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

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## 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

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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] |

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**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