# Spillover Risks on Cryptocurrency Markets: A Look from VAR-SVAR Granger Causality and Student’s-t Copulas

^{1}

^{2}

## Abstract

**:**

When you do physics you are playing against God; in finance, you are playing against God’s creatures.(Emanuel Derman)

## 1. Introduction

## 2. Literature Review

#### 2.1. Terminology and Basic Concepts

#### 2.2. Bitcoin and Cryptocurrency Markets

#### 2.3. General Spillover Risks

#### 2.4. Relevant Studies in Terms of Spillover Risks on the Cryptocurrency Markets

## 3. Data and Methodology

#### 3.1. Data

#### 3.2. Methodology

#### 3.2.1. Pearson Correlation

#### 3.2.2. Vector Autoregressive Model (VAR)

_{p}) of coefficients of lagged values of Y (Y

_{t}

_{−1}); ${B}_{0}$ is matrix with coefficients of matrix $\chi $; ${\chi}_{t}$ is the matrix (M × 1) of exogenous variables; and ${\mathrm{u}}_{\mathrm{t}}$ is the matrix (K × 1) of white noise innovations. Finally, Y

_{t}is the matrix (K

_{p}× 1) matrix with ${Y}_{t}=\left(\begin{array}{c}{y}_{t}\\ \vdots \\ {y}_{t-p+1}\end{array}\right)$.

_{t}also includes intercept terms in VAR model. Therefore, χ

_{t}will be empty when it includes no exogenous variables and no intercept terms in the model. In summary, VAR is a model with K variables regressed in linear functions. In this estimation, there are $\left(\mathrm{p}\right)$ own lagged values of variables and $\left(\mathrm{p}\right)$ lags of other (K − 1) variables, and possibly exogenous variables. Therefore, a VAR model with p lags denotes as VAR(p).

#### 3.2.3. Structural Vector Autoregressive Model (SVAR)

#### 3.2.4. Granger Causality

#### 3.2.5. Copulas Approaches

_{j}with $j\in \left\{1,\dots ,d\right\}$ can be recalled by the multivariate distribution function H by ${F}_{j}\left({x}_{j}\right)=H\left(\infty ,\dots ,\infty ,{x}_{j},\infty ,\dots ,\infty \right),\text{}{x}_{j}\text{}\in \mathbb{R}$. Therefore, ${F}_{j},\dots ,{F}_{d}$ is also known as univariate margins of H (or called as marginal distribution functions of X). One of the concise Copulas definitions is a multivariate distribution function with standard uniform univariate margins, that is, U(0, 1) margins.

## 4. Empirical Findings

#### 4.1. Correlation Matrix

#### 4.2. Test of Stationary

#### 4.3. VAR Granger Causality Findings

#### 4.4. SVAR Granger Causality Results

#### 4.5. Copulas Approach

#### 4.6. Summary of Findings

## 5. Conclusions and Implications

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Al Rahahleh, Naseem, and M. Ishaq Bhatti. 2017. Co-movement measure of information transmission on international equity markets. Physica A: Statistical Mechanics and its Applications 470: 119–31. [Google Scholar] [CrossRef]
- Al-Khazali, Osamah, Bouri Elie, and David Roubaud. 2018. The impact of positive and negative macroeconomic news surprises: Gold versus Bitcoin. Economics Bulletin 38: 373–82. [Google Scholar]
- Amisano, Gianni, and Carlo Giannini. 2012. Topics in Structural VAR Econometrics. Berlin: Springer Science & Business Media. [Google Scholar]
- Bae, Kee-Hong, G. Andrew Karolyi, and Reneé M. Stulz. 2003. A new approach to measuring financial contagion. The Review of Financial Studies 16: 717–63. [Google Scholar] [CrossRef]
- Balcilar, Mehmet, Elie Bouri, Rangan Gupta, and David Roubaud. 2017. Can volume predict Bitcoin returns and volatility? A quantiles-based approach. Economic Modelling 64: 74–81. [Google Scholar] [CrossRef]
- Boubaker, Heni, and Nadia Sghaier. 2013. Portfolio optimization in the presence of dependent financial returns with long memory: A copula based approach. Journal of Banking & Finance 37: 361–77. [Google Scholar]
- Bouoiyour, Jamal, and Refk Selmi. 2015. What does Bitcoin look like? Annals of Economics & Finance 16: 449–92. [Google Scholar]
- Bouri, Elie, Rangan Gupta, Aviral Kumar Tiwari, and David Roubaud. 2017a. Does Bitcoin hedge global uncertainty? Evidence from wavelet-based quantile-in-quantile regressions. Finance Research Letters 23: 87–95. [Google Scholar] [CrossRef]
- Bouri, Elie, Naji Jalkh, Peter Molnár, and David Roubaud. 2017b. Bitcoin for energy commodities before and after the December 2013 crash: diversifier, hedge or safe haven? Applied Economics 49: 5063–73. [Google Scholar] [CrossRef]
- Bouri, Elie, Mahamitra Das, Rangan Gupta, and David Roubaud. 2018a. Spillovers between Bitcoin and other assets during bear and bull markets. Applied Economics 50: 5935–49. [Google Scholar] [CrossRef]
- Bouri, Elie, Syed Jawad Hussain Shahzad, and David Roubaud. 2018b. Co-explosivity in the cryptocurrency market. Finance Research Letters. forthcoming. [Google Scholar] [CrossRef]
- Boyson, Nicole M., Christof W. Stahel, and Rene M. Stulz. 2010. Hedge fund contagion and liquidity shocks. The Journal of Finance 65: 1789–816. [Google Scholar] [CrossRef]
- Brandvold, Morten, Peter Molnár, Kristian Vagstad, and Ole Christian Andreas Valstad. 2015. Price discovery on Bitcoin exchanges. Journal of International Financial Markets, Institutions and Money 36: 18–35. [Google Scholar] [CrossRef]
- Brauneis, Alexander, and Roland Mestel. 2018. Price discovery of cryptocurrencies: Bitcoin and beyond. Economics Letters 165: 58–61. [Google Scholar] [CrossRef]
- Briere, Marie, Kim Oosterlinck, and Ariane Szafarz. 2015. Virtual currency, tangible return: Portfolio diversification with bitcoin. Journal of Asset Management 16: 365–73. [Google Scholar] [CrossRef]
- Catania, Leopoldo, and Mads Sandholdt. 2019. Bitcoin at High Frequency. Journal of Risk and Financial Management 12: 36. [Google Scholar] [CrossRef]
- Cheah, Eng-Tuck, and John Fry. 2015. Speculative bubbles in Bitcoin markets? An empirical investigation into the fundamental value of Bitcoin. Economics Letters 130: 32–36. [Google Scholar] [CrossRef] [Green Version]
- Cheah, Eng-Tuck, Tapas Mishra, Mamata Parhi, and Zhuang Zhang. 2018. Long memory interdependency and inefficiency in Bitcoin markets. Economics Letters 167: 18–25. [Google Scholar] [CrossRef]
- Chen, Xiaohong, and Yanqin Fan. 2006. Estimation and model selection of semiparametric copula-based multivariate dynamic models under copula misspecification. Journal of Econometrics 135: 125–54. [Google Scholar] [CrossRef]
- Cheung, Adrian, Eduardo Roca, and Jen-Je Su. 2015. Crypto-currency bubbles: An application of the Phillips–Shi–Yu (2013) methodology on Mt. Gox bitcoin prices. Applied Economics 47: 2348–58. [Google Scholar] [CrossRef]
- Chow, K. Victor, and Karen C. Denning. 1993. A simple multiple variance ratio test. Journal of Econometrics 58: 385–401. [Google Scholar] [CrossRef]
- Christodoulakis, George A., and Stephen E. Satchell. 2002. Correlated ARCH (CorrARCH): Modelling the time-varying conditional correlation between financial asset returns. European Journal of Operational Research 139: 351–70. [Google Scholar] [CrossRef]
- Ciaian, Pavel, Miroslava Rajcaniova, and d’Artis Kancs. 2016. The economics of BitCoin price formation. Applied Economics 48: 1799–815. [Google Scholar] [CrossRef]
- Cong, Rong-Gang, Yi-Ming Wei, Jian-Lin Jiao, and Ying Fan. 2008. Relationships between oil price shocks and stock market: An empirical analysis from China. Energy Policy 36: 3544–53. [Google Scholar] [CrossRef]
- Corbet, Shaen, Charles James Larkin, Brian M. Lucey, Andrew Meegan, and Larisa Yarovaya. 2017. Cryptocurrency Reaction to FOMC Announcements: Evidence of Heterogeneity Based on Blockchain Stack Position. Available online: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3073727 (accessed on 26 March 2019).
- Corbet, Shaen, Brian Lucey, and Larisa Yarovaya. 2018. Datestamping the Bitcoin and Ethereum bubbles. Finance Research Letters 26: 81–88. [Google Scholar] [CrossRef]
- Dickey, David A., and Wayne A. Fuller. 1979. Distribution of the estimators for autoregressive time series with a unit root. Journal of the American Statistical Association 74: 427–31. [Google Scholar]
- Diebold, Francis X., and Kamil Yilmaz. 2008. Measuring financial asset return and volatility spillovers, with application to global equity markets. The Economic Journal 119: 158–71. [Google Scholar] [CrossRef]
- Ding, Liang. 2010. US and Asia Pacific equity markets causality test. International Journal of Business and Management 5: 38. [Google Scholar] [CrossRef]
- Droumaguet, Matthieu, Anders Warne, and Tomasz Wozniak. 2015. Granger causality and regime inference in bayesian markov-switching vars. Journal of Applied Economtrics 32: 802–18. [Google Scholar] [CrossRef]
- Dungey, Mardi, Renée A. Fry, Brenda González-Hermosillo, and Vance L. Martin. 2011. Transmission of Financial Crises and Contagion: A Latent Factor Approach. Oxford: Oxford University Press. [Google Scholar]
- Dyhrberg, Anne Haubo. 2016. Hedging capabilities of bitcoin. Is it the virtual gold? Finance Research Letters 16: 139–44. [Google Scholar] [CrossRef]
- Dyhrberg, Anne H., Sean Foley, and Jiri Svec. 2018. How investible is Bitcoin? Analyzing the liquidity and transaction costs of Bitcoin markets. Economics Letters 171: 140–43. [Google Scholar] [CrossRef]
- Embrechts, Paul. 2009. Copulas: A personal view. Journal of Risk and Insurance 76: 639–50. [Google Scholar] [CrossRef]
- Engle, Robert. 2002. Dynamic conditional correlation: A simple class of multivariate generalized autoregressive conditional heteroskedasticity models. Journal of Business & Economic Statistics 20: 339–50. [Google Scholar]
- Feder, Christophe. 2018. Decentralization and spillovers: A new role for transportation infrastructure. Economics of Transportation 13: 36–47. [Google Scholar] [CrossRef]
- Fry, John, and Eng-Tuck Cheah. 2016. Negative bubbles and shocks in cryptocurrency markets. International Review of Financial Analysis 47: 343–52. [Google Scholar] [CrossRef]
- Galton, Francis. 1889. I. Co-relations and their measurement, chiefly from anthropometric data. Proceedings of the Royal Society of London 45: 135–45. [Google Scholar]
- Gandal, Neil, J. T. Hamrick, Moore Tyler, and Oberman Tali. 2018. Price manipulation in the Bitcoin ecosystem. Journal of Monetary Economics 95: 86–96. [Google Scholar] [CrossRef]
- Genest, Christian, Kilani Ghoudi, and L.-P. Rivest. 1995. A semiparametric estimation procedure of dependence parameters in multivariate families of distributions. Biometrika 82: 543–52. [Google Scholar] [CrossRef]
- Ghorbel, Ahmed, and Abdelwahed Trabelsi. 2014. Energy portfolio risk management using time-varying extreme value copula methods. Economic Modelling 38: 470–85. [Google Scholar] [CrossRef]
- Gkillas, Konstantinos, and Paraskevi Katsiampa. 2018. An application of extreme value theory to cryptocurrencies. Economics Letters 164: 109–11. [Google Scholar] [CrossRef]
- Granger, Clive W. J. 1969. Investigating causal relations by econometric models and cross-spectral methods. Econometrica: Journal of the Econometric Society 37: 424–38. [Google Scholar] [CrossRef]
- Greene, William H. 2008. Econometric Analysis, 6th ed.Upper Saddle River: Prentice Hall. [Google Scholar]
- Gudendorf, Gordon, and Johan Segers. 2010. Extreme-value copulas. In Copula Theory and Its Applications. Berlin and Heidelberg: Springer, pp. 127–45. [Google Scholar]
- Hammoudeh, Shawkat, and Eisa Aleisa. 2004. Dynamic relationships among GCC stock markets and NYMEX oil futures. Contemporary Economic Policy 22: 250–69. [Google Scholar] [CrossRef]
- Hiang Liow, Kim. 2012. Co-movements and correlations across Asian securitized real estate and stock markets. Real Estate Economics 40: 97–129. [Google Scholar] [CrossRef]
- Huynh, Toan Luu Duc, Sang Phu Nguyen, and Duy Duong. 2018. Contagion risk measured by return among cryptocurrencies. In International Econometric Conference of Vietnam. Cham: Springer, pp. 987–98. [Google Scholar]
- Ivanov, Ventzislav, and Lutz Kilian. 2001. A Practitioner’s Guide to Lag-Order Selection for Vector Autoregressions. CEPR Discussion Paper No. 2685. London: Centre for Economic Policy Research, Available online: http://www.cepr.org/pubs/dps/DP2685.asp (accessed on 26 March 2019).
- Ji, Qiang, Bouri Elie, Gupta Rangan, and Roubaud David. 2018a. Network causality structures among Bitcoin and other financial assets: A directed acyclic graph approach. The Quarterly Review of Economics and Finance 70: 203–13. [Google Scholar] [CrossRef]
- Ji, Qiang, Bouri Elie, Lau Chi Keung Macro, and Roubaud David. 2018b. Dynamic connectedness and integration in cryptocurrency markets. International Review of Financial Analysis. [Google Scholar] [CrossRef]
- Katsiampa, Paraskevi. 2017. Volatility estimation for Bitcoin: A comparison of GARCH models. Economics Letters 158: 3–6. [Google Scholar] [CrossRef]
- Katsiampa, Paraskevi. 2018. An Empirical Investigation of volatility Dynamics in the Cryptocurrency Market. Available online: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3202317 (accessed on 26 March 2019).
- Kotz, Samuel, and Saralees Nadarajah. 2004. Multivariate t-Distributions and Their Applications. Cambridge: Cambridge University Press. [Google Scholar]
- Koutmos, Dimitrios. 2018a. Bitcoin returns and transaction activity. Economics Letters 167: 81–85. [Google Scholar] [CrossRef]
- Koutmos, Dimitrios. 2018b. Return and volatility spillovers among cryptocurrencies. Economics Letters 173: 122–27. [Google Scholar] [CrossRef]
- Kristoufek, Ladislav. 2015. What are the main drivers of the Bitcoin price? Evidence from wavelet coherence analysis. PLoS ONE 10: e0123923. [Google Scholar] [CrossRef]
- Kundu, Srikanta, and Nityananda Sarkar. 2016. Return and volatility interdependences in up and down markets across developed and emerging countries. Research in International Business and Finance 36: 297–311. [Google Scholar] [CrossRef]
- Li, Xin, and Chong Alex Wang. 2017. The technology and economic determinants of cryptocurrency exchange rates: The case of Bitcoin. Decision Support Systems 95: 49–60. [Google Scholar] [CrossRef]
- Ljung, Greta M., and George E. P. Box. 1978. On a measure of lack of fit in time series models. Biometrika 65: 297–303. [Google Scholar] [CrossRef] [Green Version]
- Lo, Stephanie, and J. Christina Wang. 2014. Bitcoin as Money? Current Policy Perspectives. Boston: Federal Reserve Bank of Boston. [Google Scholar]
- Luo, Weiwei, Robert D. Brooks, and Param Silvapulle. 2011. Effects of the open policy on the dependence between the Chinese ‘A’stock market and other equity markets: An industry sector perspective. Journal of International Financial Markets Institutions and Money 21: 49–74. [Google Scholar] [CrossRef]
- Lütkepohl, Helmut. 2005. New Introduction to Multiple time Series Analysis. Berlin: Springer Science & Business Media. [Google Scholar]
- Maghyereh, Aktham, and Ahmad Al-Kandari. 2007. Oil prices and stock markets in GCC countries: New evidence from nonlinear cointegration analysis. Managerial Finance 33: 449–60. [Google Scholar] [CrossRef]
- Malevergne, Yannick, and Didier Sornette. 2003. Testing the Gaussian copula hypothesis for financial assets dependences. Quantitative Finance 3: 231–50. [Google Scholar] [CrossRef]
- Malevergne, Yannick, and Didier Sornette. 2006. Extreme Financial Risks: From Dependence to Risk Management. Berlin: Springer Science & Business Media. [Google Scholar]
- Nakamoto, Satoshi. 2008. Bitcoin: A Peer-to-Peer Electronic Cash System. Unpublished Manuscript. Available online: http://pdos.csail.mit.edu/6.824/papers/bitcoin.pdf (accessed on 26 March 2019).
- Narayan, Paresh Kumar, and Seema Narayan. 2010. Modelling the impact of oil prices on Vietnam’s stock prices. Applied Energy 87: 356–61. [Google Scholar] [CrossRef]
- Nasir, Muhammad Ali, Toan Luu Duc Huynh, Sang Phu Nguyen, and Duy Duong. 2019. Forecasting cryptocurrency returns and volume using search engines. Financial Innovation 5: 2. [Google Scholar] [CrossRef]
- Nguyen, Cuong C., and M. Ishaq Bhatti. 2012. Copula model dependency between oil prices and stock markets: Evidence from China and Vietnam. Journal of International Financial Markets Institutions and Money 22: 758–73. [Google Scholar] [CrossRef]
- Ogawa, Hikaru, and David E. Wildasin. 2009. Think locally, act locally: Spillovers, spillbacks, and efficient decentralized policymaking. American Economic Review 99: 1206–17. [Google Scholar] [CrossRef]
- Park, Jungwook, and Ronald A. Ratti. 2008. Oil price shocks and stock markets in the US and 13 European countries. Energy Economics 30: 2587–608. [Google Scholar] [CrossRef]
- Pearson, Karl. 1896. VII. Mathematical contributions to the theory of evolution.—III. Regression, heredity, and panmixia. Philosophical Transactions of the Royal Society of London. Series A, containing papers of a mathematical or physical character. Royal Society 187: 253–318. [Google Scholar]
- Phillips, Peter C. B., and Pierre Perron. 1988. Testing for a unit root in time series regression. Biometrika 75: 335–46. [Google Scholar] [CrossRef]
- Phillips, Peter C. B., Shuping Shi, and Jun Yu. 2015. Testing for multiple bubbles: Historical episodes of exuberance and collapse in the S&P 500. International Economic Review 56: 1043–78. [Google Scholar]
- Polasik, Michal, Anna Iwona Piotrowska, Tomasz Piotr Wisniewski, Radoslaw Kotkowski, and Geoffrey Lightfoot. 2015. Price fluctuations and the use of Bitcoin: An empirical inquiry. International Journal of Electronic Commerce 20: 9–49. [Google Scholar] [CrossRef]
- Selgin, George. 2015. Synthetic commodity money. Journal of Financial Stability 17: 92–99. [Google Scholar] [CrossRef]
- Shabri Abd. Majid, M., Ahamed Kameel Mydin Meera, Mohd Azmi Omar, and Hassanuddeen Abdul Aziz. 2009. Dynamic linkages among ASEAN-5 emerging stock markets. International Journal of Emerging Markets 4: 160–84. [Google Scholar] [CrossRef]
- Sims, Christopher A. 1980. Macroeconomics and reality. Econometrica: Journal of the Econometric Society 48: 1–48. [Google Scholar] [CrossRef]
- Snedecor, George W., and William G. Cochran. 1989. Statistical Methods. Ames: Iowa State College Press Ames. First published 1980. [Google Scholar]
- Sovbetov, Yhlas. 2018. Factors influencing cryptocurrency prices: Evidence from bitcoin, ethereum, dash, litcoin, and monero. Journal of Economics and Financial Analysis 2: 1–27. [Google Scholar]
- Stigler, Stephen M. 1986. The History of Statistics: The Measurement of Uncertainty Before 1900. Cambridge: Harvard University Press. [Google Scholar]
- Su, EnDer. 2017. Measuring and testing tail dependence and contagion risk between major stock markets. Computational Economics 50: 325–51. [Google Scholar] [CrossRef]
- Trabelsi, Nader. 2018. Are There Any Volatility Spill-Over Effects among Cryptocurrencies and Widely Traded Asset Classes? Journal of Risk and Financial Management 11: 66. [Google Scholar] [CrossRef]
- Tse, Yiu K., and Albert K. C. Tsui. 2002. A multivariate generalized autoregressive conditional heteroscedasticity model with time-varying correlations. Journal of Business & Economic Statistics 20: 351–62. [Google Scholar]
- Tu, Zhiyong, and Changyong Xue. 2018. Effect of bifurcation on the interaction between Bitcoin and Litecoin. Finance Research Letters. forthcoming. [Google Scholar] [CrossRef]
- Tudor, Cristiana. 2011. Changes in stock markets interdependencies as a result of the global financial crisis: Empirical investigation on the CEE region. Panoeconomicus 58: 525–43. [Google Scholar] [CrossRef]
- Urquhart, Andrew. 2017. Price clustering in Bitcoin. Economics Letters 159: 145–48. [Google Scholar] [CrossRef]
- Velde, François R. 2013. Bitcoin Is a Digital Currency That Was Launched in 2009, and It Has Attracted Much Attention Recently. This Article Reviews the Mechanics of the Currency and Offers Some Thoughts on Its Characteristics. Chicago Fed Letter 317: 1. [Google Scholar]
- Vinh, Vo Xuan. 2014. An empirical investigation of factors affecting stock prices in Vietnam. Journal of Economics and Development 16: 74–89. [Google Scholar]
- Wald, Abraham, and Jacob Wolfowitz. 1940. On a test whether two samples are from the same population. The Annals of Mathematical Statistics 11: 147–62. [Google Scholar] [CrossRef]
- Wei, Wang Chun. 2018. Liquidity and market efficiency in cryptocurrencies. Economics Letters 168: 21–24. [Google Scholar] [CrossRef]
- Yermack, David. 2015. Is Bitcoin a real currency? An economic appraisal. In Handbook of Digital Currency. Cambridge: Academic Press, pp. 31–43. [Google Scholar]
- Yi, Shuyue, Zishuang Xu, and Gang-Jin Wang. 2018. Volatility connectedness in the cryptocurrency market: Is Bitcoin a dominant cryptocurrency? International Review of Financial Analysis 60: 98–114. [Google Scholar] [CrossRef]
- Yilmaz, Kamil. 2010. Return and volatility spillovers among the East Asian equity markets. Journal of Asian Economics 21: 304–13. [Google Scholar] [CrossRef]
- Zhang, Bing, Zhizhen Fan, and Xindan Li. 2010. Comovement between China and US’s stock markets. Economic Research Journal 11: 141–51. [Google Scholar]
- Zivot, Eric, and Donald W. K. Andrews. 2002. Further evidence on the great crash, the oil-price shock, and the unit-root hypothesis. Journal of Business & Economic Statistics 20: 25–44. [Google Scholar]

1 | It becomes one of popular practices to perform the verification for historical online confirmation among trading parties. |

2 | It was measured by the gap between the US industrial yields and the US Treasury bond. |

3 | Least Absolute Shrinkage and Selection Operator and Vector Autoregressive Model. |

4 | Selection-order criteria based on rich set of parameters such as the Log-Likelihood (LL), the Likelihood ratio (LR), the Prediction Error (FPE), the Akaike’s Information Criterion (AIC), the Schwarz’s Bayesian Information Criterion (SBIC), and the Hannan and Quinn Information Criterion (HQIC). |

5 | The VAR model estimation for VAR Granger causality is based on the suggested lag by Lütkepohl (2005) with the L(3) term and we also employed the multivariate VAR (all of the cryptocurrencies) in our models to test the spillover effects rather than bivariable (it might be omitted the effects from other cryptocurrencies). |

Variable | Mean | Std. Dev. | Min | Max | Skewness | Kurtosis |
---|---|---|---|---|---|---|

bitcoin | 0.002163 | 0.040021 | −0.20753 | 0.225119 | −0.2623099 | 7.720781 |

ethereum | 0.004276 | 0.068703 | −0.31547 | 0.412337 | 0.4963407 | 7.554288 |

xrp | 0.003004 | 0.075708 | −0.61627 | 1.027356 | 2.987435 | 41.54075 |

litecoin | 0.001711 | 0.057338 | −0.39515 | 0.510348 | 1.271329 | 15.6589 |

stellar | 0.003104 | 0.083676 | −0.36636 | 0.723102 | 2.030118 | 18.3531 |

Bitcoin | Ethereum | xrp | Litecoin | Stellar | |
---|---|---|---|---|---|

bitcoin | 1 | ||||

ethereum | 0.3992 *** | 1 | |||

xrp | 0.3043 *** | 0.2587 *** | 1 | ||

litecoin | 0.6113 *** | 0.3871 *** | 0.3609 *** | 1 | |

stellar | 0.3661 *** | 0.2789 *** | 0.5488 *** | 0.3857 *** | 1 |

Variables | Augmented Dickey–Fuller | Phillips–Perron | Zivot–Andrews |
---|---|---|---|

bitcoin | −34.983 *** | −35.005 *** | −13.900 *** |

ethereum | −33.161 *** | −33.288 *** | −18.966 *** |

xrp | −35.585 *** | −35.934 *** | −13.027 *** |

litecoin | −34.731 *** | −34.809 *** | −12.725 *** |

stellar | −32.703 *** | −32.760 *** | −14.925 *** |

**Table 4.**VAR Granger causality results5.

Pairs | Gaussian Copula | Student’s-t Copulas |
---|---|---|

bitcoin-ethereum | 0.4148 [115.7] | 0.4334[160.1] |

bitcoin-xrp | 0.4135 [114.9] | 0.4389[162.6] |

bitcoin-litecoin | 0.6894 [397.5] | 0.7367[525.5] |

bitcoin-stellar | 0.4217 [120] | 0.4328[161.8] |

ethereum-xrp | 0.3958 [104.4] | 0.4467[145.5] |

ethereum-litecoin | 0.4484 [137.7] | 0.4793[173.5] |

ethereum-stellar | 0.3842 [97.8] | 0.4284[132.4] |

xrp-litecoin | 0.4872 [166.3] | 0.5453[268.4] |

xrp-stellar | 0.5921 [265.5] | 0.6001[330.2] |

litecoin-stellar | 0.481 [161.5] | 0.5058[207.6] |

© 2019 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Luu Duc Huynh, T.
Spillover Risks on Cryptocurrency Markets: A Look from VAR-SVAR Granger Causality and Student’s-t Copulas. *J. Risk Financial Manag.* **2019**, *12*, 52.
https://doi.org/10.3390/jrfm12020052

**AMA Style**

Luu Duc Huynh T.
Spillover Risks on Cryptocurrency Markets: A Look from VAR-SVAR Granger Causality and Student’s-t Copulas. *Journal of Risk and Financial Management*. 2019; 12(2):52.
https://doi.org/10.3390/jrfm12020052

**Chicago/Turabian Style**

Luu Duc Huynh, Toan.
2019. "Spillover Risks on Cryptocurrency Markets: A Look from VAR-SVAR Granger Causality and Student’s-t Copulas" *Journal of Risk and Financial Management* 12, no. 2: 52.
https://doi.org/10.3390/jrfm12020052