semantics> <mrow> <mi>q</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>q</mi> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math>.</p> "> Figure 11
<p>(Color online) Family of the <span class="html-italic">q</span>th-order fluctuation cross-covariance functions <math display="inline"><semantics> <mrow> <msub> <mi>F</mi> <mrow> <mi>X</mi> <mi>Y</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>q</mi> <mo>,</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>, for different values of <span class="html-italic">q</span> in steps of 0.2 The upper-most lines correspond to <math display="inline"><semantics> <mrow> <mi>q</mi> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math>, whereas the bottom ones to those for which <math display="inline"><semantics> <mrow> <msub> <mi>F</mi> <mrow> <mi>X</mi> <mi>Y</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>q</mi> <mo>,</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> are still positive (upper panel) and the <math display="inline"><semantics> <mrow> <msub> <mi>ρ</mi> <mi>q</mi> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> coefficients as functions of the temporal scale <span class="html-italic">s</span> for <math display="inline"><semantics> <mrow> <mi>q</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>q</mi> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math>, calculated for the cross-correlation between BTC/ETH and EUR/USD exchange rates (lower panel).</p> ">
Abstract
:1. Introduction
2. Data Specification and Properties
3. Fundamental Notions of the Multifractal Formalism
4. Multifractality in the Exchange Rates
5. Cross-Correlations and Their Mutliscaling Features
6. The BTC/ETH Versus the EUR/USD Rates
7. Summary
Author Contributions
Funding
Conflicts of Interest
References
- Satoshi, N. Bitcoin: A Peer-to-Peer Electronic Cash System. 2008. Available online: http://bitcoin.org/bitcoin.pdf (accessed on 9 June 2019).
- Wattenhofer, R. The Science of the Blockchain, 1st ed.; CreateSpace Independent Publishing Platform: Scotts Valley, CA, USA, 2016. [Google Scholar]
- Gerlach, J.C.; Demos, G.; Sornette, D. Dissection of Bitcoin’s Multiscale Bubble History. SSRN Electron. J. 2018, 18–30. [Google Scholar] [CrossRef]
- Shiller, R. Irrational Exuberance, 3rd ed.; Princeton University Press: Princeton, NJ, USA, 2015. [Google Scholar]
- Kwapień, J.; Drożdż, S. Physical approach to complex systems. Phys. Rep. 2012, 515, 115–226. [Google Scholar] [CrossRef]
- Ausloos, M. Statistical physics in foreign exchange currency and stock markets. Phys. A 2000, 285, 48–65. [Google Scholar] [CrossRef]
- Drożdż, S.; Kwapień, J.; Oświȩcimka, P.; Rak, R. The foreign exchange market: return distributions, multifractality, anomalous multifractality and the Epps effect. New J. Phys. 2010, 12, 105003. [Google Scholar] [CrossRef]
- Tabak, B.M.; Cajueiro, D.O. Assessing inefficiency in euro bilateral exchange rates. Phys. A 2006, 367, 319–327. [Google Scholar] [CrossRef]
- Berger, D.; Chaboud, A.; Hjalmarsson, E. What drives volatility persistence in the foreign exchange market? J. Financ. Econ. 2009, 94, 192–213. [Google Scholar] [CrossRef] [Green Version]
- Xu, Z.; Gencay, R. Scaling, self-similarity and multifractality in FX markets. Phys. A 2003, 323, 578–590. [Google Scholar] [CrossRef]
- Oh, G.; Eom, C.; Havlin, S.; Jung, W.-S.; Wang, F.; Stanley, H.E.; Kim, S. A multifractal analysis of Asian foreign exchange markets. Eur. Phys. J. B 2012, 85, 214. [Google Scholar] [CrossRef]
- Gȩbarowski, R.; Oświȩcimka, P.; Wa̧torek, M.; Drożdż, S. Multiscale cross–correlations and triangular arbitrage opportunities in the Forex. arXiv 2019, arXiv:1906.07491. [Google Scholar]
- Kristoufek, L. BitCoin meets Google Trends and Wikipedia: Quantifying the relationship between phenomena of the Internet era. Sci. Rep. 2013, 3, 3415. [Google Scholar] [CrossRef] [Green Version]
- Wei, W.-C. Liquidity and market efficiency in cryptocurrencies. Econ. Lett. 2018, 168, 21–24. [Google Scholar] [CrossRef]
- Kristoufek, L.; Vosvrda, M. Cryptocurrencies market efficiency ranking: Not so straightforward. Phys. A 2019, 531, 120853. [Google Scholar] [CrossRef]
- Kristjanpoller, W.; Bouri, E. Asymmetric multifractal cross-correlations between the main world currencies and the main cryptocurrencies. Phys. A 2019, 523, 1057–1071. [Google Scholar] [CrossRef]
- Stosic, D.; Stosic, D.; Ludermir, T.B.; Stosic, T. Multifractal behavior of price and volume changes in the cryptocurrency market. Phys. A 2019, 520, 54–61. [Google Scholar] [CrossRef]
- Stosic, D.; Stosic, D.; Ludermir, T.B.; Stosic, T. Collective behavior of cryptocurrency price changes. Phys. A 2018, 507, 499–509. [Google Scholar] [CrossRef]
- Ziȩba, D.; Kokoszczyński, R.; Śledziewska, K. Shock transmission in the cryptocurrency market. Is Bitcoin the most influential? Int. Rev. Financ. Anal. 2019, 64, 102–125. [Google Scholar] [CrossRef]
- Corbet, S.; Lucey, B.; Urquhart, A.; Yarovaya, L. Cryptocurrencies as a financial asset: A systematic analysis. Int. Rev. Financ. Anal. 2019, 62, 182–199. [Google Scholar] [CrossRef]
- Libra White Paper. Available online: https://libra.org/en-US/white-paper/ (accessed on 9 July 2019).
- Pieroni, A.; Scrapato, N.; Di Nunzio, L.; Fallucchi, F.; Raso, M. Smarter City: Smart energy grid based on Blockchain technology. Int. J. Adv. Sci. Eng. Inf. Technol. 2018, 8, 298–306. [Google Scholar] [CrossRef]
- Tan, S.; Wang, X.; Jiang, C. Privacy-preserving energy scheduling for ESCOs based on energy blockchain network. Energies 2019, 12, 1530. [Google Scholar] [CrossRef]
- Hang, L.; Kim, D.-H. Design and implementation of an integrated IoT blockchain platform for sensing data integrity. Sensors 2019, 19, 2228. [Google Scholar] [CrossRef] [PubMed]
- Nord, J.H.; Koohang, A.; Paliszkiewicz, J. The Internet of Things: Review and theoretical framework. Expert Syst. Appl. 2019, 133, 97–108. [Google Scholar] [CrossRef]
- Bariviera, A.F.; Zunino, L.; Rosso, O.A. An analysis of high-frequency cryptocurrencies prices dynamics using permutation-information-theory quantifiers. Chaos 2018, 28, 075511. [Google Scholar] [CrossRef] [PubMed]
- Kraken API. Available online: https://www.kraken.com/features/api (accessed on 1 February 2019).
- Dukascopy Data Set. Available online: https://www.dukascopy.com/swiss/english/marketwatch/historical (accessed on 1 February 2019).
- Mandelbrot, B.B. The variation of certain speculative prices. J. Bus. 1983, 36, 394–419. [Google Scholar] [CrossRef]
- Drożdż, S.; Kwapień, J.; Oświȩcimka, P.; Rak, R. Quantitative features of multifractal subtleties in time-series. EPL (Europhys. Lett.) 2009, 88, 60003. [Google Scholar] [CrossRef]
- Gopikrishnan, P.; Meyer, M.; Amaral, L.A.N.; Stanley, H.E. Inverse cubic law for the probability distribution of stock price variations. Eur. Phys. J. B 1998, 3, 139–140. [Google Scholar] [CrossRef]
- Gopikrishnan, P.; Plerou, V.; Amaral, L.A.N.; Meyer, M.; Stanley, H.E. Scaling of the distribution of fluctuations of financial market indices. Phys. Rev. E 1999, 60, 5305–5316. [Google Scholar] [CrossRef] [Green Version]
- Drożdż, S.; Kwapień, J.; Grümmer, F.; Ruf, F.; Speth, J. Are the contemporary financial fluctuations sooner converging to normal? Acta Phys. Pol. B 2003, 34, 4293–4306. [Google Scholar]
- Drożdż, S.; Forczek, M.; Kwapień, J.; Oświȩcimka, P.; Rak, R. Stock market return distributions: From past to present. Phys. A 2007, 383, 59–64. [Google Scholar] [CrossRef] [Green Version]
- Oświȩcimka, P.; Drożdż, S.; Forczek, M.; Jadach, S.; Kwapień, J. Detrended cross-correlation analysis consistently extended to multifractality. Phys. Rev. E 2014, 89, 023305. [Google Scholar] [CrossRef]
- Podobnik, B.; Stanley, H.E. Detrended cross-correlation analysis: a new method for analyzing two nonstationary time-series. Phys. Rev. Lett. 2008, 100, 084102. [Google Scholar] [CrossRef]
- Zhou, W.-X. Multifractal detrended cross-correlation analysis for two nonstationary signals. Phys. Rev. E 2008, 77, 066211. [Google Scholar] [CrossRef] [PubMed] [Green Version]
- Kwapień, J.; Oświȩcimka, P.; Drożdż, S. Detrended fluctuation analysis made flexible to detect range of cross-correlated fluctuations. Phys. Rev. E 2015, 92, 052815. [Google Scholar] [CrossRef] [PubMed] [Green Version]
- Oświȩcimka, P.; Kwapień, J.; Drożdż, S. Wavelet versus detrended fluctuation analysis of multifractal structures. Phys. Rev. E 2006, 74, 016103. [Google Scholar] [CrossRef] [PubMed] [Green Version]
- Oświȩcimka, P.; Drożdż, S.; Kwapień, J. Effect of detrending on multifractal characteristics. Acta Phys. Pol. A 2013, 123, 597–603. [Google Scholar] [CrossRef]
- Kantelhardt, J.W.; Zschiegner, S.A.; Koscielny-Bunde, E.; Havlin, S.; Bunde, A.; Stanley, H.E. Multifractal detrended fluctuation analysis of nonstationary time-series. Phys. A 2002, 316, 87–114. [Google Scholar] [CrossRef]
- Grech, D. Alternative measure of multifractal content and its application in finance. Chaos Solitons Fractals 2016, 88, 183–195. [Google Scholar] [CrossRef]
- Jiang, Z.-Q.; Xie, W.-J.; Zhou, W.-X.; Sornette, D. Multifractal analysis of financial markets. arXiv 2018, arXiv:1805.04750v1. [Google Scholar]
- Drożdż, S.; Oświȩcimka, P. Detecting and interpreting distortions in hierarchical organization of complex time-series. Phys. Rev. E 2015, 91, 030902. [Google Scholar] [CrossRef]
- Kwapień, J.; Oświȩcimka, P.; Forczek, M.; Drożdż, S. Minimum spanning tree filtering of correlations for varying time scales and size of fluctuations. Phys. Rev. E 2017, 95, 052313. [Google Scholar] [CrossRef]
- Hurst, H.E. Long-term storage capacity of reservoirs. Trans. Am. Soc. Civ. Eng. 1951, 116, 770. [Google Scholar]
- Di Matteo, T.; Aste, T.; Dacorogna, M.M. Scaling behaviors in differently developed markets. Phys. A 2003, 324, 183–188. [Google Scholar] [CrossRef]
- Drożdż, S.; Gȩbarowski, R.; Minati, L.; Oświȩcimka, P.; Wa̧torek, M. Bitcoin market route to maturity? Evidence from return fluctuations, temporal correlations and multiscaling effects. Chaos 2018, 28, 071101. [Google Scholar] [CrossRef] [PubMed]
- Rak, R.; Drożdż, S.; Kwapień, J.; Oświȩcimka, P. Detrended cross-correlations between returns, volatility, trading activity, and volume traded for the stock market companies. EPL (Europhys. Lett.) 2015, 112, 48001. [Google Scholar] [CrossRef] [Green Version]
- Wa̧torek, M.; Drożdż, S.; Oświȩcimka, P.; Stanuszek, M. Multifractal cross-correlations between the world oil and other financial markets in 2012–2017. Energy Econ. 2019, 81, 874–885. [Google Scholar] [CrossRef]
- Zhao, L.; Li, W.; Fenu, A.; Podobnik, B.; Wang, Y.; Stanley, H.E. The q-dependent detrended cross-correlation analysis of stock market. J. Stat. Mech. 2018, 023402. [Google Scholar] [CrossRef]
- Epps, T. Comovements in stock prices in the very short run. J. Am. Stat. Assoc. 1979, 74, 291–298. [Google Scholar]
- Kwapień, J.; Drożdż, S.; Speth, J. Time scales involved in emergent market coherence. Phys. A 2005, 337, 231–242. [Google Scholar] [CrossRef]
- Toth, B.; Kertesz, J. The Epps effect revisited. Quant. Financ. 2009, 9, 793–802. [Google Scholar] [CrossRef] [Green Version]
- Pal, M.; Rao, P.M.; Manimaran, P. Multifractal detrended cross-correlation analysis on gold, crude oil and foreign exchange rate time series. Phys. A 2014, 416, 452–460. [Google Scholar] [CrossRef]
- Reboredo, J.C.; Rivera-Castro, M.A.; Zebende, G.F. Oil and US dollar exchange rate dependence: A detrended cross-correlation approach. Energy Econ. 2014, 42, 132–139. [Google Scholar] [CrossRef]
- Li, J.; Lu, X.; Zhou, Y. Cross-correlations between crude oil and exchange markets for selected oil rich economies. Phys. A 2016, 453, 131–143. [Google Scholar] [CrossRef]
- Hussain, M.; Zebende, G.; Bashir, U.; Donghonga, D. Oil price and exchange rate co-movements in Asian countries: Detrended cross-correlation approach. Phys. A 2017, 465, 338–346. [Google Scholar] [CrossRef]
- Urquhart, A.; Zhang, H. Is Bitcoin a hedge or safe haven for currencies? An intraday analysis. Int. Rev. Financ. Anal. 2019, 63, 49–57. [Google Scholar] [CrossRef]
- Shahzad, S.J.H.; Bouri, E.; Roubaud, D.; Kristoufek, L.; Lucey, B. Is Bitcoin a better safe-haven investment than gold and commodities. Int. Rev. Financ. Anal. 2019, 63, 322–330. [Google Scholar] [CrossRef]
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Drożdż, S.; Minati, L.; Oświȩcimka, P.; Stanuszek, M.; Wa̧torek, M. Signatures of the Crypto-Currency Market Decoupling from the Forex. Future Internet 2019, 11, 154. https://doi.org/10.3390/fi11070154
Drożdż S, Minati L, Oświȩcimka P, Stanuszek M, Wa̧torek M. Signatures of the Crypto-Currency Market Decoupling from the Forex. Future Internet. 2019; 11(7):154. https://doi.org/10.3390/fi11070154
Chicago/Turabian StyleDrożdż, Stanisław, Ludovico Minati, Paweł Oświȩcimka, Marek Stanuszek, and Marcin Wa̧torek. 2019. "Signatures of the Crypto-Currency Market Decoupling from the Forex" Future Internet 11, no. 7: 154. https://doi.org/10.3390/fi11070154