Modeling, simulation, and prediction of global energy indices: a differential approach

doi:10.1007/s11708-021-0723-6

Frontiers in Energy

2022, Vol. 16

Issue (2): 375-392 https://doi.org/10.1007/s11708-021-0723-6

本期目录

Modeling, simulation, and prediction of global energy indices: a differential approach

Stephen Ndubuisi NNAMCHI¹(

), Onyinyechi Adanma NNAMCHI², Janice Desire BUSINGYE³, Maxwell Azubuike IJOMAH⁴, Philip Ikechi OBASI⁵

¹. Department of Mechanical Engineering, Kampala International University, 20000 Kampala, Uganda
². Department of Agricultural Engineering and Bio Resources, Michael Okpara University of Agriculture, Umudike, Umuahia, Nigeria
³. Directorate of Human Resource/Finance, Kampala International University, 20000 Kampala, Uganda
⁴. Department of Mathematics and Statistics, Faculty of Sciences, University of Port Harcourt, PMB 5323 Choba Port Harcourt, Nigeria
⁵. Department of Macroeconomic Analysis (Ministry of Finance), Budget and National Planning, Abuja, Nigeria

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Abstract：

Modeling, simulation, and prediction of global energy indices remain veritable tools for econometric, engineering, analysis, and prediction of energy indices. Thus, this paper differentially modeled, simulated, and non-differentially predicated the global energy indices. The state-of-the-art of the research includes normalization of energy indices, generation of differential rate terms, and regression of rate terms against energy indices to generate coefficients and unexplained terms. On imposition of initial conditions, the solution to the system of linear differential equations was realized in a Matlab environment. There was a strong agreement between the simulated and the field data. The exact solutions are ideal for interpolative prediction of historic data. Furthermore, the simulated data were upgraded for extrapolative prediction of energy indices by introducing an innovative model, which is the synergy of deflated and inflated prediction factors. The innovative model yielded a trendy prediction data for energy consumption, gross domestic product, carbon dioxide emission and human development index. However, the oil price was untrendy, which could be attributed to odd circumstances. Moreover, the sensitivity of the differential rate terms was instrumental in discovering the overwhelming effect of independent indices on the dependent index. Clearly, this paper has accomplished interpolative and extrapolative prediction of energy indices and equally recommends for further investigation of the untrendy nature of oil price.

Key words： energy indices differential model normalization simulation inflation/deflation predictive factor and prediction rate

收稿日期: 2020-05-07 出版日期: 2022-05-25

Corresponding Author(s): Stephen Ndubuisi NNAMCHI

引用本文:

. [J]. Frontiers in Energy, 2022, 16(2): 375-392.
Stephen Ndubuisi NNAMCHI, Onyinyechi Adanma NNAMCHI, Janice Desire BUSINGYE, Maxwell Azubuike IJOMAH, Philip Ikechi OBASI. Modeling, simulation, and prediction of global energy indices: a differential approach. Front. Energy, 2022, 16(2): 375-392.

链接本文:

https://academic.hep.com.cn/fie/CN/10.1007/s11708-021-0723-6
https://academic.hep.com.cn/fie/CN/Y2022/V16/I2/375

Fig.1

Index	Function and the differential	Regression coefficient, R²
ec	$ec (-) = 1 .07525039 − 2 .63821125 τ + 1 .74979270 τ 2$ $d ec d τ = − 2 .63821125 + 3 .4995854 τ$	0.95957781
gdp	$gdp (-) = 0 .98114756 − 0 .11750495 τ − 0 .91242700 τ 2$ $d gdp d τ = − 0 .11750495 − 1 .824854 τ$	0.97513034
cde	$gdp (-) = 0 .85504123 − 0 .41672116 τ − 0 .49400846 τ 2$ $d gdp d τ = − 0 .41672116 − 0 .98801692 τ$	0.93317944
hdi	$hdi (-) = 1 .10224884 − 2 .00347452 τ + 0 .92117598 τ 2$ $d hdi d τ = − 2 .00347452 + 1 .84235196 τ$	0.96667570
op	$op (-) = 0 .75398663 + 1 .53674211 τ − 2 .74011768 τ 2$ $d op d τ = 1 .53674211 − 5 .48023536 τ$	0.90916101

Tab.1

Index	Unit	Coefficients	ec, gdp, cde, hdi, op
Index	Unit	Coefficients	i = 1	i = 2	i = 3	i = 4	i = 5
ec	(-)	$α ′ i$	–0.40058	–2.18962	0.02215	–1.05080	0.31149
gdp	(-)	$β ′ i$	1.14178	0.20888	–0.01155	0.54794	–0.16243
cde	(-)	$δ ′ i$	–0.00625	0.11309	0.61818	0.29666	–0.08794
hdi	(-)	$ε ′ i$	–0.55319	–0.21088	–1.15273	0.01166	0.16399
op	(-)	$φ ′$	–0.48779	0.62730	3.42888	–0.03468	1.64551

Tab.2

Constant term (unexplained coefficient)	Indices
	ec	gdp	cde	hdi	op
	(-)	(-)	(-)	(-)	(-)
$g ′ i$	0.80684	–1.91392	–1.38934	–0.18983	–3.85809

Tab.3

Initial condition	Indices
	ec₀	gdp₀	cde₀	hdi₀	op₀
	(-)	(-)	(-)	(-)	(-)
$τ = 0$	1.05000	1.00000	0.85000	1.00000	0.80000

Tab.4

Energy index	Unit	Mathematical function, $∃ ? ? ? ? ? ? ? 1982 ≤ t ≤ 2017$	Regression coefficient, R²
EC	Mtoe	$EC = − 4545220 .6308 + 4531 .9472 t − 1 .1291 t 2 ?$	1.0000
GDP	US$ Billion	$GDP = 10807510 .9879 − 10918 .1087 t + 2 .7576 t 2 ?$	1.0000
CDE	Btoe	$EC = 32377 .8112 − 32 .8857 t + 0 .0084 t 2 ?$	1.0000
HDI	%	$HDI = − 444527 .2179 + 44 .0924 t − 0 .0109 t 2 ?$	1.0000
OP	US$/Mtoe	$EC = 6205651 .8570 − 6233 .62602 t + 1 .5655 t 2 ?$	1.0000

Tab.5

Tab.6

Fig.2

Fig.3

Fig.4

Fig.5

Fig.6

Fig.7

Fig.8

Fig.9

Fig.10

Fig.11

Symbol	Index	Unit
EC	Dimensional energy consumption	Mtoe
GDP	Dimensional gross domestic product	US$ Billion
CDE	Dimensional carbon dioxide emission	Btoe
HDI	Dimensional human development index	%
OP	Dimensional oil price	US$/Mtoe
ec	Normalized energy consumption	–
gdp	Normalized gross domestic product	–
cde	Normalized carbon dioxide emission	–
hdi	Normalized human development index	–
op	Normalized oil price	–
t	Dimensional time	year
τ	Normalized time	–
$α i, i = {e c, g d p, c d e, h d i, o p}$	Dimensional EC linear model coefficients	(Mtoe\|year) \|Mtoe, (Mtoe\|year) \|US$ Billion, (Mtoe\|year) \|Btoe, (Mtoe\|year) \|%, (US$ Billion\|year) \|US$ Billion
$β i, i = {g d p, e c, c d e, h d i, o p}$	Dimensional GDP linear model coefficients	(US$ Billion\|year) \|US$ Billion, (US$ Billion\|year) \|Mtoe, (US$ Billion\|year) \|Btoe, (US$ Billion\|year) \|%, (US$ Billion\|year) \|US$ Billion
$δ i, i = {c d e, e c, g d p, h d i, o p}$	Dimensional CDE linear model coefficients	(Btoe\|year) \|Btoe, (Btoe\|year) \|Mtoe, (Btoe\|year) \|US$ Billion, (Btoe\|year) \|%, (Btoe\|year) \|US$ Billion
$ε i, i = {h d i, e c, g d p, c d e, o p}$	Dimensional HDI linear model coefficients	(%\|year) \|%, (%\|year) \|Mtoe, (%\|year) \|US$ Billion, (%\|year) \|Btoe, (%\|year) \|US$ Mtoe
$φ i, i = {o p, e c, g d p, c d e, h d i}$	Dimensional OP linear model coefficients	(US$/Mtoe/year) \|US%/Mtoe, (US$/Mtoe/year) \| Mtoe, (US$/Mtoe/year) \| US$ Billion, (US$/Mtoe/year) \| Btoe, (US$/Mtoe/year) \|%
$α i', i = {e c, g d p, c d e, h d i, o p}$	Normalized ec linear model coefficients	–, –, –, –, –
$β i', ? i = {g d p, e c, c d e, h d i, o p}$	Normalized gdp linear model coefficients	–, –, –, –, –
$δ i', ? i = {c d e, e c, g d p, h d i, o p}$	Normalized cde linear model coefficients	–, –, –, –, –
$ε i', ? i = {h d i, e c, g d p, c d e, o p}$	Normalized hdi linear model coefficients	–, –, –, –, –
$φ i', ? i = {o p, e c, g d p, c d e, h d i}$	Normalized op linear model coefficients	–, –, –, –, –
$g i, ? i = {e c, g d p, c d e, h d i, o p}$	The unexplained coefficients in dimensional linear equations	Mtoe/year, (US$ Billion)/year, Btoe/year, %/year, (US$/Mtoe)/year
$g i', ? i = {e c, g d p, c d e, h d i, o p}$	The unexplained coefficients in normalized linear equations	–, –, –, –, –
${E C 0, G D P 0, C D E 0, H D I 0 O P 0}$	Reference or initial dimensional indices	Mtoe, US$ Billion, Btoe, %, US$/Mtoe
${e c 0, g d p 0, c d e 0, h d i 0, o p 0}$	Reference or initial normalized indices	–, –, –, –, –
rand( )	Random number
$R i, ? i = {e c, g d p, c d e, h d i, o p}$	Rate factors	–, –, –, –, –
R²	Regression coefficient	–
Subscripts
f	Final
0	Initial
Superscript
k	Power of time

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