Energy Demand Forecasting: Combining Cointegration ...

Research ArticleEnergy Demand Forecasting Combining Cointegration Analysisand Artificial Intelligence Algorithm

Junbing Huang Yuee Tang and Shuxing Chen

School of Economics Southwestern University of Finance and Economics Chengdu 611130 China

Correspondence should be addressed to Junbing Huang 20701432biteducn

Received 6 October 2017 Accepted 6 December 2017 Published 10 January 2018

Academic Editor Benjamin Ivorra

Copyright copy 2018 Junbing Huang et alThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Energy is vital for the sustainable development of China Accurate forecasts of annual energy demand are essential to scheduleenergy supply and provide valuable suggestions for developing related industries In the existing literature on energy use predictionthe artificial intelligence-based (AI-based) model has received considerable attention However few econometric and statisticalevidences exist that can prove the reliability of the current AI-based model an area that still needs to be addressed In this study anew energy demand forecasting framework is presented at first On the basis of historical annual data of electricity usage over theperiod of 1985ndash2015 the coefficients of linear and quadratic forms of the AI-based model are optimized by combining an adaptivegenetic algorithm and a cointegration analysis shown as an example Prediction results of the proposed model indicate that theannual growth rate of electricity demand in China will slow down However China will continue to demand about 13 trillionkilowatt hours in 2030 because of population growth economic growth and urbanization In addition the model has greateraccuracy and reliability compared with other single optimization methods

1 Introduction

Energy which is a vital input for the economic and socialdevelopment of any economy has gained special attentionCombined with globalization and industrialization globalenergy demand has been increasing continually for decadesand is expected to rise approximately 30 from 2015 to2035 in accordance with the worldwide economic growth [1]Therefore energy demand projection should be developedbecause accurate energy demand forecasts aid policy makersin improving the schedule of energy supply and providingvaluable suggestions for planning energy supply systemoperations

Given the importance of accurate energy forecasts extantstudies using different estimation methods have been under-taken since the 1970s In general these early studies canbe classified into two major categories econometric [2ndash9]and machine learning (ML) methods [10ndash23] The artificialintelligence (AI) energy forecasting model which is a classof ML method has gained popularity in recent years becauseof its superiority in time series processing and its capabilityto deal with noise data Several tools such as artificial

neural networks (ANN) genetic algorithm (GA) ant colonyoptimization (ACO) and particle swarm optimization arecommonly employed in the model [10ndash17] Compared withthe conventional econometric energy forecastingmethod theAI-based model frequently demonstrates higher predictionaccuracy in terms of mean absolute error (MAE) meansquare error (MSE)mean absolute percentage error (MAPE)and root mean square error (RMSE) [16 17] According toeconomic theories the model is feasible for predicting futureenergy demand by using the historical relationship whenthe periodical characteristics between energy demand andits explanatory variables will not change in the long termHowever the current AI-based method is referred to asthe ldquoblack-boxrdquo because it predicts energy demand withoutknowing the internal relationship between energy demandand its affecting factors [23] In addition few econometricand statistical evidences are found that can prove the relation-ship between energy demand and its factorsThis relationshipmay change in the long run based on the current AI-basedmodel

This study aims to present a more scientific AI-basedenergy demand forecasting framework that ensures the

HindawiMathematical Problems in EngineeringVolume 2018 Article ID 5194810 13 pageshttpsdoiorg10115520185194810

2 Mathematical Problems in Engineering

reliability of predicted results The electricity demand ofChina is forecasted as an example to show the process ofimplementing this framework In addition the predictedresults are beneficial for policymakers to performappropriatemeasures to bridge the electricity gap and arrange the supplyof electricity demand

The rest of the paper is organized as follows Section 2conducts a detailed literature review on the recent develop-ments of energy demand forecasting Section 3 presents thenew framework Section 4 predicts the electricity demand inChina for 2016ndash2030 under three scenarios The final sectionsummarizes the main conclusions and presents the policyimplications

2 Literature Review

Energy estimation modeling has attracted wide spread inter-est among current practitioners and academicians The com-monly used econometric techniques include cointegrationanalysis autoregressive integrated moving average (ARIMA)model partial least square regression (PLSR) and vectorerror correction model The ML method mainly refers tothe AI model support vector regression (SVR) method andGrey forecasting method Their details are described in thefollowing sections

21 Econometric Method Cointegration analysis can estab-lish a long-run relationship among variables and the fore-casting results are reliably shown through tests rangingfrom unit root to cointegration analysis [2 3] Early studiessuch as Chan and Lee [24] and Lin [2] forecasted thetotal energy and electricity demands in China respectivelyThey conducted a series of tests ranging from unit roottest to cointegration test to guarantee that a cointegrationrelationship exists between energy demand and its factors(ie the nexus will not change in themedium and long term)The ARIMA model is presented as an appropriate methodfor long-term projections [4ndash8 25] This model dependson three parameters including order of moving averageorder of differencing and order of autoregressive schemeHowever ARIMA cannot be employed with missing andnonstationary data otherwise the original data should befirst transformed by differencing Recently Cabral et al [7]considered the spatiotemporal dynamics in the conventionalARIMA model Their results confirmed that the new spa-tiotemporal model improves the electricity demand forecastsin Brazil and is paramount to achieving the goals of theBrazilian electricity sector for a secured electricity supplyContrary to the ARIMA model PLSR is a popular statisticaltool that can deal with data especially missing or highlycorrelated data [26]However PLSRwas recently discussed inthe field of energy demand estimation [26 27] For instanceZhang et al [26] employed the PLSR model to estimatethe transportation energy demand in China on the basisof GDP urbanization rate passenger turnover and freightturnoverTheir results demonstrate that the transport energydemand for 2020 will reach a level of 43313 billion tons ofcoal equivalent (BTCE) and 46826 BTCE under differentscenarios

22 MLMethod Any optimization technique requires infor-mation on future scenarios and a search for the best solutionsagainst a test criterion In this case ML techniques aresuperior and are frequently used to solve these two problemsThe ML models include several tools such as the AI SVRand Grey forecasting methods To motivate our research wefocused particularly on the AI-based model

The concept of SVR is developed from the computationof a linear regression function in a high-dimensional featurespace where the input data are mapped via a nonlinearfunction which can be found in Vapnik [28] andVapnik et al[29] Dong et al [19] were the first to employ SVR to predictthemonthly energy use of buildings in tropical regions Localweather data including monthly average outdoor dry-bulbtemperature relative humidity and global solar radiation areselected as the factors affecting energy demand Their resultsdemonstrate that the relative error rate is less than 4 Wanget al [30] applied SVR for predicting hourly electricity usein residences and compared the results with other AI-basedmethods They report that SVR improves the predictionaccuracy

Energy Grey forecasting model adopts the essential partof Grey system theory In energy demand forecasting [18] thebasic Grey model (GM (11)) was employed Recently Kangand Zhao [31] combined the moving average method andMarkov model with GM to improve the accuracy of forecast-ing results The improved Grey forecasting model demon-strates better performance compared with the conventionalGM (1 1) Xu et al [32] combine GM and the Autoregressiveand moving average model The result indicates that theimproved energy forecasting model has excellent accuracyand a high level of reliability for the case study of GuangdongProvince

AI-based prediction method predicts energy use accord-ing to its correlated variables such as population growtheconomic growth and economic structure [2ndash6 15ndash17] Forinstance Haldenbilen and Ceylan [10] proposed an AImodelbased on GA using population GDP and vehicle-km asaffecting factors to forecast the transport energy demand inTurkey Recently Gunay [23] modeled an electricity demandfunction for Turkey using the data on population GDPper capita inflation percentage unemployment percentageaverage summer temperature and average winter temper-ature Then ANN is employed to determine the optimalweights that can maximize the accuracy of the function Theaforementioned algorithms can be called the single AI-basedmethod To eliminate several essential limitations in thesealgorithms researchers also propose hybrid methods thatintegrate at least two AI algorithms such as the GA-ANN[33] and PSO-GA models [12ndash16] to improve the predictionaccuracy The hybrid combination of a single AI algorithmshows greater performance compared with other methods

The current AI-based prediction method is generallycomposed of four main steps data collection data pre-processing model training and model testing With thesuperiority in time series processing the AI-based modeldisplays a good performance in predicting future energydemands However a spurious regression problem occurs ina wide range of time series analysis in econometrics owing to

Mathematical Problems in Engineering 3

its nonstationarityThe current AI-basedmodel cannot avoidthis problem If the selected variables do not satisfy the basicrequirements of constructing a cointegration relationshipover the sample period the AI-based forecastingmodels can-not be employed tomake energy demand projections becausethe nexus between energy demand and its factors will changein the medium and long term Therefore the mechanism forpredicting energy demand should be reformulated

3 Methodology

31 Introduction to AI-Based Energy Demand Model Inthe precedent AI-based models the commonly employedindependent variables were around population GDP urban-ization industrialization energy price and energymixThreeforms of the estimation models including linear quadraticand exponential forms were then adopted for data training[10 11 15ndash17] which can be expressed as follows

119910lin = 1199080 + 119873sum119894=1

119908119894119883119894 (1)

119910qua = 1199080 + 119873sum119894=1

119908119894119883119894 + 119873sum119894=1

119873sum119895=119894+1

119896119894119895119883119894119883119895 + 119873sum119894=1

119908119873+1198941198832119894 (2)

119910exp = 1199080 + 119873sum119894=1

119908119894119883119908119894+119905119894 (3)

where models (1) (2) and (3) are the linear quadratic andexponential forms respectively In each model 119883119894 is the 119894thenergy demand-affecting factor 119873 is the number of energydemand-affecting factors and 119908119894 and 119896119894119895 are correspondingweights

The ldquofittestrdquo weights are finally searched through differentAI tools such as GA ACO and hybrid algorithms basedon the fitness function employed to monitor the forecastingaccuracy which aims to minimize the sum of squared errorbetween the actual and estimated values shown as follows

min119891 (119909) = 119898sum119895=1

(119864actual minus 119864predicted)2 (4)

where 119864actual and 119864predicted denote the actual and predictedenergy demand values respectively 119898 is the number ofobservations

After obtaining the optimal weights the model wasapplied to forecast the future energy demand under differ-ent scenarios Compared with the traditional econometricenergy demand forecasting model the proposed AI-basedmodel frequently demonstrates higher prediction accuracyHowever according to economic theory these periodicalcharacteristics of economic variables will not change inthe medium and long term when an economy remains ina consistent state Consequently their historical relation-ship between energy demand and factors in the samplingperiod should be entirely stable When this relationship wassatisfied it could be used for forecasting energy demandHowever the current AI-based energy demand forecasting

model does not determine this historical relationship througheconometric and statistical analysis This condition can berecognized as a ldquoblack-boxrdquo without knowing the internalrelationship between energy demand and its affecting fac-tors [33] Accordingly this model cannot be adopted forenergy demand prediction when the historical relationshipestimated through the AI-basedmodel will change over timeTherefore the improved AI-based model framework shouldbe presented to improve the reliability

32 Improved AI-Based Model As indicated in the above-mentioned conventional AI-based model the AI tool isdirectly applied to obtain the optimal weights for the modelafter preprocessing the original data Then the model isemployed to forecast future energy demand However theprediction results are not reliable when the variables cannotbuild a stable and long-run relationship or when the parame-ters will change over timeTherefore the model stability testsshould be performed before proceeding to obtain the fittestweights through the AI tools The cointegration analysis iswidely employed as a key econometric method to forecastmid- and long-run energy demand because it can establisha long-run relationship among variables [3] Cointegrationtheory and operations are employed to determine whether along-run relationship exists between energy demand and itsfactors To compare with the precedent AI-based model ournew framework for energy demand forecasting is shown inFigure 1(b) and the original framework described in previousliterature is presented in Figure 1(a) As shown in Figure 1if the energy demand and its factors cannot satisfy thecointegration relationship over the sample period then thismodel cannot be adopted to predict future energy demandbased on the current AI-based model because the stablerelationship between them does not exist in the medium andlong term

321 Cointegration Test According to cointegration theorythe existence of a long-run equilibrium relationship amongeconomic variables is based on the stationary linear combina-tion of a time series The cointegration relationship over thesampling period can be tested when the economic variablesare integrated at 119868(119899) at the same time or at either 119868(0) or 119868(1)Hence the first step to conduct the cointegration analysis is byemploying a unit root test approach to check the stationarityof the variables In empirical studies the methods includingaugmented DickeyndashFuller (ADF) and PhillipsndashPerron (PP)tests are commonly employed to test the time series Cointe-gration tests such as EnglendashGranger [34] JohansenndashJuselius[35] and autoregressive distributed lag (ARDL) bound test-ing approach [36 37] can be adopted after the probabilityof building a cointegration relationship among the variablesis verified EnglendashGranger method is feasible for testingsingle equation cointegration when the economic variablesare integrated at 119868(119899) simultaneously Compared with theEnglendashGranger method the JohansenndashJuselius method candetermine the number of cointegration vectors and test theexistence of cointegration among variables However theJohansenndashJuselius method can be employed when the vari-ables are integrated at 119868(119899) simultaneously Compared with


Data collection

Data preprocessing

Data trainingAI toolsThree-form-model

Performance test

Scenario setting

Forecasting energy demand

The optimal weights for the models

(a)

Data collection

Data preprocessing

AI toolsThree-form-model

Unit root test

Cointegration testLong-term relationship test

Cointegration relationship

Yes

NoOver

Data training

Performance test

Scenario setting



Stability test

(b)

Figure 1 The frameworks for the conventional and new AI-based energy demand forecasting model

the EnglendashGranger and Johansen methods ARDL boundsapproach was recently applied to test the existence of along-run equilibrium among the time series because it canestablish the long- and short-run relationships among thevariables It also extended the mandatory requirements onthe variables and can be applied even when the variables areintegrated at 119868(0) 119868(1) or fractionally cointegratedThird theARDL procedure is a more powerful approach to determinethe cointegration relationship in small samples than theJohansenndashJuselius technique Finally the problems of serialcorrelation and endogeneity are not difficult to tackle withinthe ARDL model

322 Performance Test After verifying the existence of along-run relationship among variables the next step is totest the prediction accuracy performance of the model anddeterminewhether the estimated parameterswill changewithtime Parameter inconsistency may result in poor conse-quences on inferences and lead to wrong conclusions For theJohansenndashJuselius cointegration test technique the stabilitytest for the vector autoregressive model should be conductedthrough the unit root analysis Meanwhile for the ARDLbound approach the cumulative (CUSUM) and cumulativesum of squares (CUSUMSQ) are suitable for the stability testbecause their statistics are updated recursively and plottedagainst the break points

4 Forecasting Electricity Demand in China

In this section electricity demand forecasting in China isshown as an example based on our new framework Firstwe list the electric energy demand-affecting factors andthe proxy variables based on existing electricity demandprediction literature Second given that the AI-based modeldoes not require many explanatory variables we employthe cointegration analysis to select the variables that can becontributed toward building a long-run relationship Thirdwe employ the adaptive genetic algorithm (AGA) whichis superior to conventional AI algorithms to optimize themodel Based on the above estimation three scenarios foreconomic growth namely low (ScenarioA) business as usual(Scenario B) and high (Scenario A) are set Finally theelectricity demand projections for the three scenarios areconducted

41 Electricity Demand-Affecting Factors Electricity demandcan be viewed as a causal function of several affecting factorssuch as population GDP electricity prices economic struc-ture urbanization and life styles [15ndash17] In line with Lin [2]andYu et al [15] the number of total populations is employedas a reflector of population growth on electricity demandSecondly economic growth influences the electricity demandmainly through various ways Inconsistent withmost existing


Table 1 Definition and description for the variables

Variables Definition Max Min Mean Std devE ln form of total electricity energy consume (1012 KWH) 17393 minus08873 04418 083811198831 ln form of total population (108) 26208 23594 25208 007691198832 ln form of gross domestic product (trillion Yuan RMB 1012) 26540 minus00944 12919 085781198833 ln form of the ratio of tertiary sector to GDP () 39160 33810 36459 015061198834 ln form of the urban population to the total () 40271 31659 35881 028091198835 ln form of price index for the electricity demand 26623 00000 16674 00825Note KWH denotes kilowatt hour

literature GDP is adopted as a key factor of electric energydemand Thirdly in China the amount of energy requiredto produce a unit of GDP differs significantly among thethree industries Numerous researchers have noted thatsecondary industries are the main electricity consumers [2]Therefore the economic structure shifted from the secondaryindustry (eg heavy industry) to the tertiary industry (eghigh-technology industry) may directly reduce electricityconsumption [2] In line with Feng et al [38] and Li etal [39] we take the ratio of the tertiary sector in GDP tocapture the effect of relative change in economic structureon electricity demand Fourthly urbanization in China isone of the key stages exerting an important but complicatedimpact on electricity demand In each year millions ofimmigrants moved from rural to big cities in search ofgood job opportunities which exerted a great influence onelectric energy demand This study utilizes urbanization rateto control the effect of urbanization on electricity demandLastly according to economic theory the price can affect thedemand through income and substitution effects Howeveradjusting the electricity price in China is complicated becauseit has been under the full control of the government foryears and is mainly determined by the production cost Inaddition the price among the regions differs significantlyand no practical method can estimate the electricity price inChina [2] Therefore we employ the price index for fuel andpower to denote the electricity price index

42 Data Management To forecast the electricity demandwe use 31 years of observed data from 1985 to 2015 Electricityconsumption in each year is measured in trillion (1012)kilowatt hours (KWH) and population is measured as 100million (108) persons GDP data are measured in trillionYuan (1012) RMB and adjusted to the constant price in 1985Economic structure is denoted by the ratio of output inthe tertiary industry to GDP () The share of the urbanpopulation to the total population is used to substitute theurbanization rate () To represent the price for electricity weuse the price index for fuel and power to denote the electricityprice The price index for the base year (1985) is assumed tobe 100 and the price index for other years is adjusted to theconstant price index of 1985 The definition of the variablesis shown in Table 1 The trends for electricity demand and itsfactors in the period of 1985ndash2015 are shown in Figure 2

43 AGA As mentioned in Section 2 the conventionalAI algorithms also experience low prediction accuracy

1985 1990 1995 2000 2005 2010 2015

ElectricityPopulationGDP

Economic structureUrbanizationPrice

0

1

2

3

4

5

Log

form

of v

aria

bles

minus1

Figure 2 The trends of electricity demand and its factors (1985ndash2015)

However the hybrid AI algorithms (eg PSO-GA and ANN-GA) are complicated In this study we employ AGA whichhas a more profound intelligent background and yieldsgood efficiency in optimizing global coefficients The majordifference between traditional GA and AGA is the selectionof crossover probability 119901119888 and mutation probability 119901119898In conventional GA the two probabilities are randomlydetermined or based on an inadequate reference whereasAGA relies on the fitness function to select the optimal 119901119888and 119901119898 The flowchart for AGA is shown in Figure 3 In thisfigure AGA contains major operations including initializa-tion judgement and selection crossover and mutation Thedetailed descriptions of the operations are given as follows

(A) Initialization The parameters including the num-ber of pop sizes (Pop size) and the number of genera-tions (Num generations) are first set The fitness functionscrossover probability and mutation probability should alsobe determined

(B) Judgement and Selection Population is determined andranked according to the values of fitness function The indi-vidual with a low fitness value can be selected as the optimalsolution for the problem when the number of generations isequal to the maximal number of generations otherwise theindividual with a low fitness value is selected and the rest ofthe individuals are replaced by the selected individuals


Start

Initialize the parameters

Set up the initial generation

Judge and select the individual

Calculate the fitness

The best individual

The last individual

Yes

No

The next individual

Yes

The next generation

End

The last generation

No

Adjust crossover probability

Crossover

Adjust mutation probability

Mutation

Figure 3 The flowchart of adaptive genetic algorithm

(C) Crossover To gain good performance in AGA thecrossover probability is determined by a function comparedwith a constant in conventional GA A high crossover prob-ability will be set when the fitness value is less than theaverage value otherwise a high fitness value will lead to alow crossover probability A crossover probability functionemployed in our study is shown as follows

119901119888 = 1199011198881 minus (1199011198881 minus 1199011198882) (119891

1015840 minus 119891avg)119891max minus 119891avg 119891 ge 119891avg1199011198881 119891 lt 119891avg

(5)

where 119901119888 denotes the crossover probability function and 119891maxand 119891avg represent the maximum fitness and average fitnessvalues respectively 1199011198881 = 09 and 1199011198882 = 06 are set in step(A)

(D) Mutation The selection of mutation probability valuesis the same as that for the selection of crossover probabilityvalues The mutation probability is set to 01 when the fitnessvalue is lower than the average value otherwise a high fitnessvalue will result in a high crossover probability value Thecorresponding mutation probability function is given as

119901119898 = 1199011198981 minus (1199011198981 minus 1199011198982) (119891max minus 119891)119891max minus 119891avg 119891 ge 119891avg1199011198981 119891 lt 119891avg

(6)

where 119901119898 refers to the mutation of probability function1199011198981 = 01 and 1199011198982 = 001 are determined in the first stepand119891max and119891avg represent themaximum and average fitnessdegrees for each generation respectively

5 Estimating Results and Future Projections

51 Cointegration Analysis511 Unit Root Test After data collection and preprocess thefirst step is to perform the unit root test to determine whetherthe time series satisfies the basic conditions for constructingthe cointegration relationship Considering that ADF and PPtests are distorted in small sample sizes the Ng and Perron[40] unit root test is adopted using only the intercept termand the presence of intercept and trend terms in the unit rootestimating equation The corresponding unit root tests areshown in Table 2

The first six rows in Table 2 are the unit root test resultswith the presence of an intercept term while the last six rowsare unit root test results with the presence of intercept andtrend terms This result indicates that all the time series arefirst-difference stationary at the 10 significance level withthe presence of an intercept term a situation that satisfiesthe necessary requirements for building the cointegrationrelationship of JohansenndashJuselius technique [35] and ARDLbound testing approach [36] simultaneously

512 Cointegration Test Next we conducted the test todetermine the presence of a long-run relationship using theARDL bounds testing approach The ordinary least squares(OLS) procedure is first employed for the next equationwhich is expressed as

Δ119864119905 = 1205820 + 119901sum119894=1

1205751119894Δ119864119905minus119894 + 119901sum119894=0

1205761119894Δ1198831119905minus119894 + 119901sum119894=0

1206011119894Δ1198832119905minus119894+ 119901sum119894=0

1205931119894Δ1198833119905minus119894 + 119901sum119894=0

1205741119894Δ1198834119905minus119894 + 119901sum119894=0

1205961119894Δ1198835119905minus119894


Table2Re

sults

basedon

Ng-Perron

unitroot

test

Varia

bles

Level

Thefi

rstd

ifference

Thes

econ

ddifference

MZa

MZt

MSB

MPT

MZa

MZt

MSB

MPT

MZa

MZt

MSB

MPT

Eminus73

2lowastminus171

023

402

minus1904lowastlowastlowast

minus290

015

193

minus213lowastlowast

minus093

044

1062

X 1119

174

146

14521


minus310015

145

minus194minus09

7050

1246

X 2minus13

70lowastlowastlowast

minus245

018

239


minus217022

270


minus250

019

208

X 3minus07

5lowastlowast041

055

2474


minus256

018

203


minus240

020

217

X 4minus46

8minus130

028

566

minus668lowast

minus181027

374


minus261

018

185

X 5minus22

3minus08

8039

969


minus238

018

252


minus330

015

116

Eminus217

minus097

044

3797

minus799minus179

023

1190

minus541

minus162030

1677

X 1minus316

minus107034

2485

minus041

minus025

061

8570

minus973minus22

1023

936

X 2minus36


minus425

012

270

minus1023

minus219021

920

minus1339

minus258

019

685

X 3minus16

68lowastminus28

7017

557

minus1387

minus258

019

687

minus1160

minus239

021

796

X 4minus133

1minus25

7019

691

minus675

minus182027

1350

minus1389

minus262

019

664

X5

minus048

minus020

041

4225

minus1415

minus260

018

683


minus334

015

408

Criticalvalues(intercept)

Criticalvalues(interceptand

trend

)1

level

minus1380

minus258

017

178

minus2380

minus342

014

403

5level

minus810minus198

023

317

minus1730

291

017

548

10level

minus570

minus162027

445

minus1420

minus262

018

667

Notelowast

lowastlowastandlowastlowastlowastdeno

tesig

nificance

atthe1

05and

1levels

respectiv

ely1198641198831119883211988331198834and1198835deno

tethelnform

ofele

ctric

itydemandpo

pulatio

nGDPecon

omicstr

uctureu

rbanization

and

energy

pricerespectiv

ely


Table 3 Results of bounds testing approach based on SBC

Electricity demand function 119865-statistics Lag order Cointegration1198641 = 119891(1198831 1198832 1198833 1198834 1198835) 25629 1 Inconclusive1198642 = 119891(1198831 1198832 1198833 1198834) 42134lowast 2 Yes1198643 = 119891(1198831 1198832 1198833 1198835) 25507 2 Inconclusive1198644 = 119891(1198831 1198832 1198834 1198835) 18554 2 No1198645 = 119891(1198831 1198833 1198834 1198835) 25478 2 Inconclusive1198646 = 119891(1198832 1198833 1198834 1198835) 39873lowast 2 YesCritical values119896 = 5 (lower-upper) 119896 = 4 (lower-upper)

1 level 4134 5761 4280 58405 level 2910 4193 3058 422310 level 2407 3517 2525 3560Note (1) 119864 denotes the ldquolnrdquo form of electricity demand 119883119894 (119894 = 1 sdot sdot sdot 5) stand for the ldquolnrdquo form of population GDP economic structure urbanization andenergy price respectively (2) the critical values are taken from the appendix in Narayan [37] (3) lowast denotes significance at the 10 level (4) since there areonly thirty-one samples the max lag order 119901 is 1 for 1198641 and 2 for other electric energy demand functions

+ 12058211119864119905minus1 + 120582121198831119905minus1 + 120582131198832119905minus1 + 120582141198833119905minus1+ 120582151198834119905minus1 + 120582161198835119905minus1 + 1199061119905

(7)where 119864 denotes the ldquolnrdquo form of electricity demand and119883119894 (119894 = 1 sdot sdot sdot 5) refers to the ln form of population GDPeconomic structure urbanization rate and price of electricityrespectively 1205820 is a constant parameter and 119906119905 denotesthe white-noise process Δ represents the first-differenceoperator

To obtain the optimal lag length for the equation theARDL bounds approach should estimate (119901 + 1)119896 times ofregressions (119901 and 119896 resp denote the maximum numberof lags and the number of variables) The SchwarzndashBayesiancriteria (SBC) or Akaike information criterion can then beadopted to determine the optimal lag for this regression Thebounds testing procedure based on the joint 119865-statistics andWald statistics is illustrated as follows

The null hypothesis in the equation is1198670 120582119894 = 0 againstthe alternative of 1198671 120582119894 = 0 119894 = 1 2 5 Two sets ofcritical values are reported in Pesaran et al [36] and Narayan[37] The bound statistics in Pesaran et al [36] are onlyapplicable for a sample size with more than 80 observationsotherwise Narayan [37] is appropriate Considering that oursample size is 31 (from 1985 to 2015) the critical valuesfrom Narayan [37] for the bounds 119865-test are more suitablethan those from Pesaran et al [36] to establish the reliableinferences on cointegration

Null should be rejected when the calculated 119865-statisticsexceeds the upper bound suggesting that cointegrationrelationship exists between electricity demand and its factorsNo cointegration is found when the calculated 119865-statisticsis below the low critical value However few approximateconclusions can be drawn without knowing the order ofintegration of the underlying regressors when the statisticsare located between the bounds The corresponding resultsare shown in Table 3 As mentioned by Canyurt and Ozturk[11] the AI-based model did not require many factors toestimate future energy demands The cointegration tests

(Table 3) are presented using both five input variables andfour variables respectively

As shown in Table 3 the existence of two cointegrationrelationships among the variables is confirmed Hence theelectricity demand functions including 1198642 and 1198646 can beapplied to estimate future electricity demands In the follow-ing we employ the electricity demand function 1198642 in whichpopulation GDP economic structure and urbanization areused as the independent variables to predict future electricitydemands

513 Stability Test CUSUM and CUSUMSQ are applied toshow the stability of the model as shown in Figure 4

In the figure the plots of CUSUM and CUSUMSQ arelocated within the critical bounds at the 5 significance levelwhich suggests that the model is stable Accordingly thecointegration relationship between electric energy demandand its factors is reliable

52 Estimating Results After the long-run equilibrium rela-tionship among the variables is verified AGA is employedto optimize the coefficients of (1)-(2) (since we employ theln form of variables after carrying out the weights of (1)-(2) the electric energy demand can be obtained using 119884 =119890119910lin or 119884 = 119890119910qua) The electricity demand function whichuses four factors as the economic indicators namely GDPpopulation economic structure and urbanization is selectedin the model to predict the future energy demand in China

To estimate the coefficients for the linear and quadraticforms the observed data from 1985 to 2015 are used Thelinear form for the optimal model is written as follows (forsimplicity we do not present the results in exponential form)

119864lin = minus71855 + 137541198831 + 032731198832 minus 113671198833+ 225401198834 (8)

where 119864 denotes the ldquolnrdquo form of electricity demand and119883119894 (119894 = 1 2 3 4) stands for the ldquolnrdquo form of population GDPeconomic structure and urbanization Population growtheconomic growth and urbanization are the leading forces


minus06minus04minus02

000204060810121416

2000 2004 2008 2012 2015The straight lines represent critical bounds

at 5 significance level

(a)

2000 2004 2008 2012 2015minus10

10

minus4minus2

minus6minus8

24

0

86

The straight lines represent critical boundsat 5 significance level

(b)

Figure 4 Plot of CUSUM (a) and CUSUMSQ (b)

contributing to the increase of electricity demand a findingthat is consistent with our expectations Elasticity coefficientsshow that a 1 increase in population economic growth andurbanization will produce respective increases of 1375403273 and 2254 in electricity consumption By contrasta 1 increase in the ratio of tertiary sector to GDP willproduce a 11367 decline of electric energy consumption

In addition the quadratic form for the optimal model isexpressed as

119864qua = minus14529642 + 108501321198831 minus 16101721198832minus 6268391198833 + 16288161198834 + 58594911988311198832+ 22803711988311198833 minus 68126011988311198834minus 3998711988321198833 + 11014811988321198834 + 5177811988331198834minus 196515711988321 minus 4496111988322 minus 1215211988323minus 3226311988324

(9)

53 Performance Tests To evaluate the performance of theprediction model the model must be compared with otherforecasting optimal models (GA ACO GM and OLS)using MAE MSE MAPE and RMSE The correspondingdefinitions of MAE MSE MAPE and RMSE are shown asfollows

MAE = sum119873119894=1 10038161003816100381610038161003816119910119894 minus 1199101015840119894 10038161003816100381610038161003816119873 MSE = sum119873119894=1 (119910119894 minus 1199101015840119894 )2119873

MAPE = sum119873119894=1 10038161003816100381610038161003816(119910119894 minus 1199101015840119894 ) 11991011989410038161003816100381610038161003816119873 RMSE = radicsum119873119894=1 (119910119894 minus 1199101015840119894 )2119873

(10)

where 119910119894 and 1199101015840119894 represent the actual and fitted valuesrespectively and 119873 is the number of observations All theseapproaches use the population GDP industrial proportionand urbanization rate of China as the independent vari-ables The training data (1985ndash2010) are employed to fit thehistorical relationship between electricity demand and itsfactors and the testing data (2011ndash2015) are adopted to test theperformanceThe comparison of these criteria for the testingdata among various optimal electricity demand models isreported in Table 4The table demonstrates thatMAPE of thequadratic form is the lowest compared with the linear formsoptimized by AGA and other methods (GA ACO GM andOLS) In addition the proposed linear form of AGA achievesbetter prediction accuracy than other forecasting optimalmodels The actual and simulated data for the optimal modelfrom 1985 to 2015 are also shown in Figure 5 which revealsthat the proposedmodel fits the historical data wellThus thediscussed AGA algorithm effectively enhances the estimatingprecision of the model

54 Future Projection The abovementioned framework isapplied to forecast electricity demand from 2016 to 2030based on three scenarios The trends of the affecting factorsare described as follows

GDP A declining trend is observed for the GDP growth ofChina in recent years For instance the annual GDP averagegrowth rates of China during 2005ndash2010 and 2010ndash2015 are1136 and 786 respectively Today China has entered astage of development called ldquonew normalrdquo which indicatesthat significant uncertainties may occur in the economicdevelopment of China Hence the possible impacts of differ-ent economic growth rates on electricity consumption shouldbe considered We set three scenarios for economic growthsimilar to Lin and Ouyang [3] high (Scenario A) businessas usual (Scenario B) and low (Scenario C) In Scenario Athe average growth rate of GDP between 2016 and 2020 isset as 7 In Scenario B the average growth rate is 65because China has to fulfill its national goal established in the13th Five-Year Plan In Scenario C the average growth rate


Table 4 Prediction accuracy test for the optimal model

Method Criteria MAE MSE MAPE () RMSEAGA (linear) 03122 01023 201 03198AGA (quadric) 02704 00932 173 03052GA (linear) Canyurt and Ozturk [11] 04212 01652 295 04064GA (quadric) 03408 01206 244 03473ACO (Toksari [13]) 05874 03165 415 05626GM (Hsu and Chen [18]) 06731 04239 583 06511OLS 08019 04832 868 06951

Table 5 Hypothesis of variables for the three different scenarios (unit )

Period Growth rate of GDP Growth rate ofpopulation

Growth rate ofeconomic structure

Growth rate ofurbanizationScenario A Scenario B Scenario C

2016ndash2020 70 65 60 060 20 152021ndash2025 65 60 55 070 22 082026ndash2030 60 55 50 075 25 04

LinearOriginalQuadratic

0

1

2

3

4

5

6

7

Elec

tric

ity en

ergy

cons

umpt

ion

(trill

ion

Kwh)

1994

1993

1995

2012

1990

1991

1992

1988

1987

1986

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

2014

2009

2013

1989

2015

1985

2010

2008

2011

Year

Figure 5 The original and prediction time series of electric energyconsumption

is assigned as 6 in 2016ndash2020 the lowest among the threescenarios Additional details can be found in Table 5

Population The annual growth rate of population in2010ndash2015 was approximately 05 We assume that theimplementation of the current ldquotwo-child policyrdquo will pro-mote population growth Therefore we hypothesize that theannual growth rates of population for the periods 2016ndash20202021ndash2025 and 2026ndash2030 are 060 070 and 075respectively

Economic Structure According to the 13th Five-Year Planof China the share of tertiary industries to GDP will beover 56 in 2020 indicating that the annual growth rateof tertiary industries to GDP will be at least 209 during2016ndash2020 Currently the economy of China is transitioning

from primary to secondary to tertiary industries Thereforethe annual growth rates of tertiary industries to GDP for theperiods of 2021ndash2025 and 2026ndash2030 are assumed to be 22and 25 respectively

Urbanization The rapid urbanization process of China isexpected to end in 2020 [41] Additionally the urbanizationprocess of China will follow an s-curve track which is similarto the historical experience of most developed countries[3] We assume that the average annual growth rate forurbanization will decelerate in 2020 and will further decreaseto 15 in 2016ndash2020 08 in 2021ndash2025 and 04 in2026ndash2030 In summary the projected GDP growth ratespopulation economic structure and urbanization for thethree scenarios are shown in Table 5

The electricity demand of China can be forecasted afterthe assumptions of the factors are established In Figures 6 7and 8 the national electricity demand estimates under threescenarios with the linear and quadratic forms are shownrespectively

The electricity demand of China will continue growing inthe medium and long term regardless of the adjustments ineconomic structure Under the high-growth scenario (Sce-narios A) the electricity demand will still increase rapidlybecause of the economic growth urbanization process andpopulation growth of China However the annual growthrate of electricity demand will decrease to 58 during the2016ndash2030 period in Scenario A owing to the decline inannual growth rate of economic growth and the adjustmentin economic structure This value is much lower comparedwith that in the period of 2000ndash2015 In 2020 2025 and 2030the electricity demand of China will be 82585 11139 and13821 trillion KWH according to the quadratic form of thismodel (Figure 6) The minimum predicted values for 2020combined with 2025 and 2030 were obtained by using thelinear form of the optimal model which result in 8032210758 and 13302 trillion KWH respectively under ScenarioA The maximal predicted electricity demand in Scenario


2016 2018 2020 2022 2024 2026 2028 20302

4

6

8

10

12

14

Quadric modelLinear model

Year

82585

80322

11139

10758

13821

13302

Elec

tric

ity d

eman

d (t

rillio

n KW

H)

Figure 6 Electricity demand in Scenario A


2016 2018 2020 2022 2024 2026 2028 20302

4

6

8

10

12

14

80605

78806

10661

10322

13067

12585

Year

Elec

tric

ity d

eman

d (t

rillio

n KW

H)

Figure 7 Electricity demand in Scenario B

B in 2020 is about 8 trillion KWH (Figure 7) whereas theminimum is 78806 trillionKWHaccording to the linear formof the model By 2025 the electricity demand consumptionin Scenario B will save about 04 trillion KWH comparedwith Scenario A due to the lower growth rates in GDP In2030 the electricity demand in Scenario B will consumeless than 06 trillion KWH compared with Scenario A Asshown in Figure 8 the electricity demands of China are smallunder Scenario C In this scenario the electricity demandwillconsume about 79 103 and 124 trillion KWH in 2020 2025and 2030 respectively

6 Results and Policy Conclusions

In this study we develop a new framework to predict energydemand based on the conventional AI models and cointe-gration theory To develop energy forecasts we emphasizethe use of appropriate data and econometric techniques


2016 2018 2020 2022 2024 2026 2028 20302

4

6

8

10

12

14

7921

7751

9956

12462

11994

Year

Elec

tric

ity d

eman

d (t

rillio

n KW

H)

1028

Figure 8 Electricity demand in Scenario C

rather than several computer packages for demand estima-tion techniques provided by previous studies In this newframework the energy demand-affecting factors which areused as the independent variables in the prediction modelare determined based on theoretical analysis and selectedby statistical and econometric analysis or tests Finally thefuture electricity demands of China from 2016 to 2030 arepredicted as an example for the new model by using themodified AI-based model Compared with several previousAI-based literatures we prove that the present forecastingmodel demonstrates exceptional performance in forecastingelectric energy demand

The prediction results of electricity demand indicate thatpopulation growth economic growth and urbanization arethe leading forces contributing to the increase of electricitydemand whereas economic structure adjustment is responsi-ble for the decline of electricity consumption Several specificresults are listed below an electricity demand growth isobserved in China in the following years (ie 2016ndash2030)However the future annual growth rate is lower comparedwith the last decades Based on our analysis electricitydemand will still continue to increase at an annual averagerate of about 55 and will be about 13 trillion KWH in 2030This value corresponds to nearly two times comparedwith the2015 level The forecasts would be valuable for policy makersin China in planning future energy policies

Conflicts of Interest

The authors declare that they have no conflicts of interest

References

[1] BP World Energy outlook 2017 ed Paris Francis 2017[2] B Q Lin ldquoStructural changes efficiency improvement and

electricity demand forecastingrdquo Economic Research vol 5 pp57ndash65 2003 (Chinese)

[3] B Lin and X Ouyang ldquoEnergy demand in China Compar-ison of characteristics between the US and China in rapid


urbanization stagerdquo Energy Conversion and Management vol79 pp 128ndash139 2014

[4] J W Taylor ldquoShort-term electricity demand forecasting usingdouble seasonal exponential smoothingrdquo Journal of the Opera-tional Research Society vol 54 no 8 pp 799ndash805 2003

[5] JW Taylor ldquoAn evaluation of methods for very short-term loadforecasting using minute-by-minute British datardquo InternationalJournal of Forecasting vol 24 no 4 pp 645ndash658 2008

[6] E Erdogdu ldquoElectricity demand analysis using cointegrationand ARIMA modelling a case study of Turkeyrdquo Energy Policyvol 35 no 2 pp 1129ndash1146 2007

[7] J D A Cabral L F L Legey and M V D Freitas CabralldquoElectricity consumption forecasting in Brazil A spatial econo-metrics approachrdquo Energy vol 126 pp 124ndash131 2017

[8] C Deb F Zhang J Yang S E Lee and K W Shah ldquoAreview on time series forecasting techniques for building energyconsumptionrdquoRenewableamp Sustainable Energy Reviews vol 74pp 902ndash924 2017

[9] L Frıas-Paredes F Mallor M Gaston-Romeo and T LeonldquoAssessing energy forecasting inaccuracy by simultaneouslyconsidering temporal and absolute errorsrdquo Energy Conversionand Management vol 142 pp 533ndash546 2017

[10] S Haldenbilen and H Ceylan ldquoGenetic algorithm approach toestimate transport energy demand inTurkeyrdquoEnergy Policy vol33 no 1 pp 89ndash98 2005

[11] O E Canyurt and H K Ozturk ldquoThree different applicationsof genetic algorithm (GA) search techniques on oil demandestimationrdquo Energy Conversion andManagement vol 47 no 18-19 pp 3138ndash3148 2006

[12] Z W Geem and W E Roper ldquoEnergy demand estimation ofSouth Korea using artificial neural networkrdquo Energy Policy vol37 no 10 pp 4049ndash4054 2009

[13] M Duran Toksari ldquoAnt colony optimization approach toestimate energy demand of Turkeyrdquo Energy Policy vol 35 no8 pp 3984ndash3990 2007

[14] M D Toksarı ldquoEstimating the net electricity energy generationand demand using the ant colony optimization approach caseof Turkeyrdquo Energy Policy vol 37 no 3 pp 1181ndash1187 2009

[15] S Yu K Zhu and X Zhang ldquoEnergy demand projection ofChina using a path-coefficient analysis and PSO-GA approachrdquoEnergy Conversion and Management vol 53 no 1 pp 142ndash1532012

[16] S Yu and K Zhu ldquoA hybrid procedure for energy demandforecasting in Chinardquo Energy vol 37 no 1 pp 396ndash404 2012

[17] L Liu J Huang and S W Yu ldquoPrediction of primary energydemand in China based on AGAEDE optimal modelrdquo ChineseJournal of Population Resources and Environment vol 14 no 1pp 16ndash29 2016

[18] C Hsu and C Chen ldquoApplications of improved grey predictionmodel for power demand forecastingrdquo Energy Conversion andManagement vol 44 no 14 pp 2241ndash2249 2003

[19] B Dong C Cao and S E Lee ldquoApplying support vectormachines to predict building energy consumption in tropicalregionrdquo Energy and Buildings vol 37 no 5 pp 545ndash553 2005

[20] Y S Lee and L I Tong ldquoForecasting nonlinear time series ofenergy consumption using a hybrid dynamic modelrdquo AppliedEnergy vol 94 pp 251ndash256 2012

[21] L Tang L Yu S Wang and J Li ldquoA novel hybrid ensemblelearning paradigm for nuclear energy consumption forecast-ingrdquo Applied Energy vol 93 pp 432ndash443 2012

[22] Y T Chae RHoresh YHwang andYM Lee ldquoArtificial neuralnetwork model for forecasting sub-hourly electricity usage incommercial buildingsrdquo Energy and Buildings vol 111 pp 184ndash194 2016

[23] M E Gunay ldquoForecasting annual gross electricity demandby artificial neural networks using predicted values of socio-economic indicators and climatic conditions Case of TurkeyrdquoEnergy Policy vol 90 pp 92ndash101 2016

[24] H L Chan and S L Lee ldquoForecasting the demand for energyin ChinardquoThe Energy Journal vol 17 no 1 pp 19ndash30 1996

[25] P Chujai N Kerdprasop and K Kerdprasop ldquoTime seriesanalysis of household electric consumption with ARIMA andARMA modelsrdquo in Proceedings of the International MultiCon-ference of Engineers and Computer Scientists 2013 IMECS 2013pp 295ndash300 Hong Kong China March 2013

[26] M Zhang HMu G Li and Y Ning ldquoForecasting the transportenergy demand based on PLSR method in Chinardquo Energy vol34 no 9 pp 1396ndash1400 2009

[27] M Meng D Niu and W Sun ldquoForecasting monthly electricenergy consumption using feature extractionrdquo Energies vol 4no 10 pp 1495ndash1507 2011

[28] V N Vapnik ldquoAn overview of statistical learning theoryrdquo IEEETransactions on Neural Networks and Learning Systems vol 10no 5 pp 988ndash999 1999

[29] V Vapnik S E Golowich and A Smola ldquoSupport vectormethod for function approximation regression estimation andsignal processingrdquo in Proceedings of the 10th Annual Conferenceon Neural Information Processing Systems (NIPS rsquo96) pp 281ndash287 December 1996

[30] Z Wang R S Srinivasan and J Shi ldquoArtificial intelligentmodels for improved prediction of residential space heatingrdquoJournal of Energy Engineering vol 142 no 4 Article ID04016006 2016

[31] J Kang and H Zhao ldquoApplication of improved grey modelin long-term load forecasting of power engineeringrdquo SystemsEngineering Procedia vol 3 pp 85ndash91 2012

[32] W Xu R Gu Y Liu and Y Dai ldquoForecasting energy consump-tion using a newGM-ARMAmodel based onHP filter the caseof Guangdong Province of Chinardquo Economic Modelling vol 45pp 127ndash135 2015

[33] Z Wang and R S Srinivasan ldquoA review of artificial intelligencebased building energy use prediction Contrasting the capabil-ities of single and ensemble prediction modelsrdquo Renewable ampSustainable Energy Reviews vol 75 pp 796ndash808 2017

[34] R F Engle and C W J Granger ldquoCo-integration and error cor-rection representation estimation and testingrdquo Econometricavol 55 no 2 pp 251ndash276 1987

[35] S Johansen and K Juselius ldquoMaximum likelihood estima-tion and inference on cointegrationmdashwith applications to thedemand for moneyrdquoOxford Bulletin of Economics and Statisticsvol 52 no 2 pp 169ndash210 1990

[36] M H Pesaran Y Shin and R J Smith ldquoBounds testingapproaches to the analysis of level relationshipsrdquo Journal ofApplied Econometrics vol 16 no 3 pp 289ndash326 2001

[37] P K Narayan ldquoThe saving and investment nexus for Chinaevidence from cointegration testsrdquo Applied Economics vol 37no 17 pp 1979ndash1990 2005

[38] T W Feng L Y Sun and Y Zhang ldquoThe relationship betweenenergy consumption structure economic structure and energyintensity in Chinardquo Energy Policy vol 37 no 12 pp 5475ndash54832009


[39] Y Li L Sun T Feng and C Zhu ldquoHow to reduce energyintensity in China A regional comparison perspectiverdquo EnergyPolicy vol 61 pp 513ndash522 2013

[40] S Ng and P Perron ldquoLag length selection and the constructionof unit root tests with good size and powerrdquo Econometrica vol69 no 6 pp 1519ndash1554 2001

[41] TheWorld Bank 2012 China 2030 Building a modern harmo-nious and creative high-income society USA

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reliability of predicted results The electricity demand ofChina is forecasted as an example to show the process ofimplementing this framework In addition the predictedresults are beneficial for policymakers to performappropriatemeasures to bridge the electricity gap and arrange the supplyof electricity demand

The rest of the paper is organized as follows Section 2conducts a detailed literature review on the recent develop-ments of energy demand forecasting Section 3 presents thenew framework Section 4 predicts the electricity demand inChina for 2016ndash2030 under three scenarios The final sectionsummarizes the main conclusions and presents the policyimplications

2 Literature Review

Energy estimation modeling has attracted wide spread inter-est among current practitioners and academicians The com-monly used econometric techniques include cointegrationanalysis autoregressive integrated moving average (ARIMA)model partial least square regression (PLSR) and vectorerror correction model The ML method mainly refers tothe AI model support vector regression (SVR) method andGrey forecasting method Their details are described in thefollowing sections

21 Econometric Method Cointegration analysis can estab-lish a long-run relationship among variables and the fore-casting results are reliably shown through tests rangingfrom unit root to cointegration analysis [2 3] Early studiessuch as Chan and Lee [24] and Lin [2] forecasted thetotal energy and electricity demands in China respectivelyThey conducted a series of tests ranging from unit roottest to cointegration test to guarantee that a cointegrationrelationship exists between energy demand and its factors(ie the nexus will not change in themedium and long term)The ARIMA model is presented as an appropriate methodfor long-term projections [4ndash8 25] This model dependson three parameters including order of moving averageorder of differencing and order of autoregressive schemeHowever ARIMA cannot be employed with missing andnonstationary data otherwise the original data should befirst transformed by differencing Recently Cabral et al [7]considered the spatiotemporal dynamics in the conventionalARIMA model Their results confirmed that the new spa-tiotemporal model improves the electricity demand forecastsin Brazil and is paramount to achieving the goals of theBrazilian electricity sector for a secured electricity supplyContrary to the ARIMA model PLSR is a popular statisticaltool that can deal with data especially missing or highlycorrelated data [26]However PLSRwas recently discussed inthe field of energy demand estimation [26 27] For instanceZhang et al [26] employed the PLSR model to estimatethe transportation energy demand in China on the basisof GDP urbanization rate passenger turnover and freightturnoverTheir results demonstrate that the transport energydemand for 2020 will reach a level of 43313 billion tons ofcoal equivalent (BTCE) and 46826 BTCE under differentscenarios

22 MLMethod Any optimization technique requires infor-mation on future scenarios and a search for the best solutionsagainst a test criterion In this case ML techniques aresuperior and are frequently used to solve these two problemsThe ML models include several tools such as the AI SVRand Grey forecasting methods To motivate our research wefocused particularly on the AI-based model

The concept of SVR is developed from the computationof a linear regression function in a high-dimensional featurespace where the input data are mapped via a nonlinearfunction which can be found in Vapnik [28] andVapnik et al[29] Dong et al [19] were the first to employ SVR to predictthemonthly energy use of buildings in tropical regions Localweather data including monthly average outdoor dry-bulbtemperature relative humidity and global solar radiation areselected as the factors affecting energy demand Their resultsdemonstrate that the relative error rate is less than 4 Wanget al [30] applied SVR for predicting hourly electricity usein residences and compared the results with other AI-basedmethods They report that SVR improves the predictionaccuracy

Energy Grey forecasting model adopts the essential partof Grey system theory In energy demand forecasting [18] thebasic Grey model (GM (11)) was employed Recently Kangand Zhao [31] combined the moving average method andMarkov model with GM to improve the accuracy of forecast-ing results The improved Grey forecasting model demon-strates better performance compared with the conventionalGM (1 1) Xu et al [32] combine GM and the Autoregressiveand moving average model The result indicates that theimproved energy forecasting model has excellent accuracyand a high level of reliability for the case study of GuangdongProvince

AI-based prediction method predicts energy use accord-ing to its correlated variables such as population growtheconomic growth and economic structure [2ndash6 15ndash17] Forinstance Haldenbilen and Ceylan [10] proposed an AImodelbased on GA using population GDP and vehicle-km asaffecting factors to forecast the transport energy demand inTurkey Recently Gunay [23] modeled an electricity demandfunction for Turkey using the data on population GDPper capita inflation percentage unemployment percentageaverage summer temperature and average winter temper-ature Then ANN is employed to determine the optimalweights that can maximize the accuracy of the function Theaforementioned algorithms can be called the single AI-basedmethod To eliminate several essential limitations in thesealgorithms researchers also propose hybrid methods thatintegrate at least two AI algorithms such as the GA-ANN[33] and PSO-GA models [12ndash16] to improve the predictionaccuracy The hybrid combination of a single AI algorithmshows greater performance compared with other methods

The current AI-based prediction method is generallycomposed of four main steps data collection data pre-processing model training and model testing With thesuperiority in time series processing the AI-based modeldisplays a good performance in predicting future energydemands However a spurious regression problem occurs ina wide range of time series analysis in econometrics owing to



3 Methodology


119910lin = 1199080 + 119873sum119894=1

119908119894119883119894 (1)

119910qua = 1199080 + 119873sum119894=1

119908119894119883119894 + 119873sum119894=1

119873sum119895=119894+1

119896119894119895119883119894119883119895 + 119873sum119894=1

119908119873+1198941198832119894 (2)

119910exp = 1199080 + 119873sum119894=1

119908119894119883119908119894+119905119894 (3)



min119891 (119909) = 119898sum119895=1








Data collection

Data preprocessing


Performance test

Scenario setting



(a)

Data collection

Data preprocessing


Unit root test



Yes

NoOver

Data training

Performance test

Scenario setting



Stability test

(b)













1985 1990 1995 2000 2005 2010 2015



0

1

2

3

4

5

Log

form

of v

aria

bles

minus1






Start





The best individual

The last individual

Yes

No

The next individual

Yes

The next generation

End

The last generation

No


Crossover


Mutation



119901119888 = 1199011198881 minus (1199011198881 minus 1199011198882) (119891


(5)




(6)






Δ119864119905 = 1205820 + 119901sum119894=1

1205751119894Δ119864119905minus119894 + 119901sum119894=0

1205761119894Δ1198831119905minus119894 + 119901sum119894=0

1206011119894Δ1198832119905minus119894+ 119901sum119894=0

1205931119894Δ1198833119905minus119894 + 119901sum119894=0

1205741119894Δ1198834119905minus119894 + 119901sum119894=0

1205961119894Δ1198835119905minus119894


Table2Re

sults

basedon

Ng-Perron

unitroot

test

Varia

bles

Level

Thefi

rstd

ifference

Thes

econ

ddifference

MZa

MZt

MSB

MPT

MZa

MZt

MSB

MPT

MZa

MZt

MSB

MPT

Eminus73

2lowastminus171

023

402


minus290

015

193


minus093

044

1062

X 1119

174

146

14521


minus310015

145

minus194minus09

7050

1246

X 2minus13


minus245

018

239


minus217022

270


minus250

019

208

X 3minus07

5lowastlowast041

055

2474


minus256

018

203


minus240

020

217

X 4minus46

8minus130

028

566

minus668lowast

minus181027

374


minus261

018

185

X 5minus22

3minus08

8039

969


minus238

018

252


minus330

015

116

Eminus217

minus097

044

3797

minus799minus179

023

1190

minus541

minus162030

1677

X 1minus316

minus107034

2485

minus041

minus025

061

8570

minus973minus22

1023

936

X 2minus36


minus425

012

270

minus1023

minus219021

920

minus1339

minus258

019

685

X 3minus16

68lowastminus28

7017

557

minus1387

minus258

019

687

minus1160

minus239

021

796

X 4minus133

1minus25

7019

691

minus675

minus182027

1350

minus1389

minus262

019

664

X5

minus048

minus020

041

4225

minus1415

minus260

018

683


minus334

015

408



trend

)1

level

minus1380

minus258

017

178

minus2380

minus342

014

403

5level

minus810minus198

023

317

minus1730

291

017

548

10level

minus570

minus162027

445

minus1420

minus262

018

667

Notelowast


tesig

nificance

atthe1

05and

1levels

respectiv

ely1198641198831119883211988331198834and1198835deno

tethelnform

ofele

ctric

itydemandpo

pulatio

nGDPecon

omicstr

uctureu

rbanization

and

energy

pricerespectiv

ely
















119864lin = minus71855 + 137541198831 + 032731198832 minus 113671198833+ 225401198834 (8)




000204060810121416



(a)

2000 2004 2008 2012 2015minus10

10

minus4minus2

minus6minus8

24

0

86


(b)





(9)




(10)













0

1

2

3

4

5

6

7

Elec

tric

ity en

ergy

cons

umpt

ion

(trill

ion

Kwh)

1994

1993

1995

2012

1990

1991

1992

1988

1987

1986

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

2014

2009

2013

1989

2015

1985

2010

2008

2011

Year










2016 2018 2020 2022 2024 2026 2028 20302

4

6

8

10

12

14


Year

82585

80322

11139

10758

13821

13302

Elec

tric

ity d

eman

d (t

rillio

n KW

H)



2016 2018 2020 2022 2024 2026 2028 20302

4

6

8

10

12

14

80605

78806

10661

10322

13067

12585

Year

Elec

tric

ity d

eman

d (t

rillio

n KW

H)






2016 2018 2020 2022 2024 2026 2028 20302

4

6

8

10

12

14

7921

7751

9956

12462

11994

Year

Elec

tric

ity d

eman

d (t

rillio

n KW

H)

1028






References




















































Journal of












Journal of







Volume 2018






Volume 2018










3 Methodology


119910lin = 1199080 + 119873sum119894=1

119908119894119883119894 (1)

119910qua = 1199080 + 119873sum119894=1

119908119894119883119894 + 119873sum119894=1

119873sum119895=119894+1

119896119894119895119883119894119883119895 + 119873sum119894=1

119908119873+1198941198832119894 (2)

119910exp = 1199080 + 119873sum119894=1

119908119894119883119908119894+119905119894 (3)



min119891 (119909) = 119898sum119895=1








Data collection

Data preprocessing


Performance test

Scenario setting



(a)

Data collection

Data preprocessing


Unit root test



Yes

NoOver

Data training

Performance test

Scenario setting



Stability test

(b)













1985 1990 1995 2000 2005 2010 2015



0

1

2

3

4

5

Log

form

of v

aria

bles

minus1






Start





The best individual

The last individual

Yes

No

The next individual

Yes

The next generation

End

The last generation

No


Crossover


Mutation



119901119888 = 1199011198881 minus (1199011198881 minus 1199011198882) (119891


(5)




(6)






Δ119864119905 = 1205820 + 119901sum119894=1

1205751119894Δ119864119905minus119894 + 119901sum119894=0

1205761119894Δ1198831119905minus119894 + 119901sum119894=0

1206011119894Δ1198832119905minus119894+ 119901sum119894=0

1205931119894Δ1198833119905minus119894 + 119901sum119894=0

1205741119894Δ1198834119905minus119894 + 119901sum119894=0

1205961119894Δ1198835119905minus119894


Table2Re

sults

basedon

Ng-Perron

unitroot

test

Varia

bles

Level

Thefi

rstd

ifference

Thes

econ

ddifference

MZa

MZt

MSB

MPT

MZa

MZt

MSB

MPT

MZa

MZt

MSB

MPT

Eminus73

2lowastminus171

023

402


minus290

015

193


minus093

044

1062

X 1119

174

146

14521


minus310015

145

minus194minus09

7050

1246

X 2minus13


minus245

018

239


minus217022

270


minus250

019

208

X 3minus07

5lowastlowast041

055

2474


minus256

018

203


minus240

020

217

X 4minus46

8minus130

028

566

minus668lowast

minus181027

374


minus261

018

185

X 5minus22

3minus08

8039

969


minus238

018

252


minus330

015

116

Eminus217

minus097

044

3797

minus799minus179

023

1190

minus541

minus162030

1677

X 1minus316

minus107034

2485

minus041

minus025

061

8570

minus973minus22

1023

936

X 2minus36


minus425

012

270

minus1023

minus219021

920

minus1339

minus258

019

685

X 3minus16

68lowastminus28

7017

557

minus1387

minus258

019

687

minus1160

minus239

021

796

X 4minus133

1minus25

7019

691

minus675

minus182027

1350

minus1389

minus262

019

664

X5

minus048

minus020

041

4225

minus1415

minus260

018

683


minus334

015

408



trend

)1

level

minus1380

minus258

017

178

minus2380

minus342

014

403

5level

minus810minus198

023

317

minus1730

291

017

548

10level

minus570

minus162027

445

minus1420

minus262

018

667

Notelowast


tesig

nificance

atthe1

05and

1levels

respectiv

ely1198641198831119883211988331198834and1198835deno

tethelnform

ofele

ctric

itydemandpo

pulatio

nGDPecon

omicstr

uctureu

rbanization

and

energy

pricerespectiv

ely
















119864lin = minus71855 + 137541198831 + 032731198832 minus 113671198833+ 225401198834 (8)




000204060810121416



(a)

2000 2004 2008 2012 2015minus10

10

minus4minus2

minus6minus8

24

0

86


(b)





(9)




(10)













0

1

2

3

4

5

6

7

Elec

tric

ity en

ergy

cons

umpt

ion

(trill

ion

Kwh)

1994

1993

1995

2012

1990

1991

1992

1988

1987

1986

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

2014

2009

2013

1989

2015

1985

2010

2008

2011

Year










2016 2018 2020 2022 2024 2026 2028 20302

4

6

8

10

12

14


Year

82585

80322

11139

10758

13821

13302

Elec

tric

ity d

eman

d (t

rillio

n KW

H)



2016 2018 2020 2022 2024 2026 2028 20302

4

6

8

10

12

14

80605

78806

10661

10322

13067

12585

Year

Elec

tric

ity d

eman

d (t

rillio

n KW

H)






2016 2018 2020 2022 2024 2026 2028 20302

4

6

8

10

12

14

7921

7751

9956

12462

11994

Year

Elec

tric

ity d

eman

d (t

rillio

n KW

H)

1028






References




















































Journal of












Journal of







Volume 2018






Volume 2018









Data collection

Data preprocessing


Performance test

Scenario setting



(a)

Data collection

Data preprocessing


Unit root test



Yes

NoOver

Data training

Performance test

Scenario setting



Stability test

(b)













1985 1990 1995 2000 2005 2010 2015



0

1

2

3

4

5

Log

form

of v

aria

bles

minus1






Start





The best individual

The last individual

Yes

No

The next individual

Yes

The next generation

End

The last generation

No


Crossover


Mutation



119901119888 = 1199011198881 minus (1199011198881 minus 1199011198882) (119891


(5)




(6)






Δ119864119905 = 1205820 + 119901sum119894=1

1205751119894Δ119864119905minus119894 + 119901sum119894=0

1205761119894Δ1198831119905minus119894 + 119901sum119894=0

1206011119894Δ1198832119905minus119894+ 119901sum119894=0

1205931119894Δ1198833119905minus119894 + 119901sum119894=0

1205741119894Δ1198834119905minus119894 + 119901sum119894=0

1205961119894Δ1198835119905minus119894


Table2Re

sults

basedon

Ng-Perron

unitroot

test

Varia

bles

Level

Thefi

rstd

ifference

Thes

econ

ddifference

MZa

MZt

MSB

MPT

MZa

MZt

MSB

MPT

MZa

MZt

MSB

MPT

Eminus73

2lowastminus171

023

402


minus290

015

193


minus093

044

1062

X 1119

174

146

14521


minus310015

145

minus194minus09

7050

1246

X 2minus13


minus245

018

239


minus217022

270


minus250

019

208

X 3minus07

5lowastlowast041

055

2474


minus256

018

203


minus240

020

217

X 4minus46

8minus130

028

566

minus668lowast

minus181027

374


minus261

018

185

X 5minus22

3minus08

8039

969


minus238

018

252


minus330

015

116

Eminus217

minus097

044

3797

minus799minus179

023

1190

minus541

minus162030

1677

X 1minus316

minus107034

2485

minus041

minus025

061

8570

minus973minus22

1023

936

X 2minus36


minus425

012

270

minus1023

minus219021

920

minus1339

minus258

019

685

X 3minus16

68lowastminus28

7017

557

minus1387

minus258

019

687

minus1160

minus239

021

796

X 4minus133

1minus25

7019

691

minus675

minus182027

1350

minus1389

minus262

019

664

X5

minus048

minus020

041

4225

minus1415

minus260

018

683


minus334

015

408



trend

)1

level

minus1380

minus258

017

178

minus2380

minus342

014

403

5level

minus810minus198

023

317

minus1730

291

017

548

10level

minus570

minus162027

445

minus1420

minus262

018

667

Notelowast


tesig

nificance

atthe1

05and

1levels

respectiv

ely1198641198831119883211988331198834and1198835deno

tethelnform

ofele

ctric

itydemandpo

pulatio

nGDPecon

omicstr

uctureu

rbanization

and

energy

pricerespectiv

ely
















119864lin = minus71855 + 137541198831 + 032731198832 minus 113671198833+ 225401198834 (8)




000204060810121416



(a)

2000 2004 2008 2012 2015minus10

10

minus4minus2

minus6minus8

24

0

86


(b)





(9)




(10)













0

1

2

3

4

5

6

7

Elec

tric

ity en

ergy

cons

umpt

ion

(trill

ion

Kwh)

1994

1993

1995

2012

1990

1991

1992

1988

1987

1986

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

2014

2009

2013

1989

2015

1985

2010

2008

2011

Year










2016 2018 2020 2022 2024 2026 2028 20302

4

6

8

10

12

14


Year

82585

80322

11139

10758

13821

13302

Elec

tric

ity d

eman

d (t

rillio

n KW

H)



2016 2018 2020 2022 2024 2026 2028 20302

4

6

8

10

12

14

80605

78806

10661

10322

13067

12585

Year

Elec

tric

ity d

eman

d (t

rillio

n KW

H)






2016 2018 2020 2022 2024 2026 2028 20302

4

6

8

10

12

14

7921

7751

9956

12462

11994

Year

Elec

tric

ity d

eman

d (t

rillio

n KW

H)

1028






References




















































Journal of












Journal of







Volume 2018






Volume 2018














1985 1990 1995 2000 2005 2010 2015



0

1

2

3

4

5

Log

form

of v

aria

bles

minus1






Start





The best individual

The last individual

Yes

No

The next individual

Yes

The next generation

End

The last generation

No


Crossover


Mutation



119901119888 = 1199011198881 minus (1199011198881 minus 1199011198882) (119891


(5)




(6)






Δ119864119905 = 1205820 + 119901sum119894=1

1205751119894Δ119864119905minus119894 + 119901sum119894=0

1205761119894Δ1198831119905minus119894 + 119901sum119894=0

1206011119894Δ1198832119905minus119894+ 119901sum119894=0

1205931119894Δ1198833119905minus119894 + 119901sum119894=0

1205741119894Δ1198834119905minus119894 + 119901sum119894=0

1205961119894Δ1198835119905minus119894


Table2Re

sults

basedon

Ng-Perron

unitroot

test

Varia

bles

Level

Thefi

rstd

ifference

Thes

econ

ddifference

MZa

MZt

MSB

MPT

MZa

MZt

MSB

MPT

MZa

MZt

MSB

MPT

Eminus73

2lowastminus171

023

402


minus290

015

193


minus093

044

1062

X 1119

174

146

14521


minus310015

145

minus194minus09

7050

1246

X 2minus13


minus245

018

239


minus217022

270


minus250

019

208

X 3minus07

5lowastlowast041

055

2474


minus256

018

203


minus240

020

217

X 4minus46

8minus130

028

566

minus668lowast

minus181027

374


minus261

018

185

X 5minus22

3minus08

8039

969


minus238

018

252


minus330

015

116

Eminus217

minus097

044

3797

minus799minus179

023

1190

minus541

minus162030

1677

X 1minus316

minus107034

2485

minus041

minus025

061

8570

minus973minus22

1023

936

X 2minus36


minus425

012

270

minus1023

minus219021

920

minus1339

minus258

019

685

X 3minus16

68lowastminus28

7017

557

minus1387

minus258

019

687

minus1160

minus239

021

796

X 4minus133

1minus25

7019

691

minus675

minus182027

1350

minus1389

minus262

019

664

X5

minus048

minus020

041

4225

minus1415

minus260

018

683


minus334

015

408



trend

)1

level

minus1380

minus258

017

178

minus2380

minus342

014

403

5level

minus810minus198

023

317

minus1730

291

017

548

10level

minus570

minus162027

445

minus1420

minus262

018

667

Notelowast


tesig

nificance

atthe1

05and

1levels

respectiv

ely1198641198831119883211988331198834and1198835deno

tethelnform

ofele

ctric

itydemandpo

pulatio

nGDPecon

omicstr

uctureu

rbanization

and

energy

pricerespectiv

ely
















119864lin = minus71855 + 137541198831 + 032731198832 minus 113671198833+ 225401198834 (8)




000204060810121416



(a)

2000 2004 2008 2012 2015minus10

10

minus4minus2

minus6minus8

24

0

86


(b)





(9)




(10)













0

1

2

3

4

5

6

7

Elec

tric

ity en

ergy

cons

umpt

ion

(trill

ion

Kwh)

1994

1993

1995

2012

1990

1991

1992

1988

1987

1986

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

2014

2009

2013

1989

2015

1985

2010

2008

2011

Year










2016 2018 2020 2022 2024 2026 2028 20302

4

6

8

10

12

14


Year

82585

80322

11139

10758

13821

13302

Elec

tric

ity d

eman

d (t

rillio

n KW

H)



2016 2018 2020 2022 2024 2026 2028 20302

4

6

8

10

12

14

80605

78806

10661

10322

13067

12585

Year

Elec

tric

ity d

eman

d (t

rillio

n KW

H)






2016 2018 2020 2022 2024 2026 2028 20302

4

6

8

10

12

14

7921

7751

9956

12462

11994

Year

Elec

tric

ity d

eman

d (t

rillio

n KW

H)

1028






References




















































Journal of












Journal of







Volume 2018






Volume 2018









Start





The best individual

The last individual

Yes

No

The next individual

Yes

The next generation

End

The last generation

No


Crossover


Mutation



119901119888 = 1199011198881 minus (1199011198881 minus 1199011198882) (119891


(5)




(6)






Δ119864119905 = 1205820 + 119901sum119894=1

1205751119894Δ119864119905minus119894 + 119901sum119894=0

1205761119894Δ1198831119905minus119894 + 119901sum119894=0

1206011119894Δ1198832119905minus119894+ 119901sum119894=0

1205931119894Δ1198833119905minus119894 + 119901sum119894=0

1205741119894Δ1198834119905minus119894 + 119901sum119894=0

1205961119894Δ1198835119905minus119894


Table2Re

sults

basedon

Ng-Perron

unitroot

test

Varia

bles

Level

Thefi

rstd

ifference

Thes

econ

ddifference

MZa

MZt

MSB

MPT

MZa

MZt

MSB

MPT

MZa

MZt

MSB

MPT

Eminus73

2lowastminus171

023

402


minus290

015

193


minus093

044

1062

X 1119

174

146

14521


minus310015

145

minus194minus09

7050

1246

X 2minus13


minus245

018

239


minus217022

270


minus250

019

208

X 3minus07

5lowastlowast041

055

2474


minus256

018

203


minus240

020

217

X 4minus46

8minus130

028

566

minus668lowast

minus181027

374


minus261

018

185

X 5minus22

3minus08

8039

969


minus238

018

252


minus330

015

116

Eminus217

minus097

044

3797

minus799minus179

023

1190

minus541

minus162030

1677

X 1minus316

minus107034

2485

minus041

minus025

061

8570

minus973minus22

1023

936

X 2minus36


minus425

012

270

minus1023

minus219021

920

minus1339

minus258

019

685

X 3minus16

68lowastminus28

7017

557

minus1387

minus258

019

687

minus1160

minus239

021

796

X 4minus133

1minus25

7019

691

minus675

minus182027

1350

minus1389

minus262

019

664

X5

minus048

minus020

041

4225

minus1415

minus260

018

683


minus334

015

408



trend

)1

level

minus1380

minus258

017

178

minus2380

minus342

014

403

5level

minus810minus198

023

317

minus1730

291

017

548

10level

minus570

minus162027

445

minus1420

minus262

018

667

Notelowast


tesig

nificance

atthe1

05and

1levels

respectiv

ely1198641198831119883211988331198834and1198835deno

tethelnform

ofele

ctric

itydemandpo

pulatio

nGDPecon

omicstr

uctureu

rbanization

and

energy

pricerespectiv

ely
















119864lin = minus71855 + 137541198831 + 032731198832 minus 113671198833+ 225401198834 (8)




000204060810121416



(a)

2000 2004 2008 2012 2015minus10

10

minus4minus2

minus6minus8

24

0

86


(b)





(9)




(10)













0

1

2

3

4

5

6

7

Elec

tric

ity en

ergy

cons

umpt

ion

(trill

ion

Kwh)

1994

1993

1995

2012

1990

1991

1992

1988

1987

1986

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

2014

2009

2013

1989

2015

1985

2010

2008

2011

Year










2016 2018 2020 2022 2024 2026 2028 20302

4

6

8

10

12

14


Year

82585

80322

11139

10758

13821

13302

Elec

tric

ity d

eman

d (t

rillio

n KW

H)



2016 2018 2020 2022 2024 2026 2028 20302

4

6

8

10

12

14

80605

78806

10661

10322

13067

12585

Year

Elec

tric

ity d

eman

d (t

rillio

n KW

H)






2016 2018 2020 2022 2024 2026 2028 20302

4

6

8

10

12

14

7921

7751

9956

12462

11994

Year

Elec

tric

ity d

eman

d (t

rillio

n KW

H)

1028






References




















































Journal of












Journal of







Volume 2018






Volume 2018









Table2Re

sults

basedon

Ng-Perron

unitroot

test

Varia

bles

Level

Thefi

rstd

ifference

Thes

econ

ddifference

MZa

MZt

MSB

MPT

MZa

MZt

MSB

MPT

MZa

MZt

MSB

MPT

Eminus73

2lowastminus171

023

402


minus290

015

193


minus093

044

1062

X 1119

174

146

14521


minus310015

145

minus194minus09

7050

1246

X 2minus13


minus245

018

239


minus217022

270


minus250

019

208

X 3minus07

5lowastlowast041

055

2474


minus256

018

203


minus240

020

217

X 4minus46

8minus130

028

566

minus668lowast

minus181027

374


minus261

018

185

X 5minus22

3minus08

8039

969


minus238

018

252


minus330

015

116

Eminus217

minus097

044

3797

minus799minus179

023

1190

minus541

minus162030

1677

X 1minus316

minus107034

2485

minus041

minus025

061

8570

minus973minus22

1023

936

X 2minus36


minus425

012

270

minus1023

minus219021

920

minus1339

minus258

019

685

X 3minus16

68lowastminus28

7017

557

minus1387

minus258

019

687

minus1160

minus239

021

796

X 4minus133

1minus25

7019

691

minus675

minus182027

1350

minus1389

minus262

019

664

X5

minus048

minus020

041

4225

minus1415

minus260

018

683


minus334

015

408



trend

)1

level

minus1380

minus258

017

178

minus2380

minus342

014

403

5level

minus810minus198

023

317

minus1730

291

017

548

10level

minus570

minus162027

445

minus1420

minus262

018

667

Notelowast


tesig

nificance

atthe1

05and

1levels

respectiv

ely1198641198831119883211988331198834and1198835deno

tethelnform

ofele

ctric

itydemandpo

pulatio

nGDPecon

omicstr

uctureu

rbanization

and

energy

pricerespectiv

ely
















119864lin = minus71855 + 137541198831 + 032731198832 minus 113671198833+ 225401198834 (8)




000204060810121416



(a)

2000 2004 2008 2012 2015minus10

10

minus4minus2

minus6minus8

24

0

86


(b)





(9)




(10)













0

1

2

3

4

5

6

7

Elec

tric

ity en

ergy

cons

umpt

ion

(trill

ion

Kwh)

1994

1993

1995

2012

1990

1991

1992

1988

1987

1986

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

2014

2009

2013

1989

2015

1985

2010

2008

2011

Year










2016 2018 2020 2022 2024 2026 2028 20302

4

6

8

10

12

14


Year

82585

80322

11139

10758

13821

13302

Elec

tric

ity d

eman

d (t

rillio

n KW

H)



2016 2018 2020 2022 2024 2026 2028 20302

4

6

8

10

12

14

80605

78806

10661

10322

13067

12585

Year

Elec

tric

ity d

eman

d (t

rillio

n KW

H)






2016 2018 2020 2022 2024 2026 2028 20302

4

6

8

10

12

14

7921

7751

9956

12462

11994

Year

Elec

tric

ity d

eman

d (t

rillio

n KW

H)

1028






References




















































Journal of












Journal of







Volume 2018






Volume 2018























119864lin = minus71855 + 137541198831 + 032731198832 minus 113671198833+ 225401198834 (8)




000204060810121416



(a)

2000 2004 2008 2012 2015minus10

10

minus4minus2

minus6minus8

24

0

86


(b)





(9)




(10)













0

1

2

3

4

5

6

7

Elec

tric

ity en

ergy

cons

umpt

ion

(trill

ion

Kwh)

1994

1993

1995

2012

1990

1991

1992

1988

1987

1986

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

2014

2009

2013

1989

2015

1985

2010

2008

2011

Year










2016 2018 2020 2022 2024 2026 2028 20302

4

6

8

10

12

14


Year

82585

80322

11139

10758

13821

13302

Elec

tric

ity d

eman

d (t

rillio

n KW

H)



2016 2018 2020 2022 2024 2026 2028 20302

4

6

8

10

12

14

80605

78806

10661

10322

13067

12585

Year

Elec

tric

ity d

eman

d (t

rillio

n KW

H)






2016 2018 2020 2022 2024 2026 2028 20302

4

6

8

10

12

14

7921

7751

9956

12462

11994

Year

Elec

tric

ity d

eman

d (t

rillio

n KW

H)

1028






References




















































Journal of












Journal of







Volume 2018






Volume 2018










000204060810121416



(a)

2000 2004 2008 2012 2015minus10

10

minus4minus2

minus6minus8

24

0

86


(b)





(9)




(10)













0

1

2

3

4

5

6

7

Elec

tric

ity en

ergy

cons

umpt

ion

(trill

ion

Kwh)

1994

1993

1995

2012

1990

1991

1992

1988

1987

1986

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

2014

2009

2013

1989

2015

1985

2010

2008

2011

Year










2016 2018 2020 2022 2024 2026 2028 20302

4

6

8

10

12

14


Year

82585

80322

11139

10758

13821

13302

Elec

tric

ity d

eman

d (t

rillio

n KW

H)



2016 2018 2020 2022 2024 2026 2028 20302

4

6

8

10

12

14

80605

78806

10661

10322

13067

12585

Year

Elec

tric

ity d

eman

d (t

rillio

n KW

H)






2016 2018 2020 2022 2024 2026 2028 20302

4

6

8

10

12

14

7921

7751

9956

12462

11994

Year

Elec

tric

ity d

eman

d (t

rillio

n KW

H)

1028






References




















































Journal of












Journal of







Volume 2018






Volume 2018

















0

1

2

3

4

5

6

7

Elec

tric

ity en

ergy

cons

umpt

ion

(trill

ion

Kwh)

1994

1993

1995

2012

1990

1991

1992

1988

1987

1986

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

2014

2009

2013

1989

2015

1985

2010

2008

2011

Year










2016 2018 2020 2022 2024 2026 2028 20302

4

6

8

10

12

14


Year

82585

80322

11139

10758

13821

13302

Elec

tric

ity d

eman

d (t

rillio

n KW

H)



2016 2018 2020 2022 2024 2026 2028 20302

4

6

8

10

12

14

80605

78806

10661

10322

13067

12585

Year

Elec

tric

ity d

eman

d (t

rillio

n KW

H)






2016 2018 2020 2022 2024 2026 2028 20302

4

6

8

10

12

14

7921

7751

9956

12462

11994

Year

Elec

tric

ity d

eman

d (t

rillio

n KW

H)

1028






References




















































Journal of












Journal of







Volume 2018






Volume 2018









2016 2018 2020 2022 2024 2026 2028 20302

4

6

8

10

12

14


Year

82585

80322

11139

10758

13821

13302

Elec

tric

ity d

eman

d (t

rillio

n KW

H)



2016 2018 2020 2022 2024 2026 2028 20302

4

6

8

10

12

14

80605

78806

10661

10322

13067

12585

Year

Elec

tric

ity d

eman

d (t

rillio

n KW

H)






2016 2018 2020 2022 2024 2026 2028 20302

4

6

8

10

12

14

7921

7751

9956

12462

11994

Year

Elec

tric

ity d

eman

d (t

rillio

n KW

H)

1028






References




















































Journal of












Journal of







Volume 2018






Volume 2018
























































Journal of












Journal of







Volume 2018






Volume 2018








Energy Demand Forecasting: Combining Cointegration ...

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