# Cryptocurrencies Intraday High-Frequency Volatility Spillover Effects Using Univariate and Multivariate GARCH Models

^{1}

^{2}

## Abstract

**:**

## 1. Introduction

## 2. Research Background

#### 2.1. Model Specifications

#### 2.1.1. GARCH Model

#### 2.1.2. Standard GARCH (sGARCH) Models

#### 2.1.3. EGARCH Model

#### 2.1.4. GJR-GARCH Model

#### 2.1.5. Threshold GARCH Model

#### 2.1.6. DCC-GARCH Model

#### 2.2. Methodological Development

## 3. Data and Results

#### 3.1. Estimation Results

#### 3.2. Model Selection

#### 3.3. Forecasting Volatility Accuracy

## 4. Conclusions

## Funding

## Conflicts of Interest

## Note

1 | Data are publicly available at https://www.cryptodatadownload.com/data/ (accessed on 4 May 2021). |

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**Figure 1.**Cryptocurrencies’ sample prices. Note: Data observation time period: 21 December 2020 to 23 April 2021.

**Figure 2.**One-minute log returns (${r}_{t}$) of all coins. Note: Data observation time period: 21 December 2020 to 23 April 2021.

**Figure 3.**One-minute squared returns (${r}_{t}$) of all coins. Note: Data observation time period: 21 December 2020 to 23 April 2021.

**Figure 4.**Conditional correlation between the cryptocurrencies. (

**a**) Conditional correlation between BTC and ETH; (

**b**) conditional correlation between ETH and LTC; (

**c**) conditional correlation between LTC and XRP; (

**d**) conditional correlation between BTC and XRP.

Symbol | Name | Market Cap (USD) | Price (USD) | Circulating Supply |
---|---|---|---|---|

BTC | Bitcoin | $704,141,870,936 | $37,019.80 | 18,939,768 BTC |

ETH | Ethereum | $295,477,305,134 | $2461.43 | 119,308,579 ETH |

LTC | Litecoin | $7,535,211,234 | $107.95 | 69,492,969 LTC |

XRP | Ripple | $29,254,109,616 | $0.6101 | 47,736,918,345 XRP |

Bitcoin—BTC | Ethereum—ETH | Litecoin—LTC | Ripple—XRP | |
---|---|---|---|---|

A. Descriptive statistics | ||||

Obs | 178,560 | 178,560 | 178,560 | 178,560 |

Minimum | −0.034947 | −0.045088 | −0.056805 | −0.168867 |

1-Quartile | −0.000711 | −0.000800 | −0.000779 | −0.001183 |

Mean | 0.000004 | 0.000007 | 0.000004 | 0.000004 |

Median | 0.000000 | 0.000000 | 0.000000 | 0.000000 |

3-Quartile | 0.000713 | 0.000822 | 0.000789 | 0.001156 |

Maximum | 0.035773 | 0.041179 | 0.051331 | 0.108117 |

Stdev | 0.001541 | 0.001865 | 0.002275 | 0.003355 |

Skewness | −0.022956 | −0.075367 | −0.099042 | −1.384401 |

Kurtosis | 19.791322 | 15.802376 | 19.215616 | 86.717473 |

Hurst exponent | 0.492180 | 0.492006 | 0.463128 | 0.523267 |

VaR 5% | −0.002235 | −0.002763 | −0.003451 | −0.004500 |

VaR 1% | −0.010735 | −0.011320 | −0.015664 | −0.076805 |

JB p-value | <0.001 | <0.001 | <0.001 | <0.001 |

B. Test Statistics | ||||

ADF | −58.998 ** | −59.065 ** | −60.263 ** | −57467 ** |

PP | −169567 ** | −169173 ** | −170385 ** | −172599 ** |

KPSS | 0.18957 | 0.12696 | 0.024004 | 0.21985 |

Bitcoin—BTC | Ethereum—ETH | Litecoin—LTC | |
---|---|---|---|

Bitcoin | |||

Ethereum | 0.72296 *** | ||

Litecoin | 0.54538 *** | 0.56353 *** | |

Ripple | 0.41015 *** | 0.40855 *** | 0.37183 *** |

BTC | sGARCH | EGARCH | GJRGARCH | TGARCH | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

sged | sstd | std | sged | sstd | std | sged | sstd | std | sged | sstd | std | |

$\mu $ | 0.000004 *** (0.000000) | 0.000001 (0.000002) | 0.000005 ** (0.000002) | −0.000036 *** (0.000002) | 0.000027 *** (0.000001) | 0.000026*** (0.000001) | 0.000004 *** (0.000000) | 0.000009 *** (0.000002) | 0.000008 *** (0.000002) | 0.000004 *** (0.000000) | 0.000000 (0.000002) | 0.000001 (0.000002) |

$\omega $ | 0.000000 (0.000000) | 0.000000 (0.000000) | 0.000000 (0.000000) | −0.199788 *** (0.000296) | −0.127159 *** (0.000086) | −0.128498 *** (0.000099) | 0.000000 (0.000000) | 0.000000 (0.000000) | 0.000000 (0.000000) | 0.000000 (0.000000) | 0.000008 *** (0.000001) | 0.000008 *** (0.000001) |

${\alpha}_{1}$ | 0.050000 *** (0.000000) | 0.070629 *** (0.002009) | 0.056567 *** (0.001466) | −0.027195 *** (0.001304) | −0.022736 *** (0.001235) | −0.022642 *** (0.001235) | 0.050000 *** (0.000000) | 0.054460 *** (0.001369) | 0.053428 *** (0.001243) | 0.050000 *** (0.000000) | 0.071472 *** (0.001217) | 0.071333 *** (0.001209) |

${\beta}_{1}$ | 0.900000 *** (0.000005) | 0.916645 *** (0.002002) | 0.934692 *** (0.001450) | 0.985003 *** (0.000002) | 0.990558 *** (0.000022) | 0.990458 *** (0.000022) | 0.900000 *** (0.000006) | 0.920309 *** (0.001706) | 0.921220 *** (0.001626) | 0.900000 *** (0.000005) | 0.940540 *** (0.000941) | 0.940661 *** (0.000948) |

${\gamma}_{1}$ | 0.143372 *** (0.000400) | 0.127978 *** (0.000515) | 0.128087 *** (0.000526) | 0.050000 *** (0.000000) | 0.028111 *** (0.001627) | 0.028138 *** (0.001588) | ||||||

${\eta}_{11}$ | 0.050000 *** (0.000000) | 0.213108 *** (0.010034) | 0.214260 *** (0.010001) | |||||||||

$Log\left(L\right)$ | 773619.2 | 946853.5 | 946946.3 | 945566.8 | 947018.3 | 947014.9 | 746828.2 | 947081.6 | 947056.3 | 702209 | 947359.8 | 947358 |

AIC | −8.665 | −10.605 | −10.606 | −10.591 | −10.607 | −10.607 | −8.3649 | −10.608 | −10.608 | −7.8651 | −10.611 | −10.611 |

HQ | −8.6648 | −10.605 | −10.606 | −10.591 | −10.607 | −10.607 | −8.3647 | −10.608 | −10.607 | −7.8649 | −10.611 | −10.611 |

ETH | ||||||||||||

$\mu $ | 0.000007 *** (0.000000) | 0.000000 (0.000003) | 0.000014 *** (0.000002) | 0.000008 *** (0.000002) | −0.000045 *** (0.000002) | −0.000037 *** (0.000002) | 0.000007 *** (0.000000) | −0.000003 (0.000003) | 0.000021 *** (0.000002) | 0.000007 *** (0.000000) | 0.000000 (0.000001) | 0.000000 (0.000001) |

$\omega $ | 0.000000 (0.000000) | 0.000000 (0.000000) | 0.000000 (0.000000) | −0.252306 *** (0.000314) | −0.189859 *** (0.000054) | −0.195798 *** (0.000227) | 0.000000 (0.000000) | 0.000000 (0.000000) | 0.000000 (0.000000) | 0.000000 (0.000000) | 0.000000 (0.000000) | 0.000000 (0.000000) |

${\alpha}_{1}$ | 0.050000 *** (0.000000) | 0.066440 *** (0.001338) | 0.069004 *** (0.001272) | −0.034462 *** (0.001480) | −0.031997 *** (0.001399) | −0.031576 *** (0.001391) | 0.050000 *** (0.000000) | 0.053718 *** (0.001034) | 0.051967 *** (0.000715) | 0.050000 *** (0.000000) | 0.089606 *** (0.001234) | 0.087648 *** (0.001176) |

${\beta}_{1}$ | 0.900000 *** (0.000005) | 0.928220 *** (0.001199) | 0.924150 *** (0.001249) | 0.980649 *** (0.000007) | 0.985219 *** (0.000032) | 0.984798 *** (0.000036) | 0.900000 *** (0.000006) | 0.917992 *** (0.001482) | 0.926868 *** (0.001130) | 0.900000 *** (0.000005) | 0.933196 *** (0.000876) | 0.934648 *** (0.000827) |

${\gamma}_{1}$ | 0.143349 *** (0.000423) | 0.155793 *** (0.000996) | 0.152671 *** (0.001001) | 0.050000 *** (0.000000) | 0.039489 *** (0.001635) | 0.033988 *** (0.001618) | ||||||

${\eta}_{11}$ | 0.050000 *** (0.000000) | 0.167657 *** (0.008134) | 0.172251 *** (0.008216) | |||||||||

$Log\left(L\right)$ | 745916 | 917369.2 | 917288.2 | 917453 | 917216.6 | 917137.9 | 719008.2 | 917515.1 | 917591.5 | 678231.9 | 917187.1 | 917188.2 |

AIC | −8.3547 | −10.275 | −10.274 | −10.276 | −10.273 | −10.273 | −8.0533 | −10.277 | −10.278 | −7.5966 | −10.273 | −10.273 |

HQ | −8.3545 | −10.275 | −10.274 | −10.276 | −10.273 | −10.272 | −8.0531 | −10.277 | −10.277 | −7.5964 | −10.273 | −10.273 |

sGARCH | EGARCH | GJRGARCH | TGARCH | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

sged | sstd | std | sged | sstd | std | sged | sstd | std | sged | sstd | std | |

LTC | ||||||||||||

$\mu $ | 0.000004 *** (0.000000) | 0.000002 (0.000002) | 0.000003 * (0.000002) | 0.000000 * (0.000000) | −0.000016 *** (0.000004) | 0.000000 (0.000001) | 0.000004 *** (0.000000) | −0.000001 (0.000002) | 0.000004 ** (0.000002) | 0.000004 *** (0.000000) | 0.000000 (0.000001) | 0.000000 (0.000001) |

$\omega $ | 0.000000 (0.000000) | 0.000000 (0.000000) | 0.000000 (0.000000) | −0.042510 *** (0.000038) | 0.003790 *** (0.000139) | −0.124647 *** (0.000590) | 0.000000 (0.000000) | 0.000000 (0.000000) | 0.000000 (0.000000) | 0.000000 (0.000000) | 0.000101 *** (0.000011) | 0.000020 *** (0.000004) |

${\alpha}_{1}$ | 0.050000 *** (0.000000) | 0.059881 *** (0.000658) | 0.060617 *** (0.000663) | 0.069596 *** (0.002222) | 0.042853 *** (0.009338) | −0.047306 *** (0.004832) | 0.050000 *** (0.000000) | 0.052327 *** (0.000366) | 0.053982*** (0.000360) | 0.050000*** (0.000000) | 1.000000 *** (0.006372) | 0.258998 *** (0.002287) |

${\beta}_{1}$ | 0.900000 *** (0.000005) | 0.938900 *** (0.000670) | 0.937879 *** (0.000681) | 0.992120 *** (0.000003) | 1.000000 *** (0.000001) | 0.987396 *** (0.000014) | 0.900000 *** (0.000006) | 0.939018*** (0.000671) | 0.937384 *** (0.000690) | 0.900000 *** (0.000005) | 0.899687 *** (0.001938) | 0.922289 *** (0.001787) |

${\gamma}_{1}$ | 0.339121 *** (0.001074) | 0.459831 *** (0.010359) | 0.602413 *** (0.008646) | 0.050000 *** (0.000000) | 0.014514 *** (0.001480) | 0.013659 *** (0.001496) | ||||||

${\eta}_{11}$ | 0.050000 *** (0.000000) | 0.083975 *** (0.009137) | 0.067701 *** (0.009897) | |||||||||

$Log\left(L\right)$ | 709188.6 | 888892.2 | 888860.8 | 1050125 | 891656.5 | 891469.1 | 682631.5 | 888907.3 | 888866.9 | 660488 | 893258.3 | 893294.8 |

AIC | −7.9433 | −9.9561 | −9.9558 | −11.762 | −9.9871 | −9.985 | −7.6458 | −9.9563 | −9.9558 | −7.3978 | −10.005 | −10.005 |

HQ | −7.9431 | −9.9559 | −9.9556 | −11.762 | −9.9869 | −9.9848 | −7.6456 | −9.9561 | −9.9556 | −7.3976 | −10.005 | −10.005 |

XRP | ||||||||||||

$\mu $ | 0.000004 (0.000004) | 0.000006 * (0.000004) | 0.000001 (0.000003) | −0.000023 *** (0.000001) | 0.000000 (0.000001) | 0.000000 (0.000001) | 0.000004 (0.000019) | 0.000002 (0.000004) | −0.000005 * (0.000003) | 0.000004 *** (0.000000) | 0.000000 (0.000003) | −0.000002 (0.000003) |

$\omega $ | 0.000000 ** (0.000000) | 0.000000 (0.000000) | 0.000000 (0.000000) | −0.274114 *** (0.000527) | −0.205692 *** (0.000087) | −0.198845 *** (0.000284) | 0.000000 (0.000000) | 0.000000 (0.000000) | 0.000000 (0.000000) | 0.000000 (0.000000) | 0.000013 *** (0.000001) | 0.000013 *** (0.000001) |

${\alpha}_{1}$ | 0.050000 *** (0.000000) | 0.068878 *** (0.001179) | 0.074544 *** (0.001150) | −0.014142 *** (0.002111) | −0.010385 *** (0.001973) | −0.011185 *** (0.001910) | 0.050000 *** (0.000001) | 0.061845 *** (0.000548) | 0.062147 *** (0.000622) | 0.050000 *** (0.000000) | 0.096955 *** (0.001677) | 0.097085 *** (0.001668) |

${\beta}_{1}$ | 0.900000 *** (0.000003) | 0.927172 *** (0.001102) | 0.923875 *** (0.001034) | 0.977363 *** (0.000004) | 0.982719 *** (0.000054) | 0.983362 *** (0.000026) | 0.900000 *** (0.000008) | 0.932527 *** (0.000954) | 0.930476 *** (0.001035) | 0.900000 *** (0.000001) | 0.927709 *** (0.000952) | 0.927631 *** (0.000953) |

${\gamma}_{1}$ | 0.241130 *** (0.001435) | 0.255071 *** (0.001119) | 0.241243 *** (0.002419) | 0.050000 *** (0.000001) | 0.008515 *** (0.001582) | 0.009471 *** (0.001604) | ||||||

${\eta}_{11}$ | 0.050000 *** (0.000000) | 0.057707 *** (0.009731) | 0.059406 *** (0.009682) | |||||||||

$Log\left(L\right)$ | 673665.1 | 845577.4 | 845630.5 | 845364.3 | 844559.4 | 844557.4 | 647702.6 | 845649 | 845613.5 | 612925.9 | 846029.6 | 846018.7 |

AIC | −7.5455 | −9.471 | −9.4716 | −9.4686 | −9.4596 | −9.4596 | −7.2547 | −9.4718 | −9.4714 | −6.8651 | −9.4761 | −9.4759 |

HQ | −7.5454 | −9.4709 | −9.4715 | −9.4685 | −9.4595 | −9.4595 | −7.2545 | −9.4717 | −9.4713 | −6.865 | −9.4759 | −9.4758 |

BTC | ETH | LTC | XRP | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

GJRGARCH | ||||||||||||||||

Minutes | MSE | Rank | MAE | Rank | MSE | Rank | MAE | Rank | MSE | Rank | MAE | Rank | MSE | Rank | MAE | Rank |

1 min | 0.00000743 | 17 | 0.00272521 | 18 | 0.00000485 | 7 | 0.00220320 | 10 | 0.00004644 | 14 | 0.00681453 | 15 | 0.00000742 | 8 | 0.00272411 | 11 |

5 min | 0.00000173 | 4 | 0.00076404 | 4 | 0.00001100 | 14 | 0.00185668 | 7 | 0.00001082 | 9 | 0.00191696 | 6 | 0.00002454 | 12 | 0.00269211 | 9 |

15 min | 0.00000120 | 3 | 0.00045877 | 3 | 0.00000490 | 8 | 0.00090568 | 3 | 0.00000393 | 5 | 0.00078603 | 3 | 0.00000892 | 10 | 0.00111919 | 3 |

30 min | 0.00000060 | 2 | 0.00023282 | 2 | 0.00000245 | 2 | 0.00045977 | 2 | 0.00000211 | 2 | 0.00046304 | 2 | 0.00000447 | 6 | 0.00057457 | 2 |

60 min | 0.00000033 | 1 | 0.00013856 | 1 | 0.00000126 | 1 | 0.00025217 | 1 | 0.00000107 | 1 | 0.00024752 | 1 | 0.00000228 | 1 | 0.00031409 | 1 |

sGARCH | ||||||||||||||||

Minutes | MSE | MAE | MSE | MAE | MSE | MAE | MSE | MAE | ||||||||

1 min | 0.00000578 | 13 | 0.00240351 | 16 | 0.00000296 | 4 | 0.00172090 | 6 | 0.00003905 | 13 | 0.00624863 | 13 | 0.00000337 | 3 | 0.00183641 | 6 |

5 min | 0.00000832 | 19 | 0.00257684 | 17 | 0.00002617 | 19 | 0.00465479 | 19 | 0.00005256 | 15 | 0.00660735 | 14 | 0.00005055 | 17 | 0.00649120 | 18 |

15 min | 0.00000593 | 14 | 0.00202695 | 13 | 0.00001548 | 17 | 0.00304218 | 17 | 0.00002747 | 12 | 0.00454032 | 12 | 0.00006212 | 19 | 0.00638460 | 17 |

30 min | 0.00000349 | 9 | 0.00144101 | 8 | 0.00001001 | 13 | 0.00236939 | 11 | 0.00001548 | 11 | 0.00310212 | 11 | 0.00003988 | 15 | 0.00491923 | 14 |

60 min | 0.00000294 | 6 | 0.00138984 | 7 | 0.00000969 | 12 | 0.00246646 | 13 | 0.00001218 | 10 | 0.00275465 | 10 | 0.00003060 | 13 | 0.00441387 | 13 |

EGARCH | ||||||||||||||||

Minutes | MSE | MAE | MSE | MAE | MSE | MAE | MSE | MAE | ||||||||

1 min | 0.00000780 | 18 | 0.00279231 | 19 | 0.00000677 | 10 | 0.00260150 | 14 | 0.00013980 | 20 | 0.01182353 | 20 | 0.00000404 | 5 | 0.00200991 | 7 |

5 min | 0.00001015 | 20 | 0.00284840 | 20 | 0.00003212 | 20 | 0.00521955 | 20 | 0.00012304 | 19 | 0.01001655 | 19 | 0.00005326 | 18 | 0.00669586 | 20 |

15 min | 0.00000688 | 16 | 0.00211564 | 14 | 0.00001818 | 18 | 0.00322996 | 18 | 0.00007135 | 18 | 0.00706960 | 16 | 0.00006373 | 20 | 0.00654225 | 19 |

30 min | 0.00000478 | 10 | 0.00179136 | 10 | 0.00001267 | 15 | 0.00271726 | 15 | 0.00006382 | 16 | 0.00721222 | 17 | 0.00004247 | 16 | 0.00510121 | 16 |

60 min | 0.00000490 | 11 | 0.00191453 | 11 | 0.00001428 | 16 | 0.00301768 | 16 | 0.00006664 | 17 | 0.00756150 | 18 | 0.00003789 | 14 | 0.00506421 | 15 |

TGARCH | ||||||||||||||||

Minutes | MSE | MAE | MSE | MAE | MSE | MAE | MSE | MAE | ||||||||

1 min | 0.00000321 | 8 | 0.00179101 | 9 | 0.00000454 | 6 | 0.00213031 | 9 | 0.00000494 | 6 | 0.00222331 | 8 | 0.00000761 | 9 | 0.00275831 | 12 |

5 min | 0.00000640 | 15 | 0.00219810 | 15 | 0.00000721 | 11 | 0.00237138 | 12 | 0.00000746 | 8 | 0.00241906 | 9 | 0.00000919 | 11 | 0.00269240 | 10 |

15 min | 0.00000542 | 12 | 0.00193153 | 12 | 0.00000562 | 9 | 0.00196485 | 8 | 0.00000569 | 7 | 0.00198221 | 7 | 0.00000628 | 7 | 0.00208186 | 8 |

30 min | 0.00000304 | 7 | 0.00127807 | 6 | 0.00000314 | 5 | 0.00129822 | 5 | 0.00000319 | 4 | 0.00131020 | 5 | 0.00000352 | 4 | 0.00138427 | 5 |

60 min | 0.00000244 | 5 | 0.00118351 | 5 | 0.00000251 | 3 | 0.00120136 | 4 | 0.00000253 | 3 | 0.00120950 | 4 | 0.00000272 | 2 | 0.00125883 | 4 |

60 Min | BTC | ETH | LTC | XRP |
---|---|---|---|---|

${\mathit{IR}}_{\mathit{MSE}}$ | ${\mathit{IR}}_{\mathit{MSE}}$ | ${\mathit{IR}}_{\mathit{MSE}}$ | ${\mathit{IR}}_{\mathit{MSE}}$ | |

GJR-GARCH | −0.887914 | −0.870400 | −0.911985 | −0.925626 |

EGARCH | 0.664820 | 0.474607 | 4.472185 | 0.238292 |

TGARCH | −0.169938 | −0.741103 | −0.792089 | −0.911139 |

BTC to ETH | ETH to LTC | LTC to XRP | BTC to XRP | |
---|---|---|---|---|

${\mu}_{1}$ | 0.000009 *** (0.000002) | 0.000014 *** (0.000002) | 0.000003 * (0.000002) | 0.000008 * (0.000002) |

${\mu}_{2}$ | 0.000011 *** (0.000002) | 0.000003 * (0.000002) | −0.000004 (0.000003) | −0.000004 (0.000003) |

${\omega}_{1}$ | 0.000000 (0.000000) | 0.000000 (0.000000) | 0.000000 (0.000000) | 0.000000 (0.000000) |

${\omega}_{2}$ | 0.000000 (0.000000) | 0.000000 (0.000000) | 0.000000 (0.000000) | 0.000000 (0.000000) |

${\alpha}_{11}$ | 0.077681 *** (0.000957) | 0.069304 *** (0.00218) | 0.066071 *** (0.001038) | 0.072285 *** (0.002915) |

${\alpha}_{12}$ | 0.069877 *** (0.002227) | 0.066071 *** (0.001039) | 0.070768 *** (0.001636) | 0.070768 *** (0.001533) |

${\beta}_{11}$ | 0.911222 *** (0.000939) | 0.923727 *** (0.002094) | 0.932672 *** (0.000908) | 0.917494 *** (0.002862) |

${\beta}_{12}$ | 0.922965 *** (0.002138) | 0.932672 *** (0.000907) | 0.92767 *** (0.001515) | 0.92767 *** (0.001392) |

${\nu}_{11}$ | 6.761541 *** (0.10571) | 6.077415 *** (0.091198) | 3.155579 *** (0.020067) | 6.833 *** (0.09398) |

${\nu}_{12}$ | 6.222508 *** (0.099647) | 3.155579 *** (0.020122) | 4.871043 *** (0.056171) | 4.871043 *** (0.061898) |

$Log\left(L\right)$ | 1907809 | 1783877 | 1688118 | 1774470 |

AIC | −21.369 | −20.143 | −19.062 | −20.037 |

HQ | −21.368 | −20.143 | −19.061 | −20.036 |

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## Share and Cite

**MDPI and ACS Style**

Ampountolas, A.
Cryptocurrencies Intraday High-Frequency Volatility Spillover Effects Using Univariate and Multivariate GARCH Models. *Int. J. Financial Stud.* **2022**, *10*, 51.
https://doi.org/10.3390/ijfs10030051

**AMA Style**

Ampountolas A.
Cryptocurrencies Intraday High-Frequency Volatility Spillover Effects Using Univariate and Multivariate GARCH Models. *International Journal of Financial Studies*. 2022; 10(3):51.
https://doi.org/10.3390/ijfs10030051

**Chicago/Turabian Style**

Ampountolas, Apostolos.
2022. "Cryptocurrencies Intraday High-Frequency Volatility Spillover Effects Using Univariate and Multivariate GARCH Models" *International Journal of Financial Studies* 10, no. 3: 51.
https://doi.org/10.3390/ijfs10030051