# Multivariate Analysis of Energy Commodities during the COVID-19 Pandemic: Evidence from a Mixed-Frequency Approach

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### Model Selection

## 3. Empirical Application

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

US | United States |

WTI | West Texas Intermediate |

DCC | Dynamic conditional correlation (Engle 2002) |

cDCC | Corrected DCC (Aielli 2013) |

DECO | Dynamic equicorrelation (Engle and Kelly 2012) |

MIDAS | MIxing-Data Sampling |

GM | GARCH-MIDAS (Engle et al. 2013) |

DAGM | Double Asymmetric GARCH-MIDAS model (Amendola et al. 2019) |

MCS | Model Confidence Set (Hansen et al. 2011) |

SSM | Set of Superior Models |

## Note

1 | The literature has proposed alternative distributions to capture fat tails and skewness of returns, such as the multivariate Student’s t distribution. However, according to Pesaran and Pesaran (2010), the use of the $MVN$ allows us to maintain the two-step process used to estimate the DCC model. Moreover, in order to take into consideration possible deviations from the normality assumption, all the reported standard errors are based on Quasi-Maximum Likelihood (Bollerslev and Wooldridge 1992) methods. |

## References

- Abid, Ilyes, Abderrazak Dhaoui, Stéphane Goutte, and Khaled Guesmi. 2020. Hedging and diversification across commodity assets. Applied Economics 52: 2472–92. [Google Scholar] [CrossRef]
- Aielli, Gian Piero. 2013. Dynamic conditional correlation: On properties and estimation. Journal of Business & Economic Statistics 31: 282–99. [Google Scholar]
- Akhtaruzzaman, Md, Sabri Boubaker, and Ahmet Sensoy. 2021. Financial contagion during COVID-19 crisis. Finance Research Letters 38: 101604. [Google Scholar] [CrossRef]
- Aloui, Chaker, and Samir Mabrouk. 2010. Value-at-risk estimations of energy commodities via long-memory, asymmetry and fat-tailed GARCH models. Energy Policy 38: 2326–39. [Google Scholar] [CrossRef]
- Amendola, Alessandra, Manuela Braione, Vincenzo Candila, and Giuseppe Storti. 2020. A model confidence set approach to the combination of multivariate volatility forecasts. International Journal of Forecasting 36: 873–91. [Google Scholar] [CrossRef]
- Amendola, Alessandra, and Vincenzo Candila. 2017. Comparing multivariate volatility forecasts by direct and indirect approaches. Journal of Risk 19: 33–57. [Google Scholar] [CrossRef]
- Amendola, Alessandra, Vincenzo Candila, and Giampiero M. Gallo. 2019. On the asymmetric impact of macro–variables on volatility. Economic Modelling 76: 135–52. [Google Scholar] [CrossRef]
- Arenas, Alex, Wesley Cota, Jesús Gómez-Gardeñes, Sergio Gómez, Clara Granell, Joan T. Matamalas, David Soriano-Paños, and Benjamin Steinegger. 2020. Modeling the spatiotemporal epidemic spreading of COVID-19 and the impact of mobility and social distancing interventions. Physical Review X 10: 041055. [Google Scholar] [CrossRef]
- Arouri, Mohamed El Hedi, Jamel Jouini, and Duc Khuong Nguyen. 2012. On the impacts of oil price fluctuations on European equity markets: Volatility spillover and hedging effectiveness. Energy Economics 34: 611–17. [Google Scholar] [CrossRef]
- Bai, Jushan, and Pierre Perron. 1998. Estimating and testing linear models with multiple structural changes. Econometrica 66: 47–78. [Google Scholar] [CrossRef]
- Basher, Syed Abul, and Perry Sadorsky. 2016. Hedging emerging market stock prices with oil, gold, VIX, and bonds: A comparison between DCC, ADCC and GO-GARCH. Energy Economics 54: 235–47. [Google Scholar] [CrossRef] [Green Version]
- Bauwens, Luc, Sébastien Laurent, and Jeroen V. K. Rombouts. 2006. Multivariate GARCH models: A survey. Journal of Applied Econometrics 21: 79–109. [Google Scholar] [CrossRef] [Green Version]
- Behmiri, Niaz Bashiri, Matteo Manera, and Marcella Nicolini. 2019. Understanding dynamic conditional correlations between oil, natural gas and non-energy commodity futures markets. The Energy Journal 40: 55–76. [Google Scholar] [CrossRef]
- Bollerslev, Tim. 1986. Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics 31: 307–27. [Google Scholar] [CrossRef] [Green Version]
- Bollerslev, Tim, and Jeffrey M. Wooldridge. 1992. Quasi-maximum likelihood estimation and inference in dynamic models with time-varying covariances. Econometric Reviews 11: 143–72. [Google Scholar] [CrossRef]
- Bouazizi, Tarek, Mongi Lassoued, and Zouhaier Hadhek. 2021. Oil Price Volatility Models during Coronavirus Crisis: Testing with Appropriate Models Using Further Univariate GARCH and Monte Carlo Simulation Models. International Journal of Energy Economics and Policy 11: 281–92. [Google Scholar] [CrossRef]
- Candila, Vincenzo. 2021a. Dccmidas: A Package for Estimating DCC-Based Models in R. R Package Version 0.1.0. Available online: https://www.researchgate.net/publication/350064227_dccmidas_A_package_for_estimating_DCC-based_models_in_R (accessed on 1 February 2021).
- Candila, Vincenzo. 2021b. Multivariate analysis of cryptocurrencies. Econometrics 9: 28. [Google Scholar] [CrossRef]
- Chang, Chia-Lin, Michael McAleer, and Roengchai Tansuchat. 2011. Crude oil hedging strategies using dynamic multivariate GARCH. Energy Economics 33: 912–23. [Google Scholar] [CrossRef] [Green Version]
- Chevallier, Julien. 2020. COVID-19 pandemic and financial contagion. Journal of Risk and Financial Management 13: 309. [Google Scholar] [CrossRef]
- Chevallier, Julien, and Florian Ielpo. 2013. Volatility spillovers in commodity markets. Applied Economics Letters 20: 1211–27. [Google Scholar] [CrossRef]
- Chkili, Walid, Chaker Aloui, and Duc Khuong Nguyen. 2014. Instabilities in the relationships and hedging strategies between crude oil and US stock markets: Do long memory and asymmetry matter? Journal of International Financial Markets, Institutions and Money 33: 354–66. [Google Scholar] [CrossRef]
- Colacito, Riccardo, Robert F. Engle, and Eric Ghysels. 2011. A component model for dynamic correlations. Journal of Econometrics 164: 45–59. [Google Scholar] [CrossRef] [Green Version]
- Corbet, Shaen, John W. Goodell, and Samet Günay. 2020. Co-movements and spillovers of oil and renewable firms under extreme conditions: New evidence from negative WTI prices during COVID-19. Energy Economics 92: 104978. [Google Scholar] [CrossRef] [PubMed]
- Corbet, Shaen, Charles Larkin, and Brian Lucey. 2020. The contagion effects of the COVID-19 pandemic: Evidence from gold and cryptocurrencies. Finance Research Letters 35: 101554. [Google Scholar] [CrossRef]
- Cuñado, Juncal, and Fernando Pérez de Gracia. 2003. Do oil price shocks matter? Evidence from some European countries. Energy Economics 25: 137–54. [Google Scholar] [CrossRef] [Green Version]
- 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: 2608. [Google Scholar] [CrossRef]
- Denton, Michael, Adrian Palmer, Ralph Masiello, and Petter Skantze. 2003. Managing market risk in energy. IEEE Transactions on Power Systems 18: 494–502. [Google Scholar] [CrossRef]
- Engle, Robert F. 2002. Dynamic conditional correlation: A simple class of multivariate generalized autoregressive conditional heteroskedasticity models. Journal of Business & Economic Statistics 20: 339–50. [Google Scholar]
- Engle, Robert F., Eric Ghysels, and Bumjean Sohn. 2013. Stock market volatility and macroeconomic fundamentals. Review of Economics and Statistics 95: 776–97. [Google Scholar] [CrossRef]
- Engle, Robert F., and Bryan Kelly. 2012. Dynamic equicorrelation. Journal of Business & Economic Statistics 30: 212–28. [Google Scholar]
- Falkowski, Michał. 2011. Financialization of commodities. Contemporary Economics 5: 4–17. [Google Scholar] [CrossRef] [Green Version]
- Fan, Ying, Yue-Jun Zhang, Hsien-Tang Tsai, and Yi-Ming Wei. 2008. Estimating ‘Value at Risk’of crude oil price and its spillover effect using the GED-GARCH approach. Energy Economics 30: 3156–71. [Google Scholar] [CrossRef]
- Foglia, Matteo, and Eliana Angelini. 2020. Volatility connectedness between clean energy firms and crude oil in the COVID-19 era. Sustainability 12: 1–22. [Google Scholar] [CrossRef]
- Ghorbel, Achraf, and Ahmed Jeribi. 2021. Volatility spillovers and contagion between energy sector and financial assets during COVID-19 crisis period. Eurasian Economic Review 1: 1–9. [Google Scholar]
- Ghysels, Eric, Arthur Sinko, and Rossen Valkanov. 2007. MIDAS regressions: Further results and new directions. Econometric Reviews 26: 53–90. [Google Scholar] [CrossRef]
- Gil-Alana, Luis A., and Manuel Monge. 2020. Crude Oil Prices and COVID-19: Persistence of the Shock. Energy Research Letters 1: 1–4. [Google Scholar] [CrossRef]
- Glosten, Lawrence R., Ravi Jagannathan, and David E. Runkle. 1993. On the relation between the expected value and the volatility of the nominal excess return on stocks. The Journal of Finance 48: 1779–801. [Google Scholar] [CrossRef]
- Hamilton, James D. 1983. Oil and the Macroeconomy since World War II. Journal of Political Economy 91: 228–48. [Google Scholar] [CrossRef]
- Hansen, Peter R., Asger Lunde, and James M. Nason. 2003. Choosing the best volatility models: The model confidence set approach. Oxford Bulletin of Economics and Statistics 65: 839–61. [Google Scholar] [CrossRef]
- Hansen, Peter R., Asger Lunde, and James M. Nason. 2011. The Model Confidence Set. Econometrica 79: 453–97. [Google Scholar] [CrossRef] [Green Version]
- Hauser, Philipp, Carl-Philipp Anke, J. Gutiérrez López, Dominik Möst, Hendrik Scharf, David Schönheit, and S. Schreiber. 2020. The impact of the COVID-19 crisis on energy prices in comparison to the 2008 financial crisis. In IAEE Energy Forum/Covid-19 Issue. Cleveland: International Association for Energy Economics. [Google Scholar]
- Hung, Jui-Cheng, Ming-Chih Lee, and Hung-Chun Liu. 2008. Estimation of Value-at-Risk for energy commodities via fat-tailed GARCH models. Energy Economics 30: 1173–91. [Google Scholar] [CrossRef]
- IEA. 2020. Oil Market Report—April 2020. Paris: IEA. [Google Scholar]
- Iyke, Bernard N. 2020. COVID-19: The reaction of US oil and gas producers to the pandemic. Energy Research Letters 1: 1–7. [Google Scholar] [CrossRef]
- Kang, Wensheng, Ronald A. Ratti, and Kyung Hwan Yoon. 2015. The impact of oil price shocks on the stock market return and volatility relationship. Journal of International Financial Markets, Institutions and Money 34: 41–54. [Google Scholar] [CrossRef] [Green Version]
- Karali, Berna, and Octavio A. Ramirez. 2014. Macro determinants of volatility and volatility spillover in energy markets. Energy Economics 46: 413–21. [Google Scholar] [CrossRef]
- Krehbiel, Tim, and Lee C. Adkins. 2005. Price risk in the Nymex energy complex: An extreme value approach. Journal of Futures Markets: Futures, Options, and Other Derivative Products 25: 309–37. [Google Scholar] [CrossRef]
- Ku, Yuan-Hung Hsu, Ho-Chyuan Chen, and Kuang-hua Chen. 2007. On the application of the dynamic conditional correlation model in estimating optimal time-varying hedge ratios. Applied Economics Letters 14: 503–9. [Google Scholar] [CrossRef]
- Laporta, Alessandro G., Luca Merlo, and Lea Petrella. 2018. Selection of Value at Risk models for energy commodities. Energy Economics 74: 628–43. [Google Scholar] [CrossRef]
- Laurent, Sébastien, Jeroen V.K. Rombouts, and Francesco Violante. 2013. On loss functions and ranking forecasting performances of multivariate volatility models. Journal of Econometrics 173: 1–10. [Google Scholar] [CrossRef] [Green Version]
- Lin, Boqiang, and Tong Su. 2021. Does COVID-19 open a Pandora’s box of changing the connectedness in energy commodities? Research in International Business and Finance 56: 101360. [Google Scholar] [CrossRef]
- Lv, Xiaodong, and Xian Shan. 2013. Modeling natural gas market volatility using GARCH with different distributions. Physica A: Statistical Mechanics and its Applications 392: 5685–99. [Google Scholar] [CrossRef]
- Masters, Michael W., and Adam K. White. 2008. The Accidental Hunt Brothers–Act 2: Index Speculators Have Been a Major Cause of the Recent Drop in Oil Prices, Masters Capital Management and White Knight Research and Trading. Index Speculators Have Been a Major Cause of the Recent Drop in Oil Prices. Special Update September 10: 4. [Google Scholar]
- Mishra, Amritkant. 2019. Crude oil, stock market, and foreign exchange return volatility and spillover: A GARCH DCC analysis of Indian and Japanese financial market. International Journal of Business Innovation and Research 20: 25–46. [Google Scholar] [CrossRef]
- Naeem, Muhammad A., Saqib Farid, Safwan M. Nor, and Syed J.H. Shahzad. 2021. Spillover and drivers of uncertainty among oil and commodity markets. Mathematics 9: 441. [Google Scholar] [CrossRef]
- Narayan, Paresh K. 2020. Oil price news and COVID-19—Is there any connection? Energy Research Letters 1: 13176. [Google Scholar] [CrossRef]
- Nouvellet, Pierre, Sangeeta Bhatia, Anne Cori, Kylie E. C. Ainslie, Marc Baguelin, Samir Bhatt, Adhiratha Boonyasiri, Nicholas F. Brazeau, Lorenzo Cattarino, Laura V. Cooper, and et al. 2021. Reduction in mobility and COVID-19 transmission. Nature Communications 12: 1–9. [Google Scholar] [CrossRef] [PubMed]
- Nyga-ukaszewska, Honorata, and Kentaka Aruga. 2020. Energy prices and COVID-immunity: The case of crude oil and natural gas prices in the US and Japan. Energies 13: 6300. [Google Scholar] [CrossRef]
- Pesaran, Bahram, and M. Hashem Pesaran. 2010. Conditional volatility and correlations of weekly returns and the VaR analysis of 2008 stock market crash. Economic Modelling 27: 1398–416. [Google Scholar] [CrossRef] [Green Version]
- Sadorsky, Perry. 1999. Oil price shocks and stock market activity. Energy Economics 21: 449–69. [Google Scholar] [CrossRef]
- Sadorsky, Perry. 2003. The macroeconomic determinants of technology stock price volatility. Review of Financial Economics 12: 191–205. [Google Scholar] [CrossRef]
- Sadorsky, Perry. 2012. Correlations and volatility spillovers between oil prices and the stock prices of clean energy and technology companies. Energy Economics 34: 248–55. [Google Scholar] [CrossRef]
- Sadowski, Adam, Zbigniew Galar, Robert Walasek, Grzegorz Zimon, and Per Engelseth. 2021. Big data insight on global mobility during the covid-19 pandemic lockdown. Journal of Big Data 8: 1–33. [Google Scholar] [CrossRef]
- Silvennoinen, Annastiina, and Timo Teräsvirta. 2009. Multivariate GARCH Models. Handbook of Financial Time Series; Berlin and Heidelberg: Springer, pp. 201–29. [Google Scholar]
- Silvennoinen, Annastiina, and Susan Thorp. 2013. Financialization, crisis and commodity correlation dynamics. Journal of International Financial Markets, Institutions and Money 24: 42–65. [Google Scholar] [CrossRef] [Green Version]
- US Government Accountability Office (GAO). 2003. Propane: Causes of Price Volatility, Potential Consumer Options, and Opportunities to Improve Consumer Information and Federal Oversight. Washington: US Government Accountability Office. [Google Scholar]
- Wang, Kai-Hua, and Chi-Wei Su. 2021. Asymmetric link between COVID-19 and fossil energy prices. Asian Economics Letters 1: 18742. [Google Scholar]
- Wang, Yudong, and Chongfeng Wu. 2012. Forecasting energy market volatility using GARCH models: Can multivariate models beat univariate models? Energy Economics 34: 2167–81. [Google Scholar] [CrossRef]
- Yousfi, Mohamed, Abderrazak Dhaoui, and Houssam Bouzgarrou. 2021. Risk spillover during the COVID-19 global pandemic and portfolio management. Journal of Risk and Financial Management 14: 222. [Google Scholar] [CrossRef]
- Zaremba, Adam, Renatas Kizys, David Y. Aharon, and Ender Demir. 2020. Infected Markets: Novel Coronavirus, Government Interventions, and Stock Return Volatility around the Globe. Finance Research Letters 35: 101597. [Google Scholar] [CrossRef]
- Zhang, Dayong, Min Hu, and Qiang Ji. 2020. Financial markets under the global pandemic of COVID-19. Finance Research Letters 36: 101528. [Google Scholar] [CrossRef]

**Figure 1.**Log−returns of commodities.

**Notes:**Plots of log-returns of commodities Sample period: April 2020–June 2021. Number of observations: 276.

**Figure 2.**Weekly deaths related to COVID-19 infections in the US.

**Notes:**Plot of the weekly deaths related to COVID-19 infections in the US. Sample period: March 2020–June 2021. The labels of the x-axis indicate the week and the year of the observations. The time series starts the first week of March 2020 (9 March 2020).

**Figure 3.**Volatility structural breaks.

**Notes:**The figure shows the GARCH(1,1) estimated volatility (black lines), the structural breaks (green lines), and the related 95% confidence intervals (red lines).

**Figure 4.**The plots show the estimated volatilities on the main diagonal and correlation estimated with the model GARCH-cDCC. Sample period: June 2020–June 2021.

**Figure 5.**The plots show the estimated volatilities on the main diagonal and correlation estimated with the model DAGM-cDCC. Sample period: June 2020–June 2021.

**Figure 6.**The plots show the estimated volatilities on the main diagonal and the correlation estimated with the model DAGM-DCC-MIDAS. Red lines represent the estimated long-run correlation. Sample period: June 2020 to June 2021.

Model | Functional Form |
---|---|

cDCC (Aielli 2013) | ${H}_{i,t}={D}_{i,t}{R}_{i,t}{D}_{i,t}$ |

${D}_{i,t}=diag({\sigma}_{i,t,1},\cdots ,{\sigma}_{i,t,j},\cdots ,{\sigma}_{i,t,n})$ | |

${R}_{i,t}={\left(\mathit{diag}\left({Q}_{i,t}\right)\right)}^{-1/2}{Q}_{i,t}{\left(\mathit{diag}\left({Q}_{i,t}\right)\right)}^{-1/2}$ | |

$\begin{array}{cc}{Q}_{i,t}=& (1-a-b)\mathsf{\Psi}+a\left({\mathit{\xi}}_{i-1,t}{\mathit{\xi}}_{i-1,t}^{{}^{\prime}}\right)+\hfill \\ & b{Q}_{i-1,t}\hfill \end{array}$ | |

${\mathit{\xi}}_{i,t}={D}_{i,t}^{-1}{\mathit{r}}_{i,t}$ | |

$\mathsf{\Psi}=E\left({\mathit{\xi}}_{i,t}{\mathit{\xi}}_{i,t}^{{}^{\prime}}\right)$ | |

DCC-MIDAS (Colacito et al. 2011) | ${H}_{i,t}={D}_{i,t}{R}_{i,t}{D}_{i,t}$ |

${D}_{i,t}=diag({\sigma}_{i,t,1},\cdots ,{\sigma}_{i,t,j},\cdots ,{\sigma}_{i,t,n})$ | |

${R}_{i,t}={\left(\mathit{diag}\left({Q}_{i,t}\right)\right)}^{-1/2}{Q}_{i,t}{\left(\mathit{diag}\left({Q}_{i,t}\right)\right)}^{-1/2}$ | |

$\begin{array}{cc}{Q}_{i,t}=& (1-a-b){\overline{R}}_{i,t}\left(\omega \right)+a\left({\mathit{\xi}}_{i-1,t}{\mathit{\xi}}_{i-1,t}^{{}^{\prime}}\right)+\hfill \\ & b{Q}_{i-1,t}\hfill \end{array}$ | |

${\mathit{\xi}}_{i,t}={D}_{i,t}^{-1}{\mathit{r}}_{i,t}$ | |

DECO (Engle and Kelly 2012) | ${H}_{i,t}={D}_{i,t}{R}_{i,t}^{DECO}{D}_{i,t}$ |

${D}_{i,t}=diag({\sigma}_{i,t,1},\cdots ,{\sigma}_{i,t,j},\cdots ,{\sigma}_{i,t,n})$ | |

${R}_{i,t}^{DECO}=(1-{\rho}_{i,t}){I}_{n}+{\rho}_{i,t}{J}_{n}$ | |

${\rho}_{i,t}=\frac{1}{n(n-1)}\left({\iota}^{{}^{\prime}}{R}_{i,t}\iota -n\right)$ |

**Notes**: The table shows the different specifications of the correlation models used in this paper. ${\overline{R}}_{i,t}\left(\omega \right)$ is the long-run correlation of Colacito et al. (2011), ${J}_{n}$ and $\iota $ are, respectively, a matrix and a ($n\times 1$)-vector of ones.

Min. | Max. | Mean | SD | Skew. | Kurt. | |
---|---|---|---|---|---|---|

WTI | −0.082 | 0.246 | 0.006 | 0.033 | 2.45 | 15.718 |

Europe Brent | −0.087 | 0.222 | 0.006 | 0.029 | 1.582 | 11.723 |

Heating Oil | −0.139 | 0.112 | 0.004 | 0.029 | −0.004 | 3.686 |

Propane | −0.082 | 0.172 | 0.004 | 0.03 | 0.785 | 4.604 |

Gasoline | −0.087 | 0.114 | 0.005 | 0.028 | 0.131 | 2.039 |

Kerosene | −0.13 | 0.153 | 0.005 | 0.033 | 0.553 | 3.889 |

**Notes:**The table presents the main statistics (the minimum (Min.) and maximum (Max.), the mean, standard deviation (SD), skewness (Skew.), and excess kurtosis (Kurt.)) for the close-to-close log-returns. Sample period: March 2020–June 2021. Number of observations: 271.

WTI | Brent Oil | Heating Oil | Propane | Gasoline | Kerosene |
---|---|---|---|---|---|

Mar. 2020 | Mar. 2020 | Mar. 2020 | Mar. 2020 | Mar. 2020 | Mar. 2020 |

June 2020 | June 2020 | June 2020 | June 2020 | June 2020 | June 2020 |

Dec. 2020 | Oct. 2020 |

Estimate | Std. Error | t Value | Pr (>|t|) | Sig. | |
---|---|---|---|---|---|

WTI | |||||

$\omega $ | 0.000 | 0.000 | 2.057 | 0.040 | ** |

$\alpha $ | 0.138 | 0.044 | 3.169 | 0.002 | *** |

$\beta $ | 0.786 | 0.053 | 14.814 | 0.000 | *** |

Europe Brent | |||||

$\omega $ | 0.000 | 0.000 | 2.316 | 0.021 | ** |

$\alpha $ | 0.138 | 0.053 | 2.591 | 0.010 | *** |

$\beta $ | 0.807 | 0.041 | 19.646 | 0.000 | *** |

Heating Oil | |||||

$\omega $ | 0.000 | 0.000 | 2.744 | 0.006 | *** |

$\alpha $ | 0.136 | 0.043 | 3.133 | 0.002 | *** |

$\beta $ | 0.793 | 0.046 | 17.408 | 0.000 | *** |

Propane | |||||

$\omega $ | 0.000 | 0.000 | 0.736 | 0.462 | |

$\alpha $ | 0.069 | 0.050 | 1.378 | 0.168 | |

$\beta $ | 0.867 | 0.122 | 7.120 | 0.000 | *** |

Gasoline | |||||

$\omega $ | 0.000 | 0.000 | 1.558 | 0.119 | |

$\alpha $ | 0.100 | 0.055 | 1.819 | 0.069 | * |

$\beta $ | 0.856 | 0.066 | 13.005 | 0.000 | *** |

Kerosene | |||||

$\omega $ | 0.000 | 0.000 | 2.478 | 0.013 | ** |

$\alpha $ | 0.108 | 0.029 | 3.786 | 0.000 | *** |

$\beta $ | 0.826 | 0.041 | 20.200 | 0.000 | *** |

**Notes:**The table reports the estimates of the GARCH model. The column “Std. Error” shows the Quasi-Maximum Likelihood-based standard errors. Sample Period: March 2020–June 2021, 271 daily observations. *, **, and *** indicate the significance at levels 10%, 5%, and 1%, respectively.

Estimate | Std. Error | t Value | Pr (>|t|) | Sig. | |
---|---|---|---|---|---|

WTI | |||||

$\omega $ | 0.000 | 0.000 | 2.336 | 0.019 | ** |

$\alpha $ | 0.104 | 0.044 | 2.380 | 0.017 | ** |

$\beta $ | 0.797 | 0.040 | 19.705 | 0.000 | *** |

$\gamma $ | 0.101 | 0.077 | 1.303 | 0.193 | |

Europe Brent | |||||

$\omega $ | 0.000 | 0.000 | 2.308 | 0.021 | ** |

$\alpha $ | 0.133 | 0.068 | 1.956 | 0.050 | * |

$\beta $ | 0.807 | 0.041 | 19.706 | 0.000 | *** |

$\gamma $ | 0.018 | 0.075 | 0.238 | 0.812 | |

Heating Oil | |||||

$\omega $ | 0.000 | 0.000 | 2.543 | 0.011 | ** |

$\alpha $ | 0.125 | 0.056 | 2.244 | 0.025 | ** |

$\beta $ | 0.781 | 0.052 | 15.083 | 0.000 | *** |

$\gamma $ | 0.057 | 0.091 | 0.624 | 0.532 | |

Propane | |||||

$\omega $ | 0.000 | 0.000 | 0.919 | 0.358 | |

$\alpha $ | 0.046 | 0.042 | 1.103 | 0.270 | |

$\beta $ | 0.876 | 0.059 | 14.788 | 0.000 | *** |

$\gamma $ | 0.099 | 0.081 | 1.228 | 0.219 | |

Gasoline | |||||

$\omega $ | 0.000 | 0.000 | 1.217 | 0.224 | |

$\alpha $ | 0.100 | 0.060 | 1.675 | 0.094 | * |

$\beta $ | 0.884 | 0.076 | 11.648 | 0.000 | *** |

$\gamma $ | −0.055 | 0.047 | −1.169 | 0.242 | |

Kerosene | |||||

$\omega $ | 0.000 | 0.000 | 1.919 | 0.055 | * |

$\alpha $ | 0.089 | 0.036 | 2.467 | 0.014 | ** |

$\beta $ | 0.835 | 0.042 | 19.696 | 0.000 | *** |

$\gamma $ | 0.058 | 0.068 | 0.860 | 0.390 |

**Notes:**The table reports the estimates of the GJR model. The column “Std. Error” shows the Quasi-Maximum Likelihood-based standard errors. Sample Period: March 2020–June 2021, 271 daily observations. *, **, and *** indicate the significance at levels 10%, 5%, and 1%, respectively.

Estimate | Std. Error | t Value | Pr (>|t|) | Sig. | |
---|---|---|---|---|---|

WTI | |||||

$\alpha $ | 0.000 | 1.663 | 0.000 | 1.000 | |

$\gamma $ | 0.211 | 0.137 | 1.546 | 0.122 | |

$\beta $ | 0.848 | 2.026 | 0.419 | 0.675 | |

m | −8.383 | 1.518 | −5.524 | 0.000 | *** |

${\theta}^{+}$ | 4.644 | 3.801 | 1.222 | 0.222 | |

${\omega}_{2}^{+}$ | 1.051 | 1.223 | 0.859 | 0.390 | |

${\theta}^{-}$ | −14.014 | 11.070 | −1.266 | 0.206 | |

${\omega}_{2}^{-}$ | 2.698 | 7.587 | 0.356 | 0.722 | |

Europe Brent | |||||

$\alpha $ | 0.000 | 0.190 | 0.001 | 1.000 | |

$\gamma $ | 0.246 | 0.218 | 1.130 | 0.258 | |

$\beta $ | 0.875 | 0.187 | 4.677 | 0.000 | *** |

m | −5.164 | 2.723 | −1.896 | 0.058 | * |

${\theta}^{+}$ | −1.107 | 21.944 | −0.050 | 0.960 | |

${\omega}_{2}^{+}$ | 5.226 | 9.251 | 0.565 | 0.572 | |

${\theta}^{-}$ | −8.340 | 16.254 | −0.513 | 0.608 | |

${\omega}_{2}^{-}$ | 5.078 | 2.592 | 1.959 | 0.050 | * |

Heating Oil | |||||

$\alpha $ | 0.000 | 0.043 | 0.002 | 0.998 | |

$\gamma $ | 0.087 | 0.030 | 2.874 | 0.004 | *** |

$\beta $ | 0.951 | 0.050 | 18.912 | 0.000 | *** |

m | −7.865 | 0.669 | −11.754 | 0.000 | *** |

${\theta}^{+}$ | 2.761 | 1.195 | 2.310 | 0.021 | ** |

${\omega}_{2}^{+}$ | 1.001 | 0.597 | 1.678 | 0.093 | * |

${\theta}^{-}$ | −11.238 | 3.981 | −2.823 | 0.005 | *** |

${\omega}_{2}^{-}$ | 3.580 | 1.585 | 2.258 | 0.024 | ** |

**Notes:**The table reports the estimates of the DAGM model for WTI, Europe Brent, and Heating Oil. The column “Std. Error” shows the Quasi-Maximum Likelihood-based standard errors. Sample Period: March 2020–June 2021, 271 daily observations. *, **, and *** indicate the significance at levels 10%, 5%, and 1%, respectively.

Estimate | Std. Error | t Value | Pr (>|t|) | Sig. | |
---|---|---|---|---|---|

WTI | |||||

$\alpha $ | 0.000 | 0.059 | 0.002 | 0.999 | |

$\gamma $ | 0.320 | 0.103 | 3.100 | 0.002 | *** |

$\beta $ | 0.838 | 0.084 | 9.947 | 0.000 | *** |

m | −4.009 | 0.788 | −5.088 | 0.000 | *** |

$\theta $ | −3.332 | 1.459 | −2.283 | 0.022 | ** |

${\omega}_{2}$ | 5.715 | 1.984 | 2.881 | 0.004 | *** |

Europe Brent | |||||

$\alpha $ | 0.000 | 0.033 | 0.003 | 0.998 | |

$\gamma $ | 0.220 | 0.089 | 2.475 | 0.013 | ** |

$\beta $ | 0.888 | 0.064 | 13.842 | 0.000 | *** |

m | −4.855 | 0.916 | −5.301 | 0.000 | *** |

$\theta $ | −4.902 | 1.454 | −3.372 | 0.001 | *** |

${\omega}_{2}$ | 5.599 | 1.415 | 3.958 | 0.000 | *** |

Heating Oil | |||||

$\alpha $ | 0.079 | 0.226 | 0.350 | 0.726 | |

$\gamma $ | 0.471 | 0.096 | 4.900 | 0.000 | *** |

$\beta $ | 0.685 | 0.260 | 2.636 | 0.008 | *** |

m | −2.799 | 0.533 | −5.255 | 0.000 | *** |

$\theta $ | −3.200 | 4.227 | −0.757 | 0.449 | |

${\omega}_{2}$ | 2.092 | 1.562 | 1.339 | 0.180 |

**Notes:**The table reports the estimates of the GM model for WTI, Europe Brent, and Heating Oil. The column “Std. Error” shows the Quasi-Maximum Likelihood-based standard errors. Sample Period: March 2020–June 2021, 271 daily observations. **, and *** indicate the significance at levels 10%, 5%, and 1%, respectively.

Estimate | Std. Error | t Value | Pr (>|t|) | Sig. | |
---|---|---|---|---|---|

Propane | |||||

$\alpha $ | 0.050 | 0.052 | 0.970 | 0.332 | |

$\gamma $ | 0.150 | 0.078 | 1.920 | 0.055 | * |

$\beta $ | 0.861 | 0.067 | 12.801 | 0.000 | *** |

m | −5.966 | 1.141 | −5.229 | 0.000 | *** |

$\theta $ | −0.851 | 2.370 | −0.359 | 0.720 | |

${\omega}_{2}$ | 3.139 | 1.205 | 2.606 | 0.009 | *** |

Gasoline | |||||

$\alpha $ | 0.000 | 0.028 | 0.004 | 0.997 | |

$\gamma $ | 0.062 | 0.025 | 2.507 | 0.012 | ** |

$\beta $ | 0.968 | 0.031 | 30.750 | 0.000 | *** |

m | −6.317 | 0.261 | −24.159 | 0.000 | *** |

$\theta $ | −4.478 | 0.876 | −5.115 | 0.000 | *** |

${\omega}_{2}$ | 7.042 | 1.054 | 6.680 | 0.000 | *** |

Kerosene | |||||

$\alpha $ | 0.040 | 0.089 | 0.445 | 0.656 | |

$\gamma $ | 0.178 | 0.050 | 3.528 | 0.000 | *** |

$\beta $ | 0.869 | 0.096 | 9.061 | 0.000 | *** |

m | −4.811 | 0.581 | −8.277 | 0.000 | *** |

$\theta $ | −1.159 | 0.929 | −1.247 | 0.212 | |

${\omega}_{2}$ | 23.798 | 612.792 | 0.039 | 0.969 |

**Notes**: The table reports the estimates of the GM model for Propane, Gasoline, and Kerosene. The column “Std. Error” shows the Quasi-Maximum Likelihood-based standard errors. Sample Period: March 2020–June 2021, 271 aily observations. *, **, and *** indicate the significance at levels 10%, 5%, and 1%, respectively.

Estimate | Std. Error | t Value | Pr (>|t|) | Sig. | |
---|---|---|---|---|---|

Propane | |||||

$\alpha $ | 0.183 | 0.179 | 1.022 | 0.307 | |

$\gamma $ | 0.015 | 0.472 | 0.032 | 0.974 | |

$\beta $ | 0.422 | 0.663 | 0.637 | 0.524 | |

m | −7.692 | 0.399 | −19.277 | 0.000 | *** |

${\theta}^{+}$ | 2.024 | 5.973 | 0.339 | 0.735 | |

${\omega}_{2}^{+}$ | 1.001 | 7.015 | 0.143 | 0.887 | |

${\theta}^{-}$ | −7.448 | 2.914 | −2.556 | 0.011 | ** |

${\omega}_{2}^{-}$ | 1.001 | 5.849 | 0.171 | 0.864 | |

Gasoline | |||||

$\alpha $ | 0.000 | 0.024 | 0.004 | 0.997 | |

$\gamma $ | 0.064 | 0.030 | 2.160 | 0.031 | ** |

$\beta $ | 0.967 | 0.021 | 44.981 | 0.000 | *** |

m | −6.498 | 0.349 | −18.613 | 0.000 | *** |

${\theta}^{+}$ | −2.695 | 1.786 | −1.509 | 0.131 | |

${\omega}_{2}^{+}$ | 6.397 | 1.406 | 4.550 | 0.000 | *** |

${\theta}^{-}$ | −6.136 | 2.476 | −2.478 | 0.013 | ** |

${\omega}_{2}^{-}$ | 7.803 | 1.216 | 6.416 | 0.000 | *** |

Kerosene | |||||

$\alpha $ | 0.000 | 0.111 | 0.001 | 0.999 | |

$\gamma $ | 0.075 | 0.053 | 1.401 | 0.161 | |

$\beta $ | 0.946 | 0.164 | 5.755 | 0.000 | *** |

m | −7.929 | 0.549 | −14.440 | 0.000 | *** |

${\theta}^{+}$ | 3.586 | 1.378 | 2.602 | 0.009 | *** |

${\omega}_{2}^{+}$ | 1.001 | 0.838 | 1.194 | 0.232 | |

${\theta}^{-}$ | −12.261 | 3.098 | −3.957 | 0.000 | *** |

${\omega}_{2}^{-}$ | 1.930 | 0.819 | 2.357 | 0.018 | ** |

**Notes:**The table reports the estimates of the DAGM model for Propane, Gasoline, and Kerosene. The column “Std. Error” shows the Quasi-Maximum Likelihood-based standard errors. Sample Period: March 2020 to June 2021, 271 daily observations. **, and *** indicate the significance at levels 10%, 5%, and 1%, respectively.

GARCH | GJR | GM | DAGM | ||
---|---|---|---|---|---|

cDCC | a | 0.141*** | 0.155 *** | 0.139 *** | 0.132 *** |

(0.045) | (0.045) | (0.039) | (0.033) | ||

b | 0.579 *** | 0.586 *** | 0.45 *** | 0.473 *** | |

(0.097) | (0.092) | (0.154) | (0.156) | ||

DCCMIDAS | a | 0.021 | 0.023 | 0.023 | 0.025 ** |

(0.022) | (0.023) | (0.017) | (0.012) | ||

b | 0.956 *** | 0.955 *** | 0.958 *** | 0.961 *** | |

(0.024) | (0.025) | (0.018) | (0.014) | ||

${\omega}_{2}$ | 1.001 | 1.001 | 1.001 | 1.001 | |

(0.747) | (0.652) | (0.718) | (0.896) | ||

DECO | a | 0.216 *** | 0.227 *** | 0.197 * | 0.165 ** |

(0.069) | (0.072) | (0.118) | (0.071) | ||

b | 0.439 *** | 0.424 *** | 0.353 | 0.286 | |

(0.155) | (0.15) | (0.281) | (0.415) |

**Notes:**The table reports the estimated coefficients of the correlation models (first column) according the univariate specifications reported in columns from three to six. Numbers in parentheses represent the Quasi-Maximum Likelihood-based standard errors. *, **, and *** indicate the significance at levels 10%, 5%, and 1%, respectively.

Univ. | GARCH | GARCH | GARCH | GJR | GJR | GJR | GM | GM | GM | DAGM | DAGM | DAGM |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Mult. | DCCM | cDCC | DECO | DCCM | cDCC | DECO | DCCM | cDCC | DECO | DCCM | cDCC | DECO |

RMSE | 5.744 | 5.799 | 5.859 | 5.75 | 5.817 | 5.874 | 5.827 | 5.93 | 5.971 | 5.655 | 5.736 | 5.784 |

FROB | 3.38 | 3.27 | 3.35 | 3.37 | 3.27 | 3.35 | 3.38 | 3.32 | 3.38 | 3.27 | 3.19 | 3.27 |

EUCL | 2.26 | 2.20 | 2.24 | 2.25 | 2.20 | 2.24 | 2.27 | 2.25 | 2.28 | 2.20 | 2.16 | 2.19 |

**Notes:**The table reports the average losses multiplied by 100,000. Label “DCCM” stands for DCC-MIDAS. Shades of gray denote inclusion in the SSM at significance level $\alpha =0.25$.

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. 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 (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Andreani, M.; Candila, V.; Morelli, G.; Petrella, L.
Multivariate Analysis of Energy Commodities during the COVID-19 Pandemic: Evidence from a Mixed-Frequency Approach. *Risks* **2021**, *9*, 144.
https://doi.org/10.3390/risks9080144

**AMA Style**

Andreani M, Candila V, Morelli G, Petrella L.
Multivariate Analysis of Energy Commodities during the COVID-19 Pandemic: Evidence from a Mixed-Frequency Approach. *Risks*. 2021; 9(8):144.
https://doi.org/10.3390/risks9080144

**Chicago/Turabian Style**

Andreani, Mila, Vincenzo Candila, Giacomo Morelli, and Lea Petrella.
2021. "Multivariate Analysis of Energy Commodities during the COVID-19 Pandemic: Evidence from a Mixed-Frequency Approach" *Risks* 9, no. 8: 144.
https://doi.org/10.3390/risks9080144