# Price Leadership and Volatility Linkages between Oil and Renewable Energy Firms during the COVID-19 Pandemic

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## Abstract

**:**

## 1. Introduction

## 2. Data and Methodology

#### 2.1. Data

#### 2.2. Methodology: DCC-GARCH

#### 2.3. Methodology: Price Leadership Share

## 3. Empirical Results

#### 3.1. DCC-GARCH Analysis

#### 3.2. Price Leadership Analysis

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

ADF | Augmented Dickey-Fuller |

BRENT | Brent crude oil futures |

DCC | Dynamic Conditional Correlation |

ERIX | European renewable energy index |

GARCH | Generalized Autoregressive Conditional Heteroskedasticity |

ICE | Intercontinental Exchange |

LB | Ljung-Box |

LM | Lagrange Multiplier |

MTD | Mixture Transition Distribution |

NYMEX | New Your Mercantile Exchange |

PLS | Price Leadership Share |

RMSE | Root Mean Square Error |

SXEV | STOXX Europe 600 oil & gas index |

WHO | World Health Organization |

WTI | West Texas Intermediate crude oil futures |

## References

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**Figure 1.**Price series in U.S. dollars of the four contracts from 1 September 2019 to 31 December 2020. Transactions are sampled at 1-min frequency from 8:00 a.m. to 4:50 p.m. London time.

**Figure 2.**Daily volatility series of the four contracts from 1 September 2019 to 31 December 2020, computed as standard deviation of 1-min returns from 8:00 a.m. to 4:50 p.m. London time.

**Figure 5.**Time series of deviations between predicted volatilities through DCC-GARCH(1,1) model and daily volatilities estimated as standard deviations of 1-min returns.

**Table 1.**Summary statistics of the 1-min percentage returns for the four contracts from 1 September 2019 to 31 December 2020, time range from 8:00 a.m. to 4:50 p.m. London time. The four contracts are the West Texas Intermediate crude oil futures contract (WTI), the Brent crude oil futures contract (BRENT), the STOXX Europe 600 oil & gas index (SXEV), and the European renewable energy index (ERIX).

WTI | BRENT | SXEV | ERIX | ||
---|---|---|---|---|---|

Period | |||||

Full datasetObs: 172250 | mean | −0.0001 | −0.0001 | −0.0001 | 0.0002 |

std | 0.5167 | 0.0964 | 0.0752 | 0.0604 | |

min | −102.0825 | −7.5968 | −4.4378 | −3.7572 | |

max | 83.2909 | 9.2275 | 2.4850 | 2.7950 | |

skew | −42.5313 | 2.8789 | −2.0482 | −1.2964 | |

kurt | 18,424.3171 | 779.9667 | 179.6896 | 170.1605 | |

Before COVID-19Obs: 41870 01/09/2019–31/12/2019 | mean | 0.0001 | 0.0002 | 0.0001 | 0.0000 |

std | 0.0545 | 0.0533 | 0.0335 | 0.0385 | |

min | −1.3276 | −1.3291 | −0.3874 | −1.8567 | |

max | 0.9375 | 0.8087 | 0.4583 | 1.5288 | |

skew | −0.7698 | −0.9137 | −0.0603 | −1.5519 | |

kurt | 32.8249 | 30.1682 | 11.4476 | 282.9432 | |

Chinese spreadObs: 24910 01/01/2020–10/03/2020 | mean | −0.0007 | −0.0007 | −0.0016 | 0.0002 |

std | 0.0845 | 0.0804 | 0.0725 | 0.0555 | |

min | −1.0919 | −1.4157 | −4.4378 | −2.3398 | |

max | 1.8138 | 1.6868 | 1.5918 | 1.4196 | |

skew | 0.5385 | −0.0268 | −20.5752 | −3.3521 | |

kurt | 29.3838 | 31.0702 | 1204.6331 | 199.2002 | |

Worldwide spreadObs: 38690 11/03/2020–25/06/2020 | mean | −0.0007 | −0.0007 | 0.0000 | −0.0005 |

std | 1.0833 | 0.1673 | 0.1187 | 0.0876 | |

min | −102.0825 | −7.5968 | −1.5095 | −1.5770 | |

max | 83.2909 | 9.2275 | 2.4850 | 1.5260 | |

skew | −20.5485 | 2.5072 | 0.6524 | −0.0496 | |

kurt | 4244.3328 | 379.5144 | 18.5669 | 21.1941 | |

Summer reopeningObs: 31800 26/06/2020–21/09/2020 | mean | 0.0001 | 0.0000 | −0.0004 | 0.0005 |

std | 0.0622 | 0.0563 | 0.0584 | 0.0481 | |

min | −0.8001 | −0.6795 | −0.5547 | −0.6053 | |

max | 1.0206 | 0.4540 | 0.4982 | 0.5568 | |

skew | 0.0066 | −0.0971 | −0.0057 | −0.0422 | |

kurt | 8.1460 | 4.6936 | 4.5363 | 9.3955 | |

Second spreadObs: 17490 22/09/2020–08/11/2020 | mean | 0.0003 | 0.0002 | 0.0001 | 0.0010 |

std | 0.0726 | 0.0676 | 0.0645 | 0.0611 | |

min | −0.8661 | −0.7144 | −0.8050 | −3.7572 | |

max | 0.6104 | 0.4884 | 0.9364 | 1.1464 | |

skew | −0.1302 | −0.0582 | 0.2196 | −12.7377 | |

kurt | 6.9856 | 4.3737 | 7.9225 | 830.9181 | |

VaccinesObs: 17490 09/11/2020–31/12/2020 | mean | 0.0009 | 0.0009 | 0.0016 | 0.0006 |

std | 0.0637 | 0.0573 | 0.0634 | 0.0555 | |

min | −2.7700 | −1.0395 | −0.5734 | −0.6306 | |

max | 0.7251 | 0.6735 | 0.9992 | 2.7950 | |

skew | −4.6746 | −0.3737 | 0.4145 | 7.1639 | |

kurt | 213.7327 | 15.1881 | 11.2031 | 374.2154 |

WTI | BRENT | SXEV | ERIX | |
---|---|---|---|---|

Before COVID-19 | 0.053 | 0.051 | 0.033 | 0.036 |

Chinese spread | 0.072 | 0.069 | 0.051 | 0.047 |

Worldwide spread | 0.286 | 0.140 | 0.110 | 0.081 |

Summer reopening | 0.061 | 0.055 | 0.058 | 0.047 |

Second spread | 0.071 | 0.066 | 0.063 | 0.056 |

Vaccines | 0.060 | 0.055 | 0.060 | 0.051 |

WTI | BRENT | SXEV | ERIX | |
---|---|---|---|---|

WTI | 1.000000 | 0.495386 | 0.161341 | 0.089098 |

BRENT | 0.495386 | 1.000000 | 0.665709 | 0.515934 |

SXEV | 0.161341 | 0.665709 | 1.000000 | 0.876430 |

ERIX | 0.089098 | 0.515934 | 0.876430 | 1.000000 |

**Table 4.**Summary statistics and diagnostic tests of the daily percentage log returns. ADF: Augmented Dickey-Fuller unit root test; LM: Lagrange multiplier test statistic for ARCH effect; LB: Ljung-Box test of autocorrelation. The sample includes 325 daily observations.

WTI | BRENT | SXEV | ERIX | |
---|---|---|---|---|

Panel A: summary statistics (returns in %) | ||||

mean | −0.0532 | −0.0480 | −0.0539 | 0.1002 |

std | 3.0212 | 2.1115 | 2.1455 | 1.4463 |

min | −28.5979 | −15.9417 | −16.8673 | −9.1300 |

max | 15.2176 | 11.5714 | 10.1787 | 4.6155 |

skew | −2.7681 | −0.9060 | −1.7426 | −0.9769 |

kurt | 30.3941 | 12.6321 | 16.5461 | 5.1810 |

Panel B: returns diagnostics | ||||

ADF | −8.561 *** | −18.506 *** | −6.859 *** | −6.953 *** |

LM lag 1 | 100.513 *** | 52.324 *** | 2.532 | 26.523 *** |

LM lag 2 | 104.585 *** | 60.992 *** | 4.530 | 26.527 *** |

LM lag 3 | 104.263 *** | 62.262 *** | 46.043 *** | 26.509 *** |

Panel C: squared returns diagnostics | ||||

LB lag 1 | 101.744 *** | 52.954 *** | 2.563 | 26.829 *** |

LB lag 2 | 116.732 *** | 52.991 *** | 5.018 * | 28.240 *** |

LB lag 3 | 117.808 *** | 53.007 *** | 50.329 *** | 28.240 *** |

Panel D: absolute returns diagnostics | ||||

LB lag 1 | 121.734 *** | 51.150 *** | 37.802 *** | 27.021 *** |

LB lag 2 | 171.196 *** | 54.647 *** | 63.006 *** | 37.223 *** |

LB lag 3 | 184.032 *** | 55.471 *** | 108.108 *** | 37.992 *** |

WTI | BRENT | SXEV | ERIX | |
---|---|---|---|---|

WTI | 1.000 | 0.495 | 0.161 | 0.089 |

BRENT | 0.495 | 1.000 | 0.666 | 0.516 |

SXEV | 0.161 | 0.666 | 1.000 | 0.876 |

ERIX | 0.089 | 0.516 | 0.876 | 1.000 |

WTI L1 | 0.091 | 0.331 | 0.136 | 0.078 |

BRENT L1 | 0.141 | 0.635 | 0.589 | 0.499 |

SXEV L1 | 0.135 | 0.592 | 0.821 | 0.738 |

ERIX L1 | 0.117 | 0.481 | 0.749 | 0.732 |

**Table 6.**DCC-GARCH(1,1) parameters. Panel A reports the univariate GARCH parameters for each series. Panel B reports the DCC-GARCH parameters for all four series. P-values in parentheses. LM: Lagrange multiplier test statistic for ARCH effect; LB: Ljung-Box test of autocorrelation.

Panel A: Univariate GARCH parameters | ||||

WTI | BRENT | SXEV | ERIX | |

$\mu $ | 0.095 | 0.074 | −0.032 | 0.177 *** |

(0.372) | (0.430) | (0.670) | (0.006) | |

$\omega $ | 1.161 *** | 0.114 | 0.358 | 0.310 |

(0.006) | (0.221) | (0.379) | (0.347) | |

$\kappa $ | 0.645 ** | 0.126 *** | 0.483 | 0.252 ** |

(0.036) | (0.005) | (0.100) | (0.033) | |

$\lambda $ | 0.283 ** | 0.851 *** | 0.516 * | 0.601 ** |

(0.047) | (0.000) | (0.068) | (0.023) | |

Panel B: DCC-GARCH parameters | ||||

$\alpha $ | 0.050 *** | |||

(0.000) | ||||

$\beta $ | 0.887 *** | |||

(0.000) | ||||

Panel C: DCC-GARCH residuals diagnostic | ||||

WTI | BRENT | SXEV | ERIX | |

LB | 1.787 | 0.147 | 3.194 * | 1.169 |

(0.181) | (0.701) | (0.074) | (0.280) | |

LB ($resi{d}^{2}$) | 0.996 | 0.698 | 0.038 | 0.917 |

(0.318) | (0.404) | (0.846) | (0.338) |

WTI | BRENT | SXEV | ERIX | |
---|---|---|---|---|

Chinese spread | 0.966618 | 0.914734 | 2.235645 | 0.552730 |

Worldwide spread | 23.905959 | 2.445554 | 1.473740 | 0.804769 |

Summer reopening | 0.868118 | 0.731535 | 0.354176 | 0.406645 |

Second spread | 0.353359 | 0.322304 | 0.306062 | 0.582914 |

Vaccines | 0.579485 | 0.447151 | 0.859321 | 0.622851 |

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## Share and Cite

**MDPI and ACS Style**

De Blasis, R.; Petroni, F.
Price Leadership and Volatility Linkages between Oil and Renewable Energy Firms during the COVID-19 Pandemic. *Energies* **2021**, *14*, 2608.
https://doi.org/10.3390/en14092608

**AMA Style**

De Blasis R, Petroni F.
Price Leadership and Volatility Linkages between Oil and Renewable Energy Firms during the COVID-19 Pandemic. *Energies*. 2021; 14(9):2608.
https://doi.org/10.3390/en14092608

**Chicago/Turabian Style**

De Blasis, Riccardo, and Filippo Petroni.
2021. "Price Leadership and Volatility Linkages between Oil and Renewable Energy Firms during the COVID-19 Pandemic" *Energies* 14, no. 9: 2608.
https://doi.org/10.3390/en14092608