Comparison of Forecasting India's Energy Demand ...

sustainability Article

Comparison of Forecasting India’s Energy Demand Using an MGM, ARIMA Model, MGM-ARIMA Model, and BP Neural Network Model Feng Jiang, Xue Yang and Shuyu Li * School of Economic and Management, China University of Petroleum (East China), Qingdao 266580, China; [email protected] (F.J.); [email protected] (X.Y) * Correspondence: [email protected] Received: 23 April 2018; Accepted: 21 June 2018; Published: 28 June 2018

Abstract: Better prediction of energy demand is of vital importance for developing countries to develop effective energy strategies to improve energy security, partly because those countries’ energy demands are increasing rapidly. In this work, metabolic grey model (MGM), autoregressive integrated moving average (ARIMA), MGM-ARIMA, and back propagation neural network (BP) are adopted to forecast energy demand in India, the third largest energy consumer in the world after China and the USA. The average relative errors between the actual and simulated value are 1.31% (MGM), 1.07%, 0.92% (MGM-ARIMA), and 0.39% (BP). The high prediction accuracy indicates that the prediction result is effective. The result shows that India’s energy consumption will increase by 4.75% a year in the next 14 years. Compared with the 5.1% per year on average in 1995–2016, India’s energy consumption will still continue its steady growth at about 5% growth from 2017 to 2030. Keywords: India; primary energy consumption; forecasting

1. Introduction In 2015, the primary energy consumption of India surpassed that of Russia, making India the world’s third-largest energy consumer in 2016. The primary energy consumption of India reached 723.9 million tons oil equivalent, an increase of 129% from 2000, sharing 5% of the world’s primary energy consumption. India’s energy consumption will continue to grow in the future. There are two factors driving the increases in India’s energy consumption: the low per capita energy consumption and the rapid economy growth. As the world’s second-most populous country, India’s population reached 13.04 billion in 2017, and has continued increasing at an annual rate of 1.4% [1]. The huge population leads to the low per capita energy consumption. According to the research of International Energy Agency, India’s energy consumption per capita is only one-fourth the world average. This means that India’s primary energy demand still has great room for improvement [2]. For example, more and more families will buy their first car with the improvement of living standards, and then the fuel consumption will be increased. In terms of macro economy, India has been in a high growth mode since it started economic reforms in the late 90s [3,4]. In 2015, the growth rate of India’s economy was up to 8% and India surpassed China to become the fastest growing economy in the world [5]. As is shown in the report of the World Bank, India ranked fifth in the world GDP (gross domestic product) in 2016, after the USA, China, Japan, and Germany [6]. In the future, India will need more energy to develop its economy. Also, India will become the dominant driver of the world’s energy demand [7]. Therefore, it is necessary and meaningful to predict the future primary energy consumption of India in this critical period.

Sustainability 2018, 10, 2225; doi:10.3390/su10072225

www.mdpi.com/journal/sustainability

Sustainability 2018, 10, 2225

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For India, the prediction of the primary energy consumption can provide a reference for solving supply and demand contradiction, promoting energy structural supply-side reforms, and creating energy policies. Besides, India’s energy consumption can affect the global energy market directly [8]. Thus, the predictions also offer participants more information, playing an important role in maintaining the market stability. In this paper, we selected India’s primary energy consumption from 1995 to 2016 as our data source, which comes from the BP Statistical Review of World Energy 2017 [9]. We establish four models, metabolic grey model (MGM), autoregressive integrated moving average model (ARIMA), back propagation neural network model (BP), and the combination model of MGM and ARIMA, to forecast India’s primary energy consumption by 2030. The models are based on three theories. The various methods were compared with each other, making the results more persuasive. In this paper, we use mean absolute percentage error (MAPE) and root mean square error (RMSE) to show the results’ reliability. The structure of this article is as follows: The second section is a literature review. The third section describes the methodology. The fourth section contains the forecasting process and results. The fifth section summarizes the whole paper. 2. Literature Review In recent years, energy issues have become a top concern of experts and researchers. India is a major energy consumer. In current research, many reviews of energy consumption in different Indian sectors have been made by researchers [10–16]. Besides, there are many valuable works on energy forecasting. Suganthi et al. forecasted coal, oil, natural gas, and electricity requirements [17]. Ardakani et al. forecasted long-term electrical energy consumption [18]. Mohanty et al. forecasted solar energy with application [19]. Bhattacharya et al. forecasted wood energy [20]. Various models were adopted in these articles. Most of them were simple linear models after improving or combination models based on one theory. In this area, the grey model, BP neural network model, and ARIMA model are widely used for forecasting of the time series. Compared with the conventional grey model, the improved grey model has a higher forecast accuracy, as it is able to optimize the initial condition and predict both direct and iterative manners [21–26]. The nonhomogeneous discrete grey model can better capture nonhomogeneous effects on the data [27]. In addition, GM (grey model) (1,1) by month-flame optimization with a rolling mechanism made the timeliness of the data series more clear [28,29]. Sen et al. used ARIMA to forecast the energy consumption of an Indian pig iron manufacturing organization, the results of which appeared smoother than the seasonal random trend model [10]. The ARIMA model has been improved greatly. Temporal aggregation could achieve a better estimation of the different time series components, and the forecasting combination could reduce the importance of the model selection [30]. The ARIMA model could meet the subject’s characteristics of self-similarity, periodicity, suddenness, and trends, delivering better forecasting performance in short-term forecasting [31]. So, this model has been applied broadly throughout other critical industries, such as public transport, metal prices, and the assessment of health care structures [32–39]. BP network is a feed forward neural network realized by a back propagation algorithm [21]. It a non-linear prediction model, achieving a stable prediction effect through determining the combining weights [40,41]. Researchers improved the network based on particle swarm optimization and an optimized genetic algorithm to make it ideal for many application scenarios [42–44]. Currently it is already used in energy forecasting, and the error is less than 2% [18]. Therefore, the time sequence prediction method has been widely used in in various fields. It has been already generally accepted in academia. However, recent research has mostly been based on one theory, where the conflicts between the results of different methods can be avoided and the precision is also difficult to ensure. Without comparison, it is hard to find the models with higher accuracy. In addition, compared with a single model, forecasting with multiple models gives greater superiority in the precision of results [29,45–47].


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In this paper, we used the MGM, ARIMA model, MGM-ARIMA model, and BP neural network model to forecast India’s energy demand. The models were established according to three theories: the grey theory, regression analysis theory, and neural network theory. The first two methods are linear, while the last is nonlinear. This method system solves the limitations of former researches where the time sequence prediction method is applied, and further improves the prediction accuracy. The use of three theories enriches the theoretical foundation of forecasting in our work. We hope to provide a methodological reference for analogous study. We applied this method system to forecasting India’s energy demand. As the world’s third-largest energy consumer, India’s energy demand can affect not only its own development but also the world energy market’s changes. Thus, the forecasting results will provide data referencing for the Indian government’s creation of energy policies, and offer participants more information about the world energy market. 3. Methodology The research object of this paper is the energy demand of India. The forecasting work for this dataset includes the following two characteristics: the energy consumption forecasts rely only on historical data, that is to say, this dataset belongs to univariate prediction; and the energy consumption in the next 12 years is the ultimate forecast target, indicating that a model with advantages in long-term forecasting needs to be chosen. In addition, as is stated in the literature review, the MGM, ARIMA model, and BP neural network have high accuracy in forecasting. Moreover, combination approaches covering both linear and nonlinear models further improve the accuracy. So, the MGM, ARIMA model, MGM-ARIMA model, and BP neural network model are suitable for this study. In this section, we introduce the principles of the four models. For ease of understanding, we use detailed formulas to explain their operation. The meaning of the symbols in equations is given in Table 1. Table 1. Explanation of the symbols in formulas. Notations x (0) ( k ) x (1) ( k ) xˆ (0) (k) xˆ (1) (k ) t B YN ‘α’ ‘µ’ ‘c’ αi , β i µt Yt

Explanation

Notations

Explanation

Original sequence Once accumulated sequence Prediction of raw sequence Prediction of 1-AGO sequence Time sequence Matrix of data and constants Matrix of data Constant parameter Constant term Harmonic parameter Error term of early data Initial data sequence

Yt∗

Predicted data sequence Order of the difference Order of auto-regression Order of moving average Initial residual sequence Predicted residual sequence Sample number Nodes’ number Hidden layer’ number Error sequence Expected output sequence Actual output sequence

‘d’ ‘p’ ‘q’ Et Et∗ K n i Ep t pi o pi

3.1. Metablic Gey Model (1,1) The MGM (1,1) is a widely used forecasting model. Its essence is to use the time series itself to predict future data under the condition that time series shows a clear trend. The original sequence is recorded: X (0) = x (0) ( 1 ) , x (0) ( 2 ) , . . . , x (0) ( n )

tool.

(1)

In order to make the sequence change regularly, we employ the accumulation n After accumulating, othe once accumulated sequence (1-AGO) is obtained:

X(1) = x(1) (1), x(1) (2), . . . , x(1) (n) f, where x (1) (k) = ∑ik=1 x (0) (i ), k = 1, 2, 3, . . . , n. So, if we


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obtain the accumulated sequence, the value of the predicted data sequence can be also obtained by subtraction. µ −αk e , k = 1, 2, · · · , n xˆ (0) (k + 1) = xˆ (1) (k + 1) − xˆ (1) (k ) = (1 − eα ) x (0) (1) − α

(2)

Through much experimenting, the first-order accumulated series meets a linear first-order differential equation. dx (1) + αx (1) = µ (3) dt After derivation, the relationship between the sequences xˆ (1) (k) and x (0) (k) can be described by the following formula: µ − α ( k −1) µ e + , k = 1, 2, · · · , n xˆ (1) (k) = x (0) (1) − α α

(4)

In Equation (4), we can acquire the solution as long as the parameters ‘α’ and ‘µ’ are known. ‘α’ and ‘µ’ can be solved by the least squares method. −1 BT YN [α, µ]T = BT B

(5)

h iT YN = x(0) (2), . . . , x(0) (n)

(6)

   B=  

− Z(1) ( 2 ) 1 − Z(1) ( 3 ) 1 .. .. . . − Z(1) ( n ) 1

     

(7)

In Equation (7), Z (1) (k) = 0.5x (1) (k) + 0.5x (1) (k − 1), k = 2, 3, · · · , n. Lastly, we substitute the values of ‘α’ and ‘µ’ into Equation (4), so the sequence xˆ (1) (k) can be solved, and then by calculating Equation (2), the prediction data can be also obtained. 3.2. Autoregressive Integrated Moving Average Model (ARIMA) ARIMA is short for autoregressive integrated moving average model. It is the combination of the differenced autoregressive model and moving average model, with a high accuracy of prediction. The modeling is divided into two steps. The first step involves computing the difference of a non-stationary sequence. We need use the formula below to make the original sequence Yt stationary. After d order difference, we obtain the new stationary sequence Yt∗ . Yt∗ = (1 − B)d Yt (8)   − y11 + y12 /2 1  . .. . .. In Equation (8), B =  .  1 1 − ym−1 + ym /2 1 The second step involves moving average processes and autoregressive processes. Yt∗ = c + α1 Yt−1 + α2 Yt−2 + · · · + α p Yt− p + ut

(9)

Yt∗ = ut + β 1 ut−1 + β 2 ut−2 + · · · + β q ut−q

(10)

Therefore, the complete formula for the ARIMA model is: Yt∗ = c + α1 Yt−1 + α2 Yt−2 + · · · + αk Yt−k + µt + β 1 µt−1 + β 2 µt−2 + · · · + β q µt−q

(11)


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where p denotes the order of auto-regression and q is the order of the moving average. They can be determined with the autocorrelation coefficient map and partial autocorrelation coefficient map, respectively. ‘αk ’ and ‘β k ’ are regression coefficients. 3.3. MGM-ARIMA Model This model is the combination of MGM and ARIMA. Therefore, it involves two parts. The first part involves predicting the original data spanning from 1995 to 2016 by using an MGM (1,1) model. With cumulative series and a linear first-order differential equation, we can obtain the predicted series. The theory was discussed in Section 3.1. After prediction, the error between the predictive value and original value can be easily obtained. h iT E(0) = e(0) ( 1 ) , e(0) ( 2 ) . . . , e(0) ( n )

(12)

e(0) (i) = xˆ (0) (i) − x(0) (i)

(13)

where x indicates the original series and xˆ denotes the predicted series. The second part involves predicting the error using the ARIMA model. At first, the difference of a non-stationary error sequence is computed. After that, we obtain the new stationary error sequence. Et∗ = (1 − B)d Et

(14)

We then take the moving average step and autoregressive step. Et∗ = c + α1 Et−1 + α2 Et−2 + · · · + α p Et− p + ut

(15)

Et∗ = ut + β 1 ut−1 + β 2 ut−2 + · · · + β q ut−q

(16)

The complete formula for the ARIMA model is: Et∗ = c + α1 Et−1 + α2 Et−2 + · · · + αk Et−k + µt + β 1 µt−1 + β 2 µt−2 + · · · + β q µt−q

(17)

where Et stands for the original error sequence;Et∗ represents the new stationary error sequence; p is the order of auto-regression; and q is the order of the moving average. 3.4. BP Neural Network Model BP neural network is the most successful neural network in prediction fields. It consists of an input layer, output layer, and a few hidden layers. There are a certain number of nodes on each layer and one node represents one neuron. The number can be determined by this empirical formula: n

∑ Cni i > K

(18)

i =0

where K is the sample number; ni is the number of the hidden layer’s node; n is the number of the i = 0 if i > n. input layer’s node; and Cni In the network, the upper nodes connect the lower nodes by the weight matrix. The nodes’ connection between layers is full, but on one layer there is no connection. The ordinary transfer function is the Sigmoid function. 1 f (x) = (19) 1 + e− x There are two singles flows between layers: working information and error. The working signal is from the input layer. It is the function of input data and the weight matrix. The error signal is from

𝑛𝑖

In the network, the upper nodes connect the lower nodes by the weight matrix. The nodes’ connection between layers is full, but on one layer there is no connection. The ordinary transfer function is the Sigmoid function. 𝑓(𝑥) = Sustainability 2018, 10, 2225

1 1 + 𝑒 −𝑥

(17) 6 of 17

There are two singles flows between layers: working information and error. The working signal is from the input layer. It is the function of input data and the weight matrix. The error signal is from theItoutput It is thebetween differencethe between the trueand output and expected output, and error the E p can the output layer. is thelayer. difference true output expected output, and the error 𝐸using calculated(20): using Equation (20): 𝑝 can be be calculated Equation

2 11 t −−𝑜o )2 E p𝐸𝑝== ∗ ∑(𝑡 22 ∑ 𝑝𝑖pi 𝑝𝑖pi

(8)

(20)

In the above formula, 𝑡𝑝𝑖 denotes expectedoutput output and the the true true output. In the above formula, t pi denotes thethe expected and𝑜𝑝𝑖 o pirepresents represents output. During the process of propagation, the weight matrix of the network are constantly adjusted. During the process of propagation, the weight matrix of the network are constantly adjusted. The structure is as shown in Figure 1. Finally, when the aim of the actual output being consistent The structure is as shown in Figure 1. Finally, when the aim of the actual output being consistent with with the expected output is achieved, then the network can be used for prediction directly. the expected output is achieved, then the network can be used for prediction directly.

Figure 1. The structureofofthe the back back propagation (BP) neural network. Figure 1. The structure propagation (BP) neural network.

4. Empirical Results

4. Empirical Results

This paper selected a set of data spanning from 1995 to 2016 obtained from the BP Statistical

World Energy (as shown in Figure 2). In the to period 1995–2016,from India’sthe primary ThisReview paperofselected a set2017 of data spanning from 1995 2016ofobtained BP Statistical energy consumption showed an upward trend,2). and was about 5.1% per year on energy Review of World Energy 2017 (as shown in Figure Inthe thegrowth periodrate of 1995–2016, India’s primary average. Sustainability 2018, 10, x FOR PEER REVIEW 7 of 18 consumption showed an upward trend, and the growth rate was about 5.1% per year on average.

800

10%

700

9% 8%

600

7%

500

6%

400

5%

300

4% 3%

200

2%

100

1%

0

0%

Primary Energy: Consumption/Million tonnes oil equivalent Growth rate of primary energy consumption Figure 2. India’s primary energy consumption and growth rate in 1995–2016.

Figure 2. India’s primary energy consumption and growth rate in 1995–2016. 4.1. MGM (1,1) Model Parameters The first step is to define an original sequence 𝑋 (0) = (𝑥 (0) (1), 𝑥 (0) (2), … , 𝑥 (0) (22)), where 𝑥

(0)

(1) represents India’s primary energy consumption in 1995. The second step involves the sequence accumulation, 𝑋 (1) = (𝑥 (1) (1), 𝑥 1 (2), … , 𝑥 (1) (22)), and

subsequently the establishment of the linear first-order differential equation. We can solve the parameters ‘α’ and ‘μ’ using the least squares method, which is shown in Table 2.


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4.1. MGM (1,1) Model Parameters The first step is to define an original sequence X (0)

=

x (0) (1), x (0) (2), . . . , x (0) (22) ,

where x (0) (1) represents India’s primary energy consumption in 1995. The second step involves the sequence accumulation, X (1) = x (1) (1), x1 (2), . . . , x (1) (22) , and subsequently the establishment of the linear first-order differential equation. We can solve the parameters ‘α’ and ‘µ’ using the least squares method, which is shown in Table 2. Table 2. The value of the metabolic grey model’s (MGM) parameters in 2000–2030. 2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

2010

α µ

−0.05 245.89

−0.04 260.29

−0.03 280.11

−0.03 287.79

−0.03 298.27

−0.05 295.13

−0.06 301.04

−0.06 314.42

−0.07 330.00

−0.07 355.20

−0.07 374.02

α µ

2011 −0.06 411.85

2012 −0.06 439.52

2013 −0.06 466.25

2014 −0.05 502.03

2015 −0.05 533.57

2016 −0.04 570.89

2017 −0.05 580.05

2018 −0.05 615.70

2019 −0.05 638.43

2020 −0.05 674.30

2021 −0.05 706.32

α µ

2022 −0.05 739.23

2023 −0.05 777.23

2024 −0.05 813.92

2025 −0.05 853.64

2026 −0.05 895.30

2027 −0.05 938.45

2028 −0.05 984.05

2029 −0.05 1031.6

2030 −0.05 1081.0

The third step is to obtain the fitted value (1995–2016) and the predicted value (2017–2030) with EXCEL. As is shown in Figure 3, the fitted value of the MGM is very close to the original value; however, there is a difference for the year 2013. The reason for this is that India’s primary energy consumption in 1995–2016 showed a rising trend, but it slowed down suddenly in 2013, as illustrated Sustainability 2018, 10, x FOR REVIEW 8 of 18 in Figure 2. We regard thisPEER abrupt variation as a non-linear characteristic. Yet, as a linear forecasting model, the MGM is applicable to the case where the growth rate of the original data series is relatively stable. If the original data series is characterized by nonlinear characteristics, the fitting effect of the series is relatively stable. If the original data series is characterized by nonlinear characteristics, the MGM will degrade. Thus, the fitted value of the MGM is very close to the original value, except in fitting effect of the MGM will degrade. Thus, the fitted value of the MGM is very close to the 2013. In the following section of our article, we use other models to overcome these loopholes to obtain original value, except in 2013. In the following section of our article, we use other models to a better fitting effect. overcome these loopholes to obtain a better fitting effect.

India's primary energy consumption / million tons oil equivalent

800 700 600 500 400 300 200 100 0

original value

MGM-fitted value

Figure 3. Gap between actual and MGM (1,1) prediction values. Figure 3. Gap between actual and MGM (1,1) prediction values.

4.2. ARIMA Model Parameters The condition of the ARIMA time series model is that random sequence is stationary. In order to smooth the sequence, we performed differential processing for the sequence by using the unit root test. The unit root test and difference results are shown in Table 3. Table 3. Unit root test and difference results based on Eviews 7.2.


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4.2. ARIMA Model Parameters The condition of the ARIMA time series model is that random sequence is stationary. In order to smooth the sequence, we performed differential processing for the sequence by using the unit root test. The unit root test and difference results are shown in Table 3. Table 3. Unit root test and difference results based on Eviews 7.2. Sequence

−2.961334 −2.437015 −5.767150

Q Q* Q**

Critical Value

ADF Statistic

Value of p

1%

5%

10%

−4.571559 −4.616209 −4.571559

−3.690814 −3.710482 −3.690814

−3.286909 −3.297799 −3.286909

0.1685 0.3502 0.0011

Note: Q means zero-order difference; Q* means first-order difference; Q** means second-order difference.

As illustrated Table 3, REVIEW the second-order difference is stable. Then, obtained with the help Sustainability 2018, 10, xinFOR PEER 9 of 18of EViews 7.2, our correlation coefficient graph for a stationary sequence is shown in Figure 4.

Figure Figure 4. 4. Autocorrelation Autocorrelation and and partial partial autocorrelation autocorrelation coefficients. coefficients.

According to the coefficient judgment criteria of the ARIMA model, ARIMA (2,2,1) can be According to the coefficient judgment criteria of the ARIMA model, ARIMA (2,2,1) can be used to used to predict the future consumption. Then we need to determine the goodness of fit for the predict the future consumption. Then we need to determine the2goodness of fit for the model. With the model. With the help of SPSS software, we determined that 𝑅 is 0.809 > 0.60, which means that the help of SPSS software, we determined that R2 is 0.809 > 0.60, which means that the fitting effect is fitting effect is good (Table 4). good (Table 4). Table 4. Parameters of the goodness of fit for the autoregressive integrated moving average Table 4. Parameters of the goodness of fit for the autoregressive integrated moving average (ARIMA) (ARIMA) (2,2,1) model. (2,2,1) model. Model Fit Statistics Model Number of Predictions Number of Outliers Fit Statistics StationaryModel R-Squared R-Squared Model Number of Predictions Number of Outliers Stationary0.809 R-Squared R-Squared ARIMA (2,2,1) 1 0.809 0 ARIMA (2,2,1)

1

0.809

0.809

0

Finally, the fitted result achieved by the ARIMA model is shown in Figure 5. Obviously, the fitting effectthe is fitted good,result but there is still difference the year 2013.inThe reason for this isthe thatfitting the Finally, achieved byathe ARIMAfor model is shown Figure 5. Obviously, ARIMA model is also a linear model, and it cannot deal with nonlinear characteristics. This effect is good, but there is still a difference for the year 2013. The reason for this is that the ARIMA situation willabe improved theitcombination and nonlinear model. This situation will be model is also linear model,inand cannot deal model with nonlinear characteristics.

energy consumption/ ns oil equivalent

improved in the combination model and nonlinear model. 800 700 600 500 400 300

ARIMA (2,2,1)

1

0.809

0.809

0

India's primary energy consumption/ million tons oil equivalent

Finally, the fitted result achieved by the ARIMA model is shown in Figure 5. Obviously, the fitting effect is good, but there is still a difference for the year 2013. The reason for this is that the Sustainability 2018, 10, is 2225 9 of 17 ARIMA model also a linear model, and it cannot deal with nonlinear characteristics. This situation will be improved in the combination model and nonlinear model. 800 700 600 500 400 300 200 100 0

original value

ARIMA（2,2,1）- fitted value

Figure 5. Gap between actual and ARIMA prediction values. Figure 5. Gap between actual and ARIMA prediction values.

4.3. MGM-ARIMA Model Parameters In this model, the first step is to obtain the absolute error. So, we used the consumption fitted by the MGM from 1995 to 2016. The original data and fitting results are shown in Table 5. The last column is the absolute error. Table 5. Initial fitted result based on the MGM (1,1) model. Year

Primary Energy Consumption/Million Tons of Equivalent

Initial Prediction

Absolute Error

1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016

251.5716 263.4000 275.7442 288.6670 302.1954 316.3578 329.0027 330.2666 341.8766 354.3913 381.5452 413.9138 441.6681 479.0618 508.6667 549.7625 572.7613 603.5870 644.7245 661.6280 693.5195 713.8711

251.5716 261.7342 276.1579 292.5813 299.6023 315.9773 318.0086 332.0359 345.3628 365.8556 393.6102 413.9578 450.2354 475.7145 513.2210 537.0707 568.6912 611.6017 621.4868 663.5853 685.0938 723.9023

0.0000 1.6658 −0.4137 −3.9143 2.5931 0.3805 10.9941 −1.7693 −3.4862 11.4643 12.0650 −0.0440 −8.5673 3.3473 −4.5543 12.6918 4.0701 −8.0147 23.2377 −1.9573 8.4257 10.0312

The second step is to predict the error using the ARIMA. Obviously, this sequence is not stationary. So, we performed differential processing for the sequence using the unit root test. The result in Table 6 shows that the second-order difference is stable.


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Table 6. Unit root test and difference results based on Eviews 7.2. Sequence

Critical Value

DF Statistic

−5.007479 −9.463064 −3.833027

Q Q* Q**

Value of p

1%

5%

10%

−4.467895 −4.498307 −4.667883

−3.644963 −3.658446 −3.733200

−3.261452 −3.268973 −3.310349

0.0034 0.0000 0.0422

Note: Q means zero-order difference; Q* means first-order difference; Q** means second-order difference.

As illustrated Table 6,REVIEW the second-order difference is stable. Then, we drew a correlation Sustainability 2018, 10, in x FOR PEER 11 of 18 coefficient graph for a stationary sequence (shown in Figure 6).

Figure 6. 6. Autocorrelation Autocorrelation and and partial partial autocorrelation autocorrelation coefficients. coefficients. Figure

For the third step, based on the analysis above, we decided to use the ARIMA (2,2,1) model to For the third step, based on the analysis above, we decided to use the ARIMA (2,2,1) model to predict the future error from 1995 to 2030. Then, we used SPSS software to determine the goodness predict the future error from 1995 to 2030. Then, we used2 SPSS software to determine the goodness of of fit for the model. The result in Table 7 shows that 𝑅 is 0.834 > 0.60, which means that the fitting fit for the model. The result in Table 7 shows that R2 is 0.834 > 0.60, which means that the fitting effect effect is good. is good. Table 7. Parameters of goodness of fit for the ARIMA (2,2,1) model. Table 7. Parameters of goodness of fit for the ARIMA (2,2,1) model.

Number of

Model

Predictions Number of Predictions

Model

ARIMA (2,2,1) ARIMA (2,2,1)

1

1

Model Fit Statistics Number of Outliers Model Fit Statistics Number of Outliers Stationary R-Squared R-Squared Stationary R-Squared R-Squared 0.834 0.834 0 0.834

0.834

0


Through the relations among the original consumption, the MGM (1,1) prediction Through theand relations amongprediction the original consumption, the MGM (1,1) prediction consumption, consumption, the ARIMA error, we can obtain the prediction consumption. The and the ARIMA error, we can obtain thefitting prediction The fitting curve is shown fitting curve isprediction shown in Figure 7. The excellent effectconsumption. can be seen intuitively. in Figure 7. The excellent fitting effect can be seen intuitively. 800 700 600 500 400 300 200 100 0

Model ARIMA (2,2,1)

Predictions 1

Stationary R-Squared 0.834

R-Squared 0.834

Number of Outliers 0

Through the relations among the original consumption, the MGM (1,1) prediction of 17 ARIMA prediction error, we can obtain the prediction consumption.11The fitting curve is shown in Figure 7. The excellent fitting effect can be seen intuitively.


Sustainability 2018, 10, 2225 consumption, and the

800 700 600 500 400 300 200 100 0

original value

MGM-ARIMA-fitted value

Sustainability 2018, 10, x FOR PEER REVIEW

12 of 18

Figure 7. Gap between actual and MGM-ARIMA prediction values. Figure 7. Gap between actual and MGM-ARIMA prediction values.

4.4. BP Neural Network Model Parameters 4.4. BP Neural Network Model Parameters MATLAB is an internationally recognized, outstanding mathematical application software. In MATLAB is an internationally recognized, mathematical software. particular, its neural network box offers facilitiesoutstanding for BP network modeling. application Therefore, we used InMATLAB particular, its neural network box offers facilities for BP network modeling. Therefore, we used to establish the BP neural network and predict data. The process involves three steps. MATLAB to establish the BP neural network and predict data. The process involves three steps. The first step is to establish a BP neural network. We used the special function ‘newff’ to The first is to establish BP number neural network. special function ‘newff’ determine thestep numbers of layers,a the of nodes,We andused the the transfer function, such as theto determine the numbers of layers, the number of nodes, and the transfer function, such as the following: following: ‘net = newff ([−1,1],[4,4,1][m1][m2] )’. After establishing the network, we needed to set ‘net = newff ([−1,1],[4,4,1])’. After establishing the network, we needed to set these values. these values. The is is thethe network initialization. TheThe number of nodes on the layer and Thesecond secondstep step network initialization. number of nodes oninput the input layeroutput and layer was 1,1. After many debugging repetitions, the number of nodes on each of the hidden layers output layer was 1,1. After many debugging repetitions, the number of nodes on each of the hidden was set was to 4, set 4, 1.toThe of the network is shownisin Figurein8.Figure In order toorder meet the accuracy layers 4, 4,structure 1. The structure of the network shown 8. In to meet the requirements, the permissible error is set to 0.00000001. The training iteration is 1000. accuracy requirements, the permissible error is set to 0.00000001. The training iteration is 1000.

Figure 8. Structure of the BP neural network. Figure 8. Structure of the BP neural network.

The third step is the network training simulation. We used the function ‘sim’ to achieve this. The third step is the networkthe training We used the function ‘sim’ to achieveand this. Y = sim(net,p), where y indicates outputsimulation. data, net denotes the object of the neural network, Yp=represents sim(net,p),the where y indicates the output data, net denotes the object of the neural network, and input vectors. The consumptions from 1995 to 2013 were selected as the trainingp represents the the input vectors. Thefrom consumptions from to 2013 wereThe selected as thecurve training sample, sample, and consumptions 2014 to 2016 as 1995 the test sample. predicted generated and the consumptions from 2014 to 2016 as the test sample. The predicted curve generated by MATLAB by MATLAB is shown in Figure 9. is shown in Figure 9.

The third step is the network training simulation. We used the function ‘sim’ to achieve this. Y = sim(net,p), where y indicates the output data, net denotes the object of the neural network, and p represents the input vectors. The consumptions from 1995 to 2013 were selected as the training sample, and the consumptions from 2014 to 2016 as the test sample. The predicted curve generated Sustainability 2018, 10, 2225 12 of 17 by MATLAB is shown in Figure 9.

9. Predicted curve generated by by MATLAB. MATLAB. Figure 9.


It is clear that the fitted value generated by the BP neural network is very close to the actual It is clear that the fitted value generated by the BP neural network is very close to the actual value from 1995 to 2016, as shown in Figure 10. The fitting curve almost coincides with the original value from 2018, 199510, tox2016, as shown in Figure 10. The fitting curve almost coincides with the original Sustainability FOR PEER REVIEW 13 of 18 data curve. data curve. 800 700 600 500 400 300 200 100 0

original value

BP neural network-fitted value

Figure 10. Gap between actual and BP neural network prediction values. Figure 10. Gap between actual and BP neural network prediction values.

4.5. Comparison and Evaluation of Multiple Models 4.5. Comparison and Evaluation of Multiple Models From Figures 3, 5, 7, and 10, we can see that the fitting effect was very good. However, in From Figure 3, Figure 5, Figure 7, and Figure 10, we can see that the fitting effect was very order to accurately judge the error, we calculated the MAPE (mean absolute percentage error) and good. However, in order to accurately judge the error, we calculated the MAPE (mean absolute RMSE (root mean square error) of the four models based on the following formulas. The result of percentage error) and RMSE (root mean square error) of the four models based on the following the error calculation is shown in Table 8. formulas. The result of the error calculation is shown in Table 8.

|𝑦𝑖 − 𝑥𝑖 | | y − xi | MAPE = 𝑥𝑖i

MAPE =

xi

∑(𝑦𝑖 − 𝑥𝑖 )2 RMSE = √ s y i − x i )2 ∑(𝑛 RMSE =

n

Table 8. MAPE and RMSE of the four models (%).

MAPE RMSE

MGM (1,1) 0.0131 8.2599

ARIMA 0.0107 6.1846

MGM-ARIMA 0.0092 5.3811

BP Neural Network 0.0039 2.3224


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Table 8. MAPE and RMSE of the four models (%).

MAPE RMSE

MGM (1,1)

ARIMA

MGM-ARIMA

BP Neural Network

0.0131 8.2599

0.0107 6.1846

0.0092 5.3811

0.0039 2.3224

According to the above analysis, the accuracy of all of the four models is high. From Figure 11, we can see that the average accuracy of the four models is all more than 95%. The higher prediction accuracy indicates that the prediction results are persuasive. As expected, compared with a single model, the combination (MGM-ARIMA) has higher accuracy. However, the forecasting14result Sustainability 2018, 10, x FOR model PEER REVIEW of 18 of the BP neural network model is the most reliable of all models. MGM

ARIMA

MGM-ARIMA

BP neural network

1995 2016 2015 2014

2013

2012

1 0.98 0.96 0.94 0.92 0.9 0.88 0.86 0.84 0.82 0.8

1996 1997 1998

1999

2000

2011

2001

2010

2002

2009

2003 2008

2004 2007

2005 2006

Figure time points. points. Figure 11. 11. The The fitting fitting goodness goodness value value of of multiple multiple models models at at different different time

4.6. Forecast Results 4.6. Forecast Results Based on the primary energy consumption of India from 1995 to 2016 obtained from the BP Based on the primary energy consumption of India from 1995 to 2016 obtained from the BP Statistical Review of World Energy 2017, Table 9 shows the concrete results of the final forecast of Statistical Review of World Energy 2017, Table 9 shows the concrete results of the final forecast of the four models. The prediction results (shown in Figure 12) indicate that India’s primary energy the four models. The prediction results (shown in Figure 12) indicate that India’s primary energy consumption will increase continually at a rate of 4.75% over the next 14 years. consumption will increase continually at a rate of 4.75% over the next 14 years. Table 9. Forecasting results of the four models.

2017 2018 2019 2020 2021 2022 2023 2024 2025 2026 2027 2028 2029 2030

MGM (1,1） 759.33 793.41 834.72 873.93 916.30 961.20 1007.01 1055.93 1106.76 1159.49 1215.41 1273.02 1333.86 1396.97

ARIMA 764.83 792.26 846.97 874.52 929.61 970.22 1017.07 1074.22 1115.79 1182.11 1229.01 1294.20 1354.93 1415.01

MGM-ARIMA 761.35 804.99 847.37 893.09 940.48 992.38 1045.59 1103.12 1163.49 1226.89 1294.59 1365.19 1440.26 1518.90

BP Neural Network 763.16 802.43 841.71 880.99 920.27 959.55 998.83 1038.10 1077.40 1116.70 1156.00 1195.20 1234.50 1273.80


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Table 9. Forecasting results of the four models. MGM (1,1)

ARIMA

MGM-ARIMA

BP Neural Network

2017 759.33 2018 793.41 2019 834.72 2020 873.93 2021 916.30 2022 961.20 2023 1007.01 2024 1055.93 2025 1106.76 2026 1159.49 2027 1215.41 2028 1273.02 Sustainability 2018, 10, x FOR PEER1333.86 REVIEW 2029 2030 1396.97

764.83 792.26 846.97 874.52 929.61 970.22 1017.07 1074.22 1115.79 1182.11 1229.01 1294.20 1354.93 1415.01

761.35 804.99 847.37 893.09 940.48 992.38 1045.59 1103.12 1163.49 1226.89 1294.59 1365.19 1440.26 1518.90

763.16 802.43 841.71 880.99 920.27 959.55 998.83 1038.10 1077.40 1116.70 1156.00 1195.20 1234.50 1273.80

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1600

India's primary energy consumption /million tons oil equivalent

MGM（1，1） 1500

ARIMA

1400

MGM-ARIMA

1300

BP neural network

1200 1100 1000 900 800 700 2016

2018

2020

2022

2024

2026

2028

2030

Figure 12. India’s primary energy consumption forecasted by the models. Figure 12. India’s primary energy consumption forecasted by the fourfour models.

Conclusions 5. 5. Conclusions thispaper, paper,we weestablished establishedfour fourmodels models(the (theMGM, MGM, ARIMA ARIMA model, model, MGM-ARIMA model, and InIn this BPBP neural network model) to forecast India’s energy demand. As As shown in Figure 11, all models and neural network model) to forecast India’s energy demand. shown in Figure 11,four all four have high above 95%. inthose past research, our models based are on three models haveaccuracy high accuracy aboveUnlike 95%. those Unlike in past research, ourare models basedtheories, on which overcomes theovercomes limitationsthe thatlimitations the conflicts between the results are ignored, precision is difficult three theories, which that the conflicts between the results are ignored, to ensure, and it is to hard to find a better model comparison. The comparison of multiple precision is difficult ensure, and it is hard to without find a better model without comparison. The models’ precision indicates thatprecision the combination (MGM-ARIMA) has higher accuracy than a comparison of multiple models’ indicatesmodel that the combination model (MGM-ARIMA) single model (MGMthan andaARIMA), and the BP neural network and is thethe most among allismodels. has higher accuracy single model (MGM and ARIMA), BP reliable neural network the The extraordinary precision indicates that the prediction results are persuasive. The forecasting most reliable among all models. results that India’s primaryindicates energy consumption will grow results at a rateare of about 4.75% over The show extraordinary precision that the prediction persuasive. The the next 14 years. Compared the rate of 5.1% per consumption year on average 1995–2016, energy forecasting results show thatwith India’s primary energy willfor grow at a rateIndia’s of about consumption will 14 continue its steady growth about a 5%per growth 2017 tofor 2030. This trend 4.75% over the next years. Compared with theatrate of 5.1% year from on average 1995–2016, is consistent our evaluation. In theits future, with the increase energy demand, India’s energy with consumption will continue steady growth at aboutofa the 5% primary growth from 2017 to energy and climate change will be increasingly prominent. Indian 2030. Thisproblems trend is consistent with our evaluation. In the future, with theThe increase ofgovernment the primary and other demand, national governments should efforts to control the supply and demand of energy. energy energy problems andmake climate change will be both increasingly prominent. The Indian Suggested concrete measures are as follows: government and other national governments should make efforts to control both the supply and demand of energy. Suggested concrete measures are as follows: (i)

For India itself, government decision-makers should secure the energy supply from the longterm benefits. The Indian government should take vigorous action to develop some new and renewable energy sources such as wind energy, hydro energy, solar energy, terrestrial heat, biomass energy, etc.


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(i)

For India itself, government decision-makers should secure the energy supply from the long-term benefits. The Indian government should take vigorous action to develop some new and renewable energy sources such as wind energy, hydro energy, solar energy, terrestrial heat, biomass energy, etc. (ii) For the world market, India’s increasing energy demand is an assault. Participating nations should increase communication to promote the development of new energy together. Only by diversifying the energy mix can the energy supply fundamentally be secured. (iii) Curtailing energy demand is also vital. India should vigorously conserve energy in various sectors, popularize energy-conserving technology and equipment, and improve energy efficiency. For example, adjusting energy prices can cut down consumption to some degree. In addition, the highest precision of the BP neural network implies that the research still leaves something to be desired. In this paper, we employed the time vector as the only input parameter. However, the BP neural network has more value in the research of a complicated system affected by various factors. Though the forecasting result using one factor has high accuracy already, its superiority is not fully realized. Therefore, the BP neural network’s application to energy forecasting needs further exploration. Author Contributions: F.J. and S.L. performed the experiments, analyzed the data, and contributed reagents/materials/analysis tools. R.L. conceived and designed the experiments and wrote the paper. All authors read and approved the final manuscript. Funding: This work was supported by the Shandong Provincial Natural Science Foundation, China (ZR2018MG016), the Initial Founding of Scientific Research for the Introduction of Talents of China University of Petroleum (East China) (YJ2016002), and the Fundamental Research Funds for the Central Universities (17CX05015B). We received grants in support of our research work. We also received funds to cover the costs of publishing in open access. Acknowledgments: We would like to thank the editor and three anonymous reviewers for their constructive comments and helpful suggestions, which helped us to improve the manuscript. Conflicts of Interest: The authors declare no conflict of interest.

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