# Application of Grey System Model to Forecast the Natural Gas Imports in China

Authors: Zhuan-Zhuan Shi; Xiao-Yi Gou; Bo Zeng
Journal: Mathematical Problems in Engineering
 (2021)

---

## Abstract

China’s natural gas imports will keep an upward trend in the future due to its increasing demands. A comparatively accurate prediction of natural gas imports will help the Chinese government make appropriate decisions when formulating energy policies. In this paper, a new grey predication model, GPM_NGI model, was proposed to forecast China’s natural gas imports. Compared with GM (1, 1) and DGM (1, 1) model, the proposed new model performed better in the simulation process and bore smaller mean relative percentage error when used in simulating China’s natural gas imports from 2011 to 2019. Then, the new model was employed to forecast China’s natural gas imports from 2020 to 2022. The results showed that China’s natural gas imports would continue to grow rapidly over the next three years. Therefore, in order to strike a balance between the natural gas supply and demand in the future and avoid overdependence on imports, the Chinese government should take effective measures from both the supply and demand ends, such as making better use of shale gas, wind, and solar energy as well as reducing the industrial dependence on natural gas.


---

## Body

## 1. Introduction

As one of the three most commonly-known fossil energy resources, natural gas is featured by its environmental friendliness, utilization security, and high heat production which coal and oil cannot be on par with when used in city gas and industrial fuel supply. It is globally acknowledged that natural gas is probably the most cost-efficient clean energy with low carbon. The recent years have witnessed a climbing growth rate of natural gas demands in China and the upward trend will continue in the next few years due to the following reasons. Firstly, the Chinese government highly emphasizes the importance of environmental conservation and stresses the use of “clean, low-carbon, safe, and cost-efficient” energies, which are clearly demonstrated in The 13th Five-Year Plan for Energy Development of People’s Republic of China [1] and The CPC Central Committee’s Suggestions on the Formation of the 14th Five-Year Plan and the Long-Term Goals for the Year 2035 [2]. Natural gas, as one of the clean energies, will serve as “a bridge for the energy structure transformation in China” [3]. Secondly, the natural gas consumption in China keeps increasing in recent years, with the apparent consumption being 306.4 billion cubic meters in 2019 and an increasing rate of 8.6% compared with that of 2018, accounting for 8.1% of the primary energy consumption [4]. However, the average level of the proportion of natural gas consumption in the primary energy consumption worldwide is 24% [5], which means that there may be a great space for the natural gas demand growth in China in the future.Both exploitation and importation are feasible ways for China to gratify its needs of natural gas. However, the exploitation of China’s natural gas has been facing great challenges due to the scarcity of natural reserves, lack of sophisticated technologies, and high cost of exploitation. Therefore, importation seems to become the best solution for China to strike the balance between the natural gas demand and supply in the foreseeable future. In 2018, China’s natural gas import reached 125.4 billion cubic meters, ranking top in the world with a percentage of 9.8 in the global total natural gas imports. Meanwhile, China’s dependence on natural gas importation reached as high as 45.3% in the same year [6].As is mentioned above, the demand, consumption, and imports of natural gas in China are and will be increasing within a long duration of time. A comparatively accurate prediction of natural gas imports will help the Chinese government be fully aware of the real situation of China’s natural gas demand and supply in the future, make early preparations for maintaining the balance between the two, and take effective measures to guarantee the sufficient supply of energy, avoiding the possible threats and risks that may be brought about by overdependence on natural gas and its imports. The results of this paper can also be valuable references for the scientific assessment of China’s natural gas importation capacity and the formulation of related policies on China’s natural resources exploitation and importation.The prerequisite for forecasting China’s natural gas imports in the future more accurately is a scientific and feasible mathematical model. Many scholars have adopted different models to predict the demands, production, and imports of natural gas. Shaikh used logistic modeling analysis to forecast the natural gas demands in China [7]. Mu and Li established a system dynamics model to forecast the demands and consumption of China’s natural gas [8]. Zhang and Yang built up Bayesian Model Averaging to forecast the natural gas consumption in China [9]. Szoplik set up artificial neural networks to forecast natural gas consumption within a short period of time [10]. Bai developed a structure-calibrated support vector regression approach to forecast daily natural gas consumption [11]. As for imports of natural gas, fewer studies have been found compared with the other two research branches mentioned above. Wei, Cui, and Hu et al. employed a grey model to predict China’s natural gas import demand through sea from 2018 to 2020 [12]. Li and Pu developed a new method based on genetic algorithm and extreme learning machine to predict China’s natural gas imports from 2019 to 2028 [13]. A few combined models have also been proposed to forecast the natural gas consumption based on detailed analysis on its dominant influencing factors [14, 15]. Traditional prediction methods could explain the relationship between the consequences and influencing factors to some extent; however, due to lack of enough data and the complexity of factors that affect the demands and imports of natural gas imports in China, the prediction precision needs to be further improved.The grey prediction model, one of the most important components of the grey system theory initiated by Professor Deng Julong in 1983, has been widely used and proved effective in solving uncertain problems with inaccurate data and incomplete information [16–20]. The grey prediction model has been successfully applied in the fields of energy, transportation, and agriculture as well as finance prediction and optimization [21–25]. The basic model of grey prediction theory is GM (1, 1) model, a univariate grey prediction model with first-order derivative, which is most commonly used to predict issues of time sequence data with approximately homogeneous exponential growth [26]. In many cases, GM (1, 1) model did greatly improve the accuracy of prediction results; however, the error caused by discrete parameters but continuous time response function is always a problem [27]. Xie and Liu proposed discrete grey model, short for DGM (1, 1), which unifies parameter estimation and the model by making both of them in discrete form. DGM (1, 1) model can effectively eliminate the problems caused by the leap from the parameter estimation method based on difference equations to the time response function based on differential equations in modeling [28]. However, the shortcoming of DGM (1, 1) was quickly found by some diligent scholars. A few studies claimed that the growth rate of the simulation value in DGM (1, 1) model was constant, which was prone to large deviation in the simulation of nonhomogeneous exponential sequences [29–31]. To solve the problem, Zhan and Shi proposed a new grey model applicable to nonhomogeneous exponential sequences, NHGM (1, 1, k) model for short. The new model could simulate and predict all data sequences in accordance with nonhomogeneous exponential characteristics [32].Since its very advent, NHGM (1, 1,k) model has been optimized a few times [33, 34] and applied in various practical problems. For example, Chen employed the unbiased NGM (1, 1, k) model to analyze and predict the landslide displacement in deformation monitoring [35]. Chen Nana et al. applied the unbiased nonhomogeneous grey model to evaluate the combined performance of science and finance in Hainan province, China [36]. The problem of the traditional NHGM (1, 1, k) model lies in the difficulty of iterating its time response function. In this paper, we will learn from the SIGM modeling of [37] and optimize the traditional NHGM (1, 1, k) model based on the discrete grey model of differential equation and then employ the optimized model to forecast China’s natural gas imports in the years to come.


## 2. Grey Prediction Model of Natural Gas Imports

The classical GM (1, 1) model contains parametersa and b, with the former being called a development coefficient and the latter a grey actuating quantity. Indeed, the classical GM (1, 1) model is a two-parameter grey prediction model whose inherent structure makes it only applicable in the modeling and prediction of approximately homogeneous exponential sequences which often appear in an ideal state. The sequences with approximately nonhomogeneous exponential growth characteristics are more than common in our real life since the world is full of complexity and uncertainty.In order to forecast China’s natural gas imports in the future more scientifically and accurately, we learned from the modeling idea of SIGM model in [37], extended the basic form of GM (1, 1) model [x1k+az1k=b], and constructed a new grey prediction model which is suitable for the modeling and prediction of nonhomogeneous exponential sequences. The new model has proved to be more superior in its structure and modeling capability. To make it more convenient to write and read, the new grey prediction model of natural gas imports will be abbreviated as GPM_NGI in the following parts.


### 2.1. The Basic Form of GPM_NGI Model

Definition 1.
LetG0=g01,g02,…,g0n,g0k≥0,, k=1,2,…,n, G1 be the 1-AGO sequence of G0; that is,(1)G1=g11,g12,…,g1n,where g1k=∑i=1kg0i, k=1,2,…,n. And Z1 is called the mean sequence generated by consecutive neighbors of G1, i.e.,(2)Z1=z12,z13,…,z1n,where z1k=0.5×g1k+g1k−1, k=2,3,…,n; then,(3)g0k+az1k=kb+c,is a differential equation with first derivative and one variable [37, 38]. The parameter a is called a development coefficient, which reflects the trend of the system-g0k. The parameter b is called a grey actuating quantity, which represents all the grey information that may affect the development of the system. kb means that the value of b is linearly correlated with the time point-k. The parameter c is called a random disturbance term or random error term, which is used to represent the information with accidentalness or weak influences beyond the dominant variables.


### 2.2. Parameter Estimation of GPM_NGI Model

Parameter estimation is one of the most important steps in constructing the grey prediction model. Its basic idea is to use the least square method to estimate the parametersa, b, and c of GPM_NGI model on the condition that the square sum of the simulation error of the original sequence is the smallest.Theorem 1 (see [37]).
LetG0,G1, and Z1 be just like Definition 1, and p^=a,b,cT is the parameter vector, and(4)Y=g02g03⋮g0n,B=−z1221−z1331⋮⋮⋮−z1nn1,and then the parameter vector of equation (3) can be estimated using the least square method, which satisfies(5)p^=a,b,cT=BTB−1BTY.Proof.
SubstitutingG0,G1, and Z1 into equation (3), we can obtain(6)g02+az12=2b+c,g03+az13=3b+c,⋮g0n+az1n=nb+c,and equation (6) can also be expressed as(7)Y=Bp^.
Replacingg0k with −az1k+kb+c, we can get an error sequence, that is,(8)ε=Y−Bp^,
Assuming that(9)s=εTε=Y−Bp^TY−Bp^=∑k=2ng0k+az1k−kb−c2,the parameter vector p^=a,b,cT that minimizes s should satisfy(10)∂s∂a=2∑k=2ng0k+az1k−kb−cz1k=0,∂s∂b=−2∑k=2ng0k+az1k−kb−ck=0,∂s∂c=−2∑k=2ng0k+az1k−kb−c=0.
After combining, we obtain(11)∑k=2ng0k+az1k−kb−cz1k=0,∑k=2ng0k+az1k−kb−ck=0,∑k=2ng0k+az1k−kb−c=0.
According to equation (11), we get(12)BTε=0⟹BTY−Bp^=0⟹BTY−BTBp^=0⟹σ^=BTB−1BTY.
End of proof.


### 2.3. The Time Response Function of GPM_NGI Model

Parameter estimation is the very first step of constructing a grey prediction model. It is obvious that the basic form of GPM_NGI model,g0k+az1k=kb+c, solely cannot realize the forecasting of the development trend of the system g^0k. The time response function of GPM_NGI model, which shows the functional relationship between the system g^0k and the time point k, needs to be established to calculate the value of g^0k at different time points.According to Definition1, we know that(13)g1k=∑i=1kg0k,k=1,2,…,n,so(14)g0k=g1k−g1k−1,k=2,3,…,n,and(15)z1k=0.5×g1k+g1k−1,k=2,3,…,n.Substituting equations (14) and (15) into equation (3), when k=2,3,…,n, we can obtain(16)g1k−g1k−1+0.5a×g1k+g1k−1=kb+c.The above equation can be recast as(17)g1k=1−0.5a1+0.5ag1k−1+b1+0.5ak+c1+0.5a.According to equation (17), when k=2,3, we can obtain(18)g^12=1−0.5a1+0.5ag11+2⋅b1+0.5a+c1+0.5a,(19)g^13=1−0.5a1+0.5ag^12+3⋅b1+0.5a+c1+0.5a.Substituting equation (18) into equation (19), after being reorganized, we can get(20)g^13=1−0.5a1+0.5a2g11+1−0.5a1+0.5a2⋅b1+0.5a+c1+0.5a↘↘+3⋅b1+0.5a+c1+0.5a.Similarly, if we putg1u−1 into g1u(u = 2, 3, …, n), after being rearranged, we can get(21)g^1u=1−0.5a1+0.5au−1g11+1−0.5a1+0.5au−22⋅b1+0.5a+c1+0.5a+⋯+1−0.5a1+0.5a1u−1⋅b1+0.5a+c1+0.5a+1−0.5a1+0.5a0u⋅b1+0.5a+c1+0.5a,and equation (21) can be simplified as(22)g^1u=g11⋅1−0.5a1+0.5au−1+∑h=0u−2u−h⋅b1+0.5a+c1+0.5a⋅1−0.5a1+0.5ah.According to Definition1, we know that g^0k=g^1k−g^1k−1, so(23)g^0k=g11⋅1−0.5a1+0.5ak−1+∑h=0k−2k−h⋅b1+0.5a+c1+0.5a⋅1−0.5a1+0.5ah−↘↘g11⋅1−0.5a1+0.5ak−2−∑h=0k−3k−h−1⋅b1+0.5a+c1+0.5a⋅1−0.5a1+0.5ah.After rearranging equation (23), we can obtain(24)g^0k=x011−0.5a1+0.5a−1+2⋅b1+0.5a+c1+0.5a1−0.5a1+0.5ak−2↘↘+∑h=0k−3b1+0.5a1−0.5a1+0.5ah.Let(25)α=g011−0.5a1+0.5a−1+2⋅b1+0.5a+c1+0.5a,(26)β=1−0.5a1+0.5a,γ=b1+0.5a.and equation (24) can be simplified as(27)g^0k=αβk−2+∑h=0k−3γβh.Then, equation(27) is called the time response function of GPM_NGI model, k=2,3,…,n . When k=2,3,…,n , g^0k is called simulated values and when t=n+1,n+2,… , g^0k is called predicted values [35].


## 2.1. The Basic Form of GPM_NGI Model

Definition 1.
LetG0=g01,g02,…,g0n,g0k≥0,, k=1,2,…,n, G1 be the 1-AGO sequence of G0; that is,(1)G1=g11,g12,…,g1n,where g1k=∑i=1kg0i, k=1,2,…,n. And Z1 is called the mean sequence generated by consecutive neighbors of G1, i.e.,(2)Z1=z12,z13,…,z1n,where z1k=0.5×g1k+g1k−1, k=2,3,…,n; then,(3)g0k+az1k=kb+c,is a differential equation with first derivative and one variable [37, 38]. The parameter a is called a development coefficient, which reflects the trend of the system-g0k. The parameter b is called a grey actuating quantity, which represents all the grey information that may affect the development of the system. kb means that the value of b is linearly correlated with the time point-k. The parameter c is called a random disturbance term or random error term, which is used to represent the information with accidentalness or weak influences beyond the dominant variables.


## 2.2. Parameter Estimation of GPM_NGI Model

Parameter estimation is one of the most important steps in constructing the grey prediction model. Its basic idea is to use the least square method to estimate the parametersa, b, and c of GPM_NGI model on the condition that the square sum of the simulation error of the original sequence is the smallest.Theorem 1 (see [37]).
LetG0,G1, and Z1 be just like Definition 1, and p^=a,b,cT is the parameter vector, and(4)Y=g02g03⋮g0n,B=−z1221−z1331⋮⋮⋮−z1nn1,and then the parameter vector of equation (3) can be estimated using the least square method, which satisfies(5)p^=a,b,cT=BTB−1BTY.Proof.
SubstitutingG0,G1, and Z1 into equation (3), we can obtain(6)g02+az12=2b+c,g03+az13=3b+c,⋮g0n+az1n=nb+c,and equation (6) can also be expressed as(7)Y=Bp^.
Replacingg0k with −az1k+kb+c, we can get an error sequence, that is,(8)ε=Y−Bp^,
Assuming that(9)s=εTε=Y−Bp^TY−Bp^=∑k=2ng0k+az1k−kb−c2,the parameter vector p^=a,b,cT that minimizes s should satisfy(10)∂s∂a=2∑k=2ng0k+az1k−kb−cz1k=0,∂s∂b=−2∑k=2ng0k+az1k−kb−ck=0,∂s∂c=−2∑k=2ng0k+az1k−kb−c=0.
After combining, we obtain(11)∑k=2ng0k+az1k−kb−cz1k=0,∑k=2ng0k+az1k−kb−ck=0,∑k=2ng0k+az1k−kb−c=0.
According to equation (11), we get(12)BTε=0⟹BTY−Bp^=0⟹BTY−BTBp^=0⟹σ^=BTB−1BTY.
End of proof.


## 2.3. The Time Response Function of GPM_NGI Model

Parameter estimation is the very first step of constructing a grey prediction model. It is obvious that the basic form of GPM_NGI model,g0k+az1k=kb+c, solely cannot realize the forecasting of the development trend of the system g^0k. The time response function of GPM_NGI model, which shows the functional relationship between the system g^0k and the time point k, needs to be established to calculate the value of g^0k at different time points.According to Definition1, we know that(13)g1k=∑i=1kg0k,k=1,2,…,n,so(14)g0k=g1k−g1k−1,k=2,3,…,n,and(15)z1k=0.5×g1k+g1k−1,k=2,3,…,n.Substituting equations (14) and (15) into equation (3), when k=2,3,…,n, we can obtain(16)g1k−g1k−1+0.5a×g1k+g1k−1=kb+c.The above equation can be recast as(17)g1k=1−0.5a1+0.5ag1k−1+b1+0.5ak+c1+0.5a.According to equation (17), when k=2,3, we can obtain(18)g^12=1−0.5a1+0.5ag11+2⋅b1+0.5a+c1+0.5a,(19)g^13=1−0.5a1+0.5ag^12+3⋅b1+0.5a+c1+0.5a.Substituting equation (18) into equation (19), after being reorganized, we can get(20)g^13=1−0.5a1+0.5a2g11+1−0.5a1+0.5a2⋅b1+0.5a+c1+0.5a↘↘+3⋅b1+0.5a+c1+0.5a.Similarly, if we putg1u−1 into g1u(u = 2, 3, …, n), after being rearranged, we can get(21)g^1u=1−0.5a1+0.5au−1g11+1−0.5a1+0.5au−22⋅b1+0.5a+c1+0.5a+⋯+1−0.5a1+0.5a1u−1⋅b1+0.5a+c1+0.5a+1−0.5a1+0.5a0u⋅b1+0.5a+c1+0.5a,and equation (21) can be simplified as(22)g^1u=g11⋅1−0.5a1+0.5au−1+∑h=0u−2u−h⋅b1+0.5a+c1+0.5a⋅1−0.5a1+0.5ah.According to Definition1, we know that g^0k=g^1k−g^1k−1, so(23)g^0k=g11⋅1−0.5a1+0.5ak−1+∑h=0k−2k−h⋅b1+0.5a+c1+0.5a⋅1−0.5a1+0.5ah−↘↘g11⋅1−0.5a1+0.5ak−2−∑h=0k−3k−h−1⋅b1+0.5a+c1+0.5a⋅1−0.5a1+0.5ah.After rearranging equation (23), we can obtain(24)g^0k=x011−0.5a1+0.5a−1+2⋅b1+0.5a+c1+0.5a1−0.5a1+0.5ak−2↘↘+∑h=0k−3b1+0.5a1−0.5a1+0.5ah.Let(25)α=g011−0.5a1+0.5a−1+2⋅b1+0.5a+c1+0.5a,(26)β=1−0.5a1+0.5a,γ=b1+0.5a.and equation (24) can be simplified as(27)g^0k=αβk−2+∑h=0k−3γβh.Then, equation(27) is called the time response function of GPM_NGI model, k=2,3,…,n . When k=2,3,…,n , g^0k is called simulated values and when t=n+1,n+2,… , g^0k is called predicted values [35].


## 3. Forecasting of China’s Natural Gas Imports

Natural gas imports are affected by not only the demand and supply as well as energy structure, but also the related national policies. The data are full of uncertainty since the real situation is far more than complicated. The statistical data of natural gas imports from 2011 to 2019 (see Table1) will serve as modeling sample in this paper.Table 1
China’s Natural Gas Imports from 2011 to 2019 (unit: 100 million cubic meters).
Year201120122013201420152016201720182019Production312.0421.0525.0591.0611.0746.0946.31254.01340.0Data from China Energy Website (http://www.china5e.com/).


### 3.1. The Construction of GPM_NGI Model for China’s Natural Gas Imports Forecasting

(i)
Select experimental data for constructing GPM_NGI model of China’s natural gas imports forecasting.From Table1, we can see that the data available are limited, so all the data will be used to do modeling. The original sequence is(28)G0=g01,g02,…,g09=312,421,525,591,611,746,946.3,1254,1340.According to Definition1, we can get(29)G1=g11,g12,…,g19=312,733,1258,1849,2460,3206,4152.3,5406.3,6746.3Z1=z12,z13,…,z19=522.5,995.5,1553.5,2154.5,2833,3679.15,4779.3,6076.3.(ii)
Calculate the parameters of GPM_NGI model for China’s natural gas imports forecasting; to check the simulation and prediction performance of GPM_NGI model, we grouped the raw data into two categories. Specifically, the first seven numbers were used as simulation data for the model building while the remaining two were used as reserved data to test the prediction error of the model.According to Theorem1, the parameter matrix can be set up and the parameter vector, p^=a,b,cT, can be calculated as follows:(30)B=−z1221−z1331⋮⋮⋮−z1nn1=−522.521−995.531⋮⋮⋮−3679.1571,Y=g02g03⋮g0n=421525⋮946.3.The values of the parameter vector are shown below:(31)p^=a,b,cT=BTB−1BTY,=−0.3525,−125.9916,517.3421.(iii)
Construct the time response function of GPM_NGI model for China’s natural gas imports forecasting.As shown in Section2.3, substitute the values of the parameter vector into equations (25) and (26), and we can get the values of α,β,γ.(32)α=g011−0.5a1+0.5a−1+2⋅b1+0.5a+c1+0.5a=455.6647,β=1−0.5a1+0.5a=1.4280,γ=b1+0.5a=−152.9514.Substitutingα,β,γ into equation (27), we can obtain the time response function of GPM_NGI model:(33)g^0k=αβk−2+∑h=0k−3γβh=455.6647×1.4280k−2−152.9514∑h=0k−31.4280h.


### 3.2. Simulation of China’s Natural Gas Imports

According to equation (33), the simulation value and simulation error of GPM_NGI model can be calculated when k=2,3,…,9. At the same time, we also employed GM (1, 1) model and DGM (1, 1) model to simulate China’s natural gas imports as comparison. Their simulated data and simulated errors are shown in Table 2 and Figure 1, respectively.Table 2
Simulation of different models for China’s natural gas imports from 2012 to 2019.
kReal valueGPM_NGIDGM (1, 1)GM (1, 1)Simulated valueSimulation error (%)Simulated valueSimulation error (%)Simulated valueSimulation error (%)Data for simulation2421455.668.2339421.360.0846419.580.3374%3525497.725.1961490.946.4882489.006.8568%4591557.775.6220572.013.2136569.913.5685%5611643.535.3238666.479.0779664.218.7080%6746765.982.6786776.524.0916774.103.7672%7946.3940.840.5767904.754.3903902.184.6620%Mean relative simulation percentage error4.60524.55774.65Data for prediction812541190.545.06101054.1615.93611051.4616.1519%913401547.0915.45431228.248.34031225.438.5503%Mean relative prediction percentage error10.257612.138212.3511Global mean relative percentage error6.01836.45286.5752Figure 1
Comparison of simulation percentage errors by different models. (a) Year. (b) The type of model.
(a)(b)As can be seen from Figures1(a) and 1(b), GPM_NGI model has better global performances than GM (1, 1) and DGM (1, 1) all through the eight year. Figure 1(b) indicates that GPM_NGI model bears the smallest mean relative prediction percentage error compared with the other two. Besides, compared with DGM (1, 1) model and GM (1, 1) model, GPM_NGI model has the smallest global mean relative simulation error. In general, GPM_NGI model performs best in the forecast of China’s natural gas imports, indicating that it can be used to forecast China’s natural gas imports in the medium term.


### 3.3. Forecasting of China’s Natural Gas Imports

Due to the better performance of GPM_NGI model in simulation capability, we applied it to the forecasting of China’s natural gas imports from 2020 to 2022, the results of which can be found in Table3. Based on the real values of natural gas imports from 2011 to 2019 and the predictive values of natural gas imports from 2020 to 2023, the line chart of China’s natural gas imports from 2011 to 2022 is drawn in Figure 2.Table 3
The predicted China’s natural gas Imports from 2020 to 2022 (unit: 100 million cubic meters).
Year202020212022Production2056.232783.273821.45Figure 2
Line chart of China’s natural gas imports from 2011 to 2022.


## 3.1. The Construction of GPM_NGI Model for China’s Natural Gas Imports Forecasting

(i)
Select experimental data for constructing GPM_NGI model of China’s natural gas imports forecasting.From Table1, we can see that the data available are limited, so all the data will be used to do modeling. The original sequence is(28)G0=g01,g02,…,g09=312,421,525,591,611,746,946.3,1254,1340.According to Definition1, we can get(29)G1=g11,g12,…,g19=312,733,1258,1849,2460,3206,4152.3,5406.3,6746.3Z1=z12,z13,…,z19=522.5,995.5,1553.5,2154.5,2833,3679.15,4779.3,6076.3.(ii)
Calculate the parameters of GPM_NGI model for China’s natural gas imports forecasting; to check the simulation and prediction performance of GPM_NGI model, we grouped the raw data into two categories. Specifically, the first seven numbers were used as simulation data for the model building while the remaining two were used as reserved data to test the prediction error of the model.According to Theorem1, the parameter matrix can be set up and the parameter vector, p^=a,b,cT, can be calculated as follows:(30)B=−z1221−z1331⋮⋮⋮−z1nn1=−522.521−995.531⋮⋮⋮−3679.1571,Y=g02g03⋮g0n=421525⋮946.3.The values of the parameter vector are shown below:(31)p^=a,b,cT=BTB−1BTY,=−0.3525,−125.9916,517.3421.(iii)
Construct the time response function of GPM_NGI model for China’s natural gas imports forecasting.As shown in Section2.3, substitute the values of the parameter vector into equations (25) and (26), and we can get the values of α,β,γ.(32)α=g011−0.5a1+0.5a−1+2⋅b1+0.5a+c1+0.5a=455.6647,β=1−0.5a1+0.5a=1.4280,γ=b1+0.5a=−152.9514.Substitutingα,β,γ into equation (27), we can obtain the time response function of GPM_NGI model:(33)g^0k=αβk−2+∑h=0k−3γβh=455.6647×1.4280k−2−152.9514∑h=0k−31.4280h.


## 3.2. Simulation of China’s Natural Gas Imports

According to equation (33), the simulation value and simulation error of GPM_NGI model can be calculated when k=2,3,…,9. At the same time, we also employed GM (1, 1) model and DGM (1, 1) model to simulate China’s natural gas imports as comparison. Their simulated data and simulated errors are shown in Table 2 and Figure 1, respectively.Table 2
Simulation of different models for China’s natural gas imports from 2012 to 2019.
kReal valueGPM_NGIDGM (1, 1)GM (1, 1)Simulated valueSimulation error (%)Simulated valueSimulation error (%)Simulated valueSimulation error (%)Data for simulation2421455.668.2339421.360.0846419.580.3374%3525497.725.1961490.946.4882489.006.8568%4591557.775.6220572.013.2136569.913.5685%5611643.535.3238666.479.0779664.218.7080%6746765.982.6786776.524.0916774.103.7672%7946.3940.840.5767904.754.3903902.184.6620%Mean relative simulation percentage error4.60524.55774.65Data for prediction812541190.545.06101054.1615.93611051.4616.1519%913401547.0915.45431228.248.34031225.438.5503%Mean relative prediction percentage error10.257612.138212.3511Global mean relative percentage error6.01836.45286.5752Figure 1
Comparison of simulation percentage errors by different models. (a) Year. (b) The type of model.
(a)(b)As can be seen from Figures1(a) and 1(b), GPM_NGI model has better global performances than GM (1, 1) and DGM (1, 1) all through the eight year. Figure 1(b) indicates that GPM_NGI model bears the smallest mean relative prediction percentage error compared with the other two. Besides, compared with DGM (1, 1) model and GM (1, 1) model, GPM_NGI model has the smallest global mean relative simulation error. In general, GPM_NGI model performs best in the forecast of China’s natural gas imports, indicating that it can be used to forecast China’s natural gas imports in the medium term.


## 3.3. Forecasting of China’s Natural Gas Imports

Due to the better performance of GPM_NGI model in simulation capability, we applied it to the forecasting of China’s natural gas imports from 2020 to 2022, the results of which can be found in Table3. Based on the real values of natural gas imports from 2011 to 2019 and the predictive values of natural gas imports from 2020 to 2023, the line chart of China’s natural gas imports from 2011 to 2022 is drawn in Figure 2.Table 3
The predicted China’s natural gas Imports from 2020 to 2022 (unit: 100 million cubic meters).
Year202020212022Production2056.232783.273821.45Figure 2
Line chart of China’s natural gas imports from 2011 to 2022.


## 4. Conclusion

The forecast results showed that China’s natural gas imports would continue to keep an upward trend in the next few years, with the imports being 382.15 billion cubic meters in 2022, 12 times as much as that of 2011. This is mainly because natural gas is a kind of clean energy, which is in line with the concept of green development advocated by the Chinese government in recent years. Besides, China’s GDP growth rate still keeps higher than 6% despite of its slowing down in economic development recently, which leads to the increase of natural gas imports as before. Meanwhile, the increasing natural gas imports are closely related with the growing natural gas demands in China. Zeng et al. had predicted China’s natural gas demands and the results showed that China’s natural gas demand would be about 340 billion cubic meters in 2020 [37, 39]. The predictive result of the natural gas import in 2020 in this essay is 205.62 billion cubic meters, accounting for about 60% of the predictive demand in the same year. It shows that the supply of China’s natural gas is still heavily dependent on imports and its production is insufficient. Although the trend of trade globalization is inevitable and keeps accelerating in recent years, we have to realize the threats and risks that overdependence on natural gas imports may bring to China’s energy security and industrial development since the global energy geopolitical game is increasingly fiercer.In order to reduce the risks of overdependence on natural gas imports, China can take effective measures from both the supply and demand ends. From the perspective of supply, the idea of diversified energy consumption should be advocated and unconventional energy, such as shale gas, solar energy, and wind energy, can be further exploited and utilized. Firstly, China is abundant in recoverable shale gas reserves, covering 20% of the world total. Therefore, increasing the utilization of shale gas, such as cultivating industrial clusters for shale gas utilization and offering governmental support, can effectively alleviate the pressure of natural gas supply. Secondly, China started early in the field of solar power generation, but there are some problems in the solar photovoltaic industry, such as raw materials’ overdependence on imports, lack of core technology and equipment, and insufficient development of domestic market, etc. Hence we need to increase investment in science and technology to overcome technical difficulties in solar energy development and carry out favorable policies to enhance the market vitality. Thirdly, as one of the most important unconventional energy resources with rich reserves and wide distribution, wind energy should be made better use of. However, the prerequisite to fully develop wind energy is to fully understand its strong random volatility and the difficulty in accurate prediction. The utilization rate of wind power energy could be improved only if the prediction precision of wind power was improved. In terms of demand, the government should give more favorable policies to encourage industrial enterprises to use unconventional energies since natural gas is limited in the final analysis. Besides, the utilization rate of the existing natural gas can be improved through technological innovation, which is also a consideration of reducing the huge demand for natural gas from the very beginning.



---

*Source: 5524479-2021-04-02.xml*