Modeling the dependence structure of CO₂ emissions and energy consumption based on the Archimedean copula approach: the case of the United States

ABSTRACT

In this paper, we aimed to investigate the relationship between energy consumption and carbon dioxide (CO₂) emission quantities. To explain the dependence structure, we employed asymmetric Archimedean copulas and determined the best fitting multi-parameter Archimedean copula based on the λ–function. A goodness-of-fit improvement can be obtained by using concordance invariant and tail dependence preserving transforms. The association of CO₂ emission quantities and energy consumption is characterized by the transformed convex sum of the Gumbel and Clayton copula, indicating evidence of joint extreme occurrences when both of the variables increase or decrease in the industrial sector. Also, the Kendall hazard scenario approach was used to evaluate the probability of extreme events. The results provide valuable information for researchers who model changes in CO₂ emission quantities with energy consumption.

KEYWORDS:

• Energy consumption modeling
• CO₂ emissions
• Archimedean copula
• tail dependence
• goodness-of-fit
• Kendall hazard scenario

Abbreviations

U.S.	=	United States
ASEAN	=	Association of Southeast Asian nations
FDI	=	Foregin direct investment
EIA	=	The U.S. energy Information Administration
MMmt	=	Million metric tons
Tmt	=	Trillion metric tons
Btu	=	British thermal units
TCDE	=	The total amount of CO2 emission
TEC	=	Total energy consumption
GCCS	=	Convex sum of Gumbel and Clayton copula
GCCS – T	=	Transformed convex sum of the Gumbel and Clayton copula
CvM	=	Cramér-von Mises

Nomenclature

CO2	=	Carbon dioxide
$\phi (t)$	=	Archimedean copula generator function
$\lambda (t)$	=	Archimedean copula lambda function
${\lambda }_{Cl}(t)$	=	$\lambda -$ function of Clayton copula
${\lambda }_{Gu}(t)$	=	$\lambda -$ function of Gumbel copula
$\tau$	=	Kendall’s tau coefficient
${\lambda }_U$	=	Upper tail dependence
${\lambda }_L$	=	Lower tail dependence
$K(t)$	=	Kendall distribution function
$K_n(t)$	=	Empirical estimate of Kendall distribution function

Acknowledgments

We thank the anonymous referees and the editor for their helpful suggestions which improved the presentation of the paper.