Title Science and Technology Indonesia e-ISSN:2580-4391 p-ISSN:2580-4405 Vol. 7, No. 2, April 2022 Research Paper Dynamic Modeling and Forecasting Data Energy Used and Carbon Dioxide (CO2) Edwin Russel1,5, Wamiliana2*, Nairobi3, Warsono2, Mustofa Usman2, Jamal I. Daoud4 1Department of Management, Faculty of Economics & Business, Universitas Lampung, 35145, Indonesia2Department of Mathematics, Faculty of Mathematics and Sciences, Universitas Lampung, 35145, Indonesia3Department of Development Economics, Faculty of Economics & Business, Universitas Lampung, 35145, Indonesia4Department of Science in Engineering, Kulliyyah of Engineering, International Islamic University Malaysia, 50728, Malaysia5Doctoral Student, Department of Mathematics, Faculty of Mathematics and Sciences, Universitas Lampung, 35145, Indonesia *Corresponding author: wamiliana.1963@fmipa.unila.ac.id AbstractThe model of Vector Autoregressive (VAR) with cointegration is able to be modified by Vector Error Correction Model (VECM). Becauseof its simpilicity and less restrictions the VECM is applied in many studies. The correlation among variables of multivariate time seriesalso can be explained by VECM model, which can explain the effect of a variable or set of variables on others using Granger Causality,Impulse Response Function (IRF), and Forecasting. In this study, the relationship of Energy Used and CO2 will be discussed. Thedata used here were collected over the year 1971 to 2018. Based on the comparison of some criteria: Akaike Information CriterionCorrected (AICC), Hannan-Quin Information Criterion (HQC), Akaike Information Criterion (AIC) and Schwarz Bayesian Criterion(SBC) for some VAR(p) model with p= 1,2,3,4,5, the best model with smallest values of AICC, HQC, AIC and SBC is at lag 2 (p= 2). Thenthe best model found is VECM (2) and further analysis such as Granger Causality, IRF, and Forecasting will be based on this model. KeywordsCarbon Dioxide (CO2), Energy Used, Cointegration, VAR Model, VECM Model Received: 5 January 2022, Accepted: 2 April 2022 https://doi.org/10.26554/sti.2022.7.2.228-237 1. INTRODUCTION Currently, studies on the phenomenon of global warming caused by the use of fossil fuels, Energy Used, the use of elec- tricity consumption, and the increment of the steel industry have been conducted by many scientists (Anjana and Kandpal, 1997; Sakamoto and Tonooka, 2000; Di Lorenzo et al., 2013; Aye and Edoja, 2017; Balsalobre et al., 2018; Mahmood et al., 2019; Wasti and Zaidi, 2020; Munir et al., 2020). Developed countries have sought to reduce the amount of CO2 emissions (known as one of the representative greenhouse gases) (UN UNCED, 1992; UN UNCED, 1996; Mahmood et al., 2019). Developed countries that use a lot of fossil fuels, use more electricity to produce CO2 emissions, for example, Japan con- tributed about 5% of world CO2 emissions in 1990 (OECD, 2005). Since the era of the industrial revolution began in the early 19th century, the growth in the use of fuels (fossil), the discovery and increasing of electricity consumption, and the increase in the steel industry have caused substantial climate change and global warming. CO2 emissions to the atmosphere have caused an increase in the greenhouse eect and caused the surface tem- perature of the earth to increase (EPA, 2017). Therefore, in- dustrialization growth, intensive use of fossil fuels, and electric- ity use have damaged the environment and stimulated global warming (Dong et al., 2018; Al Araby, 2019). Carbon Dioxide (CO2) is considered to be one of the most dominant causes of increasing global warming and climate change (IPCC, 2014; Al Araby, 2019; Hasnisah et al., 2019). Increasing energy use and concerns about global warming and climate change, have encouraged many developed countries and companies to apply strategies in order to cut energy use and increase clean energy production (Benedetti et al., 2017; Faizah, 2018). Economic growth in many developed countries is closely related to increasing CO2 emissions (Mirza and Kanwal, 2017; Charfeddine, 2017; Hanif, 2018). Increased CO2 emissions are positively correlated with energy consumption, the use of fossil fuels and electricity, which causes an increase in pollution. Thus, manydeveloped countries have targeted using renewable energy sources to reduce CO2 emissions in an eort to reduce pollution (Balogh and Jámbor, 2017; Ito, 2017; Balsalobre et al., 2018). Abolhosseini et al. (2014) have investigated the eect of renewable energy on reducing the emission of CO2. The studies about the correlation between the emission of CO2 and the use of electricity have been conducted by many https://crossmark.crossref.org/dialog/?doi=10.26554/sti.2022.7.2.228-237&domain=pdf https://doi.org/10.26554/sti.2022.7.2.228-237 Russel et. al. Science and Technology Indonesia, 7 (2022) 228-237 scientists, including (Tamba et al., 2017; Bah and Azam, 2017; Akpan and Akpan, 2012). The VAR or VECM model for modeling energy and eco- nomics have been used by many researchers because of too many problems concerning energy, climate change, CO2 and renewable energy (Forero, 2019; Warsono et al., 2019a, War- sono et al., 2019b; Wang et al., 2018; Ito, 2017). The used of VECM modeling to nd the correlation between food price in- dex and crude oil price had been investigated by Aynur (2013). Yu et al. (2006) investigated the correlation between the price of vegetable oil and higher crude oil using causality approach and cointegration. The correlation and Forecasting between index’s prices coal of two coal companies using VAR model was discussed by Warsono et al. (2019a). In order to analyze macroeconomic data, Sims (1980) in- troduced VAR model. In economy and nance, VAR model plays an important role (Kirchgässner et al., 2012; Hamilton, 1994). VAR model are natural tool for Forecasting (Lütkepohl, 2013). Vector Error Correction Model (VECM) will be used by modifying VAR model if the data has cointegration. If the variables have a common stochastic’s trend, then theyare called cointegrated (Engle and Granger, 1987; Granger, 1981). The VAR model is not convenient to be used if cointegration occurs in the variables. In this case specic parameterizations will be considered, and VECM is the commonly used model to elaborate the cointegration among the variables. There are a lot of researchs that have been done concerning the eect on Forecasting by cointegration (Lütkepohl, 2005; Campiche et al., 2007; Yu et al., 2008; Hunter et al., 2017). The comparison the forecasts generated from an estimated VECM model by assuming that the cointegrating rank and the lag order are known, with those from an estimated Vector Autoregressive (VAR) model in levels with the correct lag was investigatedbyEngleandYoo(1987). Theresult is thatVECM model is better than VAR model, because VECM allows us to explain the correlation of the long-run and the short-run of nonstationary variables. The aim of this research is to explain the patterns of the relationship between Carbon Dioxide (CO2) and Energy Used using VECM approach in an Indonesian case. Studies on mod- eling the correlation between CO2 and Energy Used using multivariate time series data by means of VECM modeling are relatively rare. Therefore, this study is an attempt to ll this gap by analyzing the data Energy Used and Carbon Dioxide (CO2) using VECM approach. 2. THE METHOD In this study, the method to analyze the data Energy Used and Carbon Dioxide (CO2) is a VECM model, with the following steps: rst, the assumptions stationary data will be checked; second, the optimal lag will be determined for the Vector Au- toregression (VAR) model using the AICC, HQC, AIC, and BSC criterion information; third, after the optimal lag has been obtained, the cointegration test will be carried out by using the Johansen test; fourth, after obtaining rank cointegration, the VECM model is built. Based on the best VECM model ob- tained, the analysis of IRF, Granger Causality and Forecasting is carried out (Hamilton, 1994; Lütkepohl, 2005; Tsay, 2014; Wei, 2019). 2.1 Dynamic Modeling In studying time series data, we often face with many variables, Yit, where i= 1, 2, ..., p and the data are taken in a sequence of time, t. Let Yt= [Y1t, Y2t, ..., Ypt]’, where Yit is the ith component variable at time t and it is a random variable for each i and t (Wei, 2019). Because most of standard method of statistical theory on random samples are not applicable, so dierent methods are needed (Tsay, 2014; Wei, 2019). In decision making, we need to get accurate prediction of those variables, and it require understanding the relationships among those variables. It is assuming that the data is stationar. By checking the plot of the data we know the stationary of the data. If the data are uctuating around certain number then it is stationary, if not then the data are nonstationary. Besides, we also can use Augmented Dickey-Fuller (ADF) test. Autocorrelation Function (ACF) graph also can be used. The ADF-test with lag-p, is dened as: ΔYt = 𝛼 + 𝜙Yt−1 + p−1∑︁ i=1 𝜙i ∗ ΔYt−i + ut (1) ΔYt= Yt-Yt−1 and ut is white noise. Ho: 𝜙= 0 is the null hypothesis, and Ha: 𝜙<0 is the alternative hypothesis, 𝛼= 0.05 is level of signicance. If 𝜏<-2.57, then it rejects Ho, or if the p value<0.05 (Tsay, 2005; Brockwell and Davis, 2002). The test statistic is ADF 𝜏 = 𝜙 Se(𝜙) (2) 2.2 Cointegration Granger(1983) whorst statedthetermcointegration. Granger (1983) has investigated of how the relationship between coin- tegration and modeling with error correction. This study has attracted much attention in econometric, nancial and in vari- ous elds of science involving multivariate time series data that has a cointegration between variables (Johansen, 1995; Engle and Granger, 1987). Over the past 25 years, this approach has contributed a lot to various scientic studies, for example in the elds of nance, business, and environment. Cointegration is the key concepts of in econometrics and modern time series analysis. Thedevelopmentofmethodof inferential andestimation is given by Johansen (1988). In general, Yt is nonstationary with order d, I(d) process, if (1-B)dYt= Zt , where Zt is stationary and invertable (Mittnik et al., 2007; Tsay, 2005, Tsay, 2014). If there is a cointegration, then the rank of the cointegration should be tested (Tsay, 2005; Tsay, 2014), and to test the rank © 2022 The Authors. Page 229 of 237 Russel et. al. Science and Technology Indonesia, 7 (2022) 228-237 of cointegration we can use Trace test and test of maximum eigenvalues. For Trace test, the null hypothesis: there are at most r positive eigenvalues, and the test: Tr(r) = −T k∑︁ i=r+1 ln(1 − _̂ i) (3) The test for maximum eigen value: the null hypothesis: there are r positive eigen values, and the test statistics: _max(r, r + 1) = −T ln(1 − _̂ i) (4) _̂ i=estimateofeigenvalue,T=totalnumberofobservations, and k= total number of endogeneous variables. 2.3 Vector Autoregressive In the modeling with Vector Autoregressive (VAR) models means that the future values of the process are weighted sum of present and past values with some noises (Mittnik et al., 2007). Tsay (2014) and Wei (2019) stated that this model is used comprehensively in business, nancial and econometric studies because: (1) the model is easy to estimate; (2) the VAR model have been investigated expansively in the literature (Warsono et al., 2019a, Warsono et al., 2019b; Wei, 2006; Lütkepohl, 2005; Lütkepohl,2013), and(3) VectorAutoregressionmodels in multivariate analysis are like multivariate linear regression. The k-dimensional VAR process with order p, VAR(p) is: Yt = `0 + Φ1Yt−1 + ..... + ΦpYp + ut (5) or Φp(B)Yt = `0 + ut (6) Where ut is k-dimensional vector white noise process with mean vector 0kxl and variance covariance matrix ∑ , VWN(0,∑ ), Φp(B) = I − Φ1B − ... − ΦpBp. (7) If the roots of |𝛾pI-𝛾p−1Φ1- ...-Φp|= 0 are all lie inside the unit circle, then VAR model is invertible and it will be stationary. 2.4 Vector Error Correction Model A modied VAR model which has cointegration among the variables. If r≤k is the rank of cointegration, p is the lag of endogeneous variable, the general form of VECM(p) is: ΔYt = ΠYt−1 + p−1∑︁ i=1 ΓiΔYt−i + ut (8) Some advantages of VECM(p) model’s applications: (1) The multicollinearity is reduced, (2) All information about long-run impacts is summarized in the level matrix (denoted by Π), (3) The easier of the interpretation of estimates, and (4) VECM model is easier to interprete (Juselius, 2006). The criteria of information AIC, SBC, are used to nd the best model of VECM(p). 2.5 Normality Test To check the normality of residual, the Jarque-Bera (JB) test is used. Besides, the residuals plot’s performance will be consid- ered. The JB Test is: JB = n − k 6 [ S2 + (K-3)2 4 ] (9) where: n = Number of Samples S = Expected Skewness = 1 n ∑n i=1(Yi − Ȳ) 3 ( 1n ∑n i=1(Yi − Ȳ)2)3/2 (10) K = Expected Excess Kurtosis = 1 n ∑n i=1(Yi − Ȳ) 4 ( 1n ∑n i=1(Yi − Ȳ)2)2 (11) k = The Number of Independent Variables Jarque-Bera test has x2 distribution (Jarque and Bera, 1987). 2.6 Test for Granger Causality Many researchers have argued concerning the meaning and nature of causality, and the important role of casuality in the study economic (Sampson, 2001). Consider a VAR(p) model (Wei, 2019). Φp(B)Yt = \0 + ut (12) The vector Yt is partitioned into two components, Yt=��Y ′it,Y ′2t��’, then the Equation (12) can be written as:[ Φ11(B) Φ12(B) Φ21(B) Φ22(B) ] [ Y1t Y2t ] = [ \1 \2 ] + [ u1t u2t ] (13) If the value of Φ12(B)= 0, then Equation (13) can be written as follows: Φ12(B)Y1t = \1 + u1t Φ22(B)Y2t = \2 + Φ21(B)Y1t + u2t (14) The interpretation is as follows: the future values of Y2t are impacted by its own past and the past of Y1t. The future values of Y1t are impacted by its own past. This idea is called as the Granger Causality, because it is rst introduced by Granger (1969). © 2022 The Authors. Page 230 of 237 Russel et. al. Science and Technology Indonesia, 7 (2022) 228-237 2.7 Impulse Response Function Consider the VAR model as follows (Hamilton, 1994): Yt = ` + `t + Ψ1ut−1 + Ψ2ut−2 + ..... The interpretation of matrix Ψs is as follows: 𝜕Yt+s 𝜕Y′t = Ψs. If the value of ut is changed by 𝛿1, at the same time ut−1 is changed by 𝛿2, ..., and the ut−n is changed by 𝛿n, so that the combined impact to the value of vector Yt+s is as follows: ΔYt+s = 𝜕Yt+s 𝜕Y1t 𝛿1 + 𝜕Yt+s 𝜕Y2t 𝛿2 + ... + 𝜕Yt+s 𝜕Ynt 𝛿n = Ψs𝛿 (15) Where 𝛿=(𝛿1, 𝛿2, ..., 𝛿n)’andthegraphof therow i, column j element of Ψs 𝜕Yi,t+s 𝜕Y jt as a function of s is called Impulse Response Function. 3. RESULTS AND DISCUSSION To analysis the data Energy Used and CO2, the SAS program is used (SAS/ETS 13.2, 2014). The assumption of stationarity will be checked by: (1) evaluate the behavior of the plot of data, (2) ACF plot of data, and (3) Augmented Dickey Fuller test. The data used in this research are the use of Energy (ENR) and Carbone Dioxide (CO2) emission. The plot of the data is shown in Figure 1. Figure 1. Plot of Energy Used (ENR) and CO2 Emission Table 1. Unit Roots Test orADFTest forEnergyUsed and CO2 Variable Type Lags Rho p-Value Tau p-Value Energy (ENR) Zero Mean 2 0.8776 0.8835 3.30 0.9996 Single Mean 2 -0.0717 0.9497 -0.12 0.9401 Trend 2 -8.2149 0.5260 -1.90 0.6384 CO2 Zero Mean 2 1.4082 0.9545 2.80 0.9983 Single Mean 2 0.5399 0.9752 0.49 0.9843 Trend 2 -9.9202 0.3909 -1.82 0.6779 Figure 2. Trend and Correlation Analyisis of Energy Used (ENR) Figure 3. Trend and Correlation Analysis of CO2 From Figure 1, we can see that Energy Used and CO2 emission, the trend are increase and uctuative. Figure 2 and 3 the plot of Autocorrelation Function (ACF) for Energy and CO2 the autocorrelations are decrease veryslowly. From Table 1, ADF test for Energy (ENR) and CO2 the Tau-test for single mean at lag 2 not signicant with p-values= 0.9401 and 0.9843, respectively. These means that Energy Used and CO2 are non-stationary. To attain the stationary data, the dierencing method is used. Figure 4. Trend and Correlation Analyisis of Energy Used after Dierencing, d=1 From Figures 4 and 5 of data ENR and CO2 after dif- ferencing with d= 1, the data are uctuated around certain © 2022 The Authors. Page 231 of 237 Russel et. al. Science and Technology Indonesia, 7 (2022) 228-237 Figure 5. Trend and Correlation Analyisis of CO2 after Dierencing, d=1 Table 2. ADF Unit Roots Test of Energy (ENR) and CO2 after Dierencing, d=1 Variable Type Lags Rho p-Value Tau p-Value Energy (ENR) Zero Mean 2 -51.8104 <0.0001 -3.42 0.0011 Single Mean 2 -1962.80 0.0001 -4.57 0.0007 Trend 2 320.6803 0.9999 -4.66 0.0030 CO2 Zero Mean 2 -14.7087 0.0050 -2.33 0.0205 Single Mean 2 -98.1031 0.0003 -4.50 0.0008 Trend 2 -98.1986 <0.0001 -4.43 0.0055 number, the data are stationary. The ADF test for data ENR and CO2 the Tau-test= -4.57 with p-value= 0.0007, Tau-test= -4.57 with p-value= 0.0008, respectively. Thus, after the rst dierencing, the data ENR and CO2 are stationary. 3.1 Test for Lag Optimum By using criteria AIC, SBC, HQC and AICC, we nd the best VAR model from endogeneous variables that are ENR and CO2, where the results are as follows: Table 3. Criteria to Select of Lag VAR Model for All Endoge- neous Variables VAR(p) Lag Order Selection Criteria Criteria VAR(1) VAR(2) VAR(3) VAR(4) VAR(5) AICC -10.9638 -11.2889* -11.0036 -10.7606 -10.5612 HQC -10.8947 -11.2045* -10.9383 -10.7620 -10.6956 AIC -10.9857 -11.3567* -11.1520 -11.0375 -11.0329 SBC -10.7375 -10.9387* -10.5609 -10.2697 -10.0848 From Table 3, at lag 2, the smallest information criteria (*) of AICC, AIC, and HQC occur. Thus, the test of cointegration is conducted at lag 2. 3.2 Test for Cointegration Table 4 is the result of cointegration testing with the null hy- pothesis: rank= r, no cointegration with the alternative: rank>r, there is cointegration. From Table 4 we can conclude that the test results are that rank>r= 1, or rank r= 2. Based on these results, the VECM model with cointegration rank= 2 will be used. 3.3 The Estimation of Parameters VECM(2) Model Based on the above analysis, we have chosen the model for Energy Used (ENR) and CO2 data is VECM(2) with the coin- tegration rank= 2 as the best model. Table 5 is the estimate parameter of (𝛽), the long-run parameter Beta Estimate. Table 6 give an estimate parameter (𝛼), Adjustment Coecient Alpha Estimates, and Table 7 give the estimate parameter Π= 𝛼*𝛽 ’. The estimate parameters of VECM(2) is: ΔYt = ΠYt−1 + Γ1ΔYt−1 + Yt (16) Δ [ Yt ] = [ −0.7393 0.0355 4.5149 −1.6776 ] Yt−1+[ −0.1151 −0.0130 −3.1509 0.6297 ] ΔYt−1 + [ Yt1 Yt2 ] (17) Figure 6. Prediction Error Normality for Energy (ENR) Figure 7. Prediction Error Normality for CO2 3.4 Normality of Residual Table 9 is the result of testing with the null hypothesis: the residuals are not correlated. The results for models AR(1), AR(1,2), AR(1,2,3) and AR(1,2,3,4), the null hypothesis was not rejected. So the residuals are not correlated. Table 10 is the result of the normality distribution test for residual ENR and CO2 data, the results show that the JB test for both ENR and CO2 data is rejected with p-value<0.0001. So the residuals are not normally distributed. However, if we look at the results © 2022 The Authors. Page 232 of 237 Russel et. al. Science and Technology Indonesia, 7 (2022) 228-237 Table 4. Cointegration Rank Test Using Trace Statistics H0:Rank= r H1:Rank>r Eigenvalue Trace p-Value Drift in ECM Drift in Process 0 0 0.6653 67.5644 <0.0001 Constant Linear 1 1 0.4250 22.6894 <0.0001 Table 5. The Long-Run Parameter Beta Estimate (𝛽) when Rank= 2 Variable 1 2 ENR(3) -3.04277 15.87431 CO2 1.00000 1.00000 Table 6. Adjustment Coecient Alpha (𝛼) Estimates when Rank= 2 Variable 1 2 ENR(3) 0.06894 -0.03336 CO2 -1.64649 -0.03118 of Figures 6 and 7, it shows that the residual distribution for the ENR and CO2 data is not far enough from the normal distribution. Table 10 also shows that the ARCH eect where the results conclude that there is no ARCH eect with p-values for ENR and CO2 data are 0.4890 and 0.8696, respectively. 3.5 Test for Stability Model Table 11 is the result of the analysis of the root AR charac- teristic polynomial and it is found that all modulus<1. So the VECM(2) model has high stability. 3.6 Test for The Fitness of Model Model VECM(2) given in (17) can be written as follows: ΔYt1 = −0.7393Yt1−1 + 0.0355Yt2−1 − 0.1151Yt1−1− 0.0130Yt2−1 + Yt1 (18) ΔYt2 =4.5142Yt1−1 − 1.6776Yt2−1 − 3.1509Yt1−1+ 0.6297Yt2−1 + Yt2 (19) The VECM(2) model in Equation (17) if described in the form of two univariate models with dependent variables ENR and CO2 (model (18) and model (19)), respectively. Table 12 is a test of signicance for models (18) and (19) and both models are signicant with p-values of 0.0001 and <0.0001. The R-square for ENR is 0.4258, this means that 42.58% the variance of ENR is explained by the model (18) and the R- square forCO2 is0.7115. Thismeans that71.15%thevariance of CO2 is explained by the model (19). Table 7. The Estimate Parameter Π= 𝛼*𝛽 ’ Variable ENR(3) CO2 ENR(3) -0.73932 0.03558 CO2 4.51488 -1.67767 Table 8. Model Parameter Estimates Equation Parameter Estimate Standard Error t Value p- Value Variable D_ENR AR1_1_1 -0.73932 0.20510 ENR(t-1) AR1_1_2 0.03558 0.03844 CO2(t-1) AR2_1_1 -0.11508 0.15586 -0.74 0.4650 D_ENR(t-1) AR2_1_2 -0.01300 0.02941 -0.44 0.6611 D_CO2(t-1) D_CO2 AR1_2_1 4.51488 1.02976 ENR(t-1) AR1_2_2 -1.67767 0.19301 CO2(t-1) AR2_2_1 -3.15094 0.78252 -4.03 0.0003 D_ENR(t-1) AR2_2_2 0.62977 0.14766 4.26 0.0001 D_CO2(t-1) 3.7 Analysis Granger-Causality One of a key question about VAR model or VECM model is how useful some variables are for Forecasting others, and this question usually addressed when we study about the relation- ship and Forecasting among economic variables (Hamilton, 1994). The null hypothesis of the Granger Causality test is that Group 1 is induced only by itself and not by Group 2 (SAS/ETS 13.2, 2014). Figure 8. Impulse Response Function for Shock in Variabel Energy (ENR) Table13showsthat theENRasGroup1andCO2 asGroup 2 (test 1). The result with Chi-square test=1.09 with p-value is 0.5808>0.05, thus we can conclude that there is no evidence to reject the null hypothesis. Therefore, ENR is induced by itself and not by CO2. This means that past information on CO2 does not aect current Energy Used (ENR). From the test © 2022 The Authors. Page 233 of 237 Russel et. al. Science and Technology Indonesia, 7 (2022) 228-237 Table 9. Univariate Model AR Diagnostics Variable AR1 AR2 AR3 AR4 F Value p-value F Value p-value F Value p-value F Value p-value ENR 1.17 0.2861 2.19 0.1264 2.48 0.0777 1.70 0.1745 CO2 0.35 0.5594 0.21 0.8077 0.15 0.9316 0.41 0.8031 Table 10. Univariate Model White Noise Diagnostics Variable Durbin Watson Normality ARCH Chi-Square p-Value F Value p-Value ENR 2.02723 21.81 <0.0001 0.49 0.4890 CO2 2.12368 93.22 <0.0001 0.03 0.8696 Table 11. Test for Stability Model Index Real Imaginary Modulus Radian Degree 1 0.54588 0.00000 0.5459 0.0000 0.0000 2 -0.07088 0.82042 0.8235 1.6570 94.9380 3 -0.07088 -0.82042 0.8235 -1.6570 -94.9380 4 -0.30641 0.00000 0.3064 3.1416 180.0000 results for test 2 shows that the CO2 as Group 1 and ENR as Group 2, the results show where Chi-square test= 21.78 with p-value is <0.0001, the null hypothesis is rejected. Therefore, CO2 is inuenced not only by past information from itself (CO2), but also by information of the past of Energy Used (ENR). So, there is Granger Causal of ENR to CO2. Figure 9. Impulse Response Function for Shock in Variabel CO2 3.8 Impulse Response Function (IRF) Figure 8 is the graph of Impulse Response Function if there is a shock 1 standard deviation in ENR and its eect to the variable ENR and CO2. If there is a shock of one standard deviation inENR, this causes theENRgives responsepositively for the rst four years and after that the eect getting smaller and smaller. The response of ENR itself from the rst year Table 12. Test for Signicant of The Model Variable R-Square Standard Deviation F Value p-Value ENR 0.4258 0.02513 9.14 0.0001 CO2 0.7115 0.12619 30.42 <0.0001 to the fourth year are: 0.1456, 0.1671, 0.1329, and 0.0738, respectively. If there is a shock of one standard deviation in ENR, this causes the CO2 gives response uctuatively from the rst year up to the twelf year, in the rst and second year the response are positive, the three and fourth year the response are negative, in the fth and sixth year the response are positive. In the seventh and eight year the responses are negative. After the tenth year the impact are getting smaller toward to the equilibrium condition. The response of CO2 from the rst year to the eight years are: 1.3639, 3.2842, -0.3296, -1.3446, 0.7917, 1.0298, -0.5649, and -0.5514, respectively. Figure 10. Model and Forecasts for ENR Figure 9 is the graph of Impulse Response Function if there is a shock 1 standard deviation in CO2 and its impact to the variables Energy (ENR) and itself CO2. Shock of one standard deviation in causes the ENR gives a response uctuatively, but only has small impact. In the rst and second year the response is positive, in the third year to the fourth year the response is negative. For Energy (ENR) the response from the rst year to the third year are: 0.0226, 0.0152, and -0.0093. After the fourth year the response getting smaller tend to the zero poin (equilibrium point). Shock of one standard deviation in CO2, causes the CO2 itself gives a response uctuatively. In the rst © 2022 The Authors. Page 234 of 237 Russel et. al. Science and Technology Indonesia, 7 (2022) 228-237 Table 13. Test for Granger-Causality Test Group Variable Null hypotheses (H0) Chi-Square p-Value Conclusion 1 Group 1. variables: ENR Group 2. variables: CO2 H01 : ENR is aected by itself and not by CO2 1.09 0.5808 Do not reject H0 2 Group 1. variables: CO2 Group 2. variables: ENR H02 : CO2 is aected by itself and not by ENR 21.78 <0.0001 Reject H0 year to the second year the responses are negative, in the third and fourth year the response is positive, in the fth and sixth year the response is negative. The response of CO2 from the rst year to the eight years are: -0.0479, -0.5967, 0.1506, 0.4038, -0.1488, -0.2467, 0.1391, and 0.1494. Table 14. Forecasting for The Next Sixth Periods of Energy (ENR) and CO2 Variable Obs Forecast Standard Error 95% Condence Limits ENR3 45 0.87741 0.02513 0.82815 0.92667 46 0.88757 0.03827 0.81255 0.96258 47 0.89682 0.05068 0.79750 0.99614 48 0.89405 0.06241 0.77173 1.01636 49 0.89052 0.07319 0.74707 1.03397 50 0.89437 0.08252 0.73264 1.05610 CO2 45 2.27649 0.12619 2.02917 2.52381 46 2.39082 0.17699 2.04393 2.73772 47 2.09083 0.21615 1.66718 2.51449 48 2.07781 0.24947 1.58886 2.56676 49 2.29274 0.28385 1.73640 2.84909 50 2.27709 0.31352 1.66259 2.89158 Figure 11. Model and Forecasts for CO2 3.9 Forecasting In Forecasting data for Energy Used (ENR) and CO2, we used model given in Equation (18) and (19), the models are signif- icant with p-values 0.0001 and <0.0001 and with R-squares 0.4258 and 0.7115. These univariate models will be used for Forecasting. Figures 10 and 11 showthat the univariate models (18) and (19) t very well with the ENR and CO2 data where the observation values are very closed to their predictive values. So, the models used are very reliable and sound good. The Forecasting for the next six years, the values are not to much variation, but the condence interval of Forecasting are bigger as the period longer (Table 14). 4. CONCLUSIONS This research has investigated and examined the correlation between Energy Used (ENR) and CO2 emission. There is cointegration correlation between Energy used and CO2 emis- sion with the rank=2. By using smallest criteria of information of AICC, HQC, AIC and HQC, the best model is VAR(p) with lag p=2. By cointegration test and smallest criteria of infor- mation the best model is VECM(p) with lag p=2. From the Granger Causality it was found that there is unidirection eect namely there is causal eect of Energy Used to CO2 emission. From Impulse Response Function analysis shows that if there is shock of one standard deviation of Energy Used, the impact on EnergyUsed itself is small, but the impact on CO2 emission is uctuated and relatively long periode of time to attain the stability condition. if there is shock of one standard deviation of CO2 emission, the impact on Energy Used is small, but the impact on CO2 emission itself is uctuate and relatively long periode of time to attain the stability condition. The Forecast- ing result for the next six period by using model VECM(2) the Energy Used showed ther trend is increase, while the emission uctuate. 5. ACKNOWLEDGMENT The authors would like to thank Universitas Lampung for par- tially nancial support for this study. REFERENCES Abolhosseini, S., A. Heshmati, and J. Altmann (2014). The Ef- fectofRenewableEnergyDevelopmentonCarbonEmission Reduction: an Empirical Analysis for The EU-15 Countries. Available at SSRN 2403126, (7987); 1–27 Akpan, G. E. and U. F. 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Study on The Dy- namic Relationship Between Economic Growth and China Energy Based on Cointegration Analysis and Impulse re- sponse Function. ChinaPopulation, Resources andEnvironment, 18(4); 56–61 © 2022 The Authors. Page 237 of 237 INTRODUCTION THE METHOD Dynamic Modeling Cointegration Vector Autoregressive Vector Error Correction Model Normality Test Test for Granger Causality Impulse Response Function RESULTS AND DISCUSSION Test for Lag Optimum Test for Cointegration The Estimation of Parameters VECM(2) Model Normality of Residual Test for Stability Model Test for The Fitness of Model Analysis Granger-Causality Impulse Response Function (IRF) Forecasting CONCLUSIONS ACKNOWLEDGMENT