Prediction Models of Energy Consumption Structure of Shandong Province of China

: In order to predict the energy consumption structure of Shandong province of China, linear regression model, gray model and ARIMA model are constructed respectively. On the basis of the single predicted results, the optimal weighted combination model is constructed for combination prediction of Shandong province's energy consumption structure. The empirical test shows that combination prediction model can effectively increase the prediction accuracy, providing a new method for the energy consumption structure prediction.


INTRODUCTION
Energy has very important effect on economy and environment.On one hand, energy is the core impetus and strength source of economic development and a lot of energy need to be consumed in the process of the economic development; on the other hand, energy consumption will bring about some environmental problems and produce waste gas, waste water and solid waste.Energy consumption structure refers to the structure and the ratio relationship of all kinds of energy in total energy consumption.In 2010, the primary energy consumption structure of Shandong province of China is that, coal 76.21%, oil 21.98%, power 0.09% and other 1.81%.The coal-based energy consumption structure determines that the economic development of Shandong province is based on the high pollution, which is not harmonious with the low carbon target of today's world.Therefore, scientific prediction of energy consumption structure of Shandong province is conducive to make effective policies on optimization of energy consumption structure and achieve energyeconomy-environment system's coordinated development.At present, prediction models of energy consumption structure include statistical prediction (Wei et al., 2006), grey prediction (Chen et al., 2007), neural network prediction (Li et al., 2009) and time series prediction (Huang et al., 2004).Consideration the simplicity, applicability of prediction, this study uses regression prediction, gray prediction and ARIMA prediction models to predict energy consumption structure of Shandong province and makes combination prediction on the basis of three prediction models.

SINGLE PREDICTION MODELS OF ENERGY CONSUMPTION STRUCTURE
Regression prediction model: Assuming that there is a time series X = {x 1 , x 2 , …, x n }, where x i means the energy consumption of the i th year, we use the time serial number as variable and make linear regression on energy consumption.The steps are as follows: Step 1: Input all samples into the least squares estimation equation and get the least squares estimation of parameters ܽ ො and ܾ : (1) where, ‫ݐ‬ ̅ and ‫̅ݔ‬ ௧ stand for the mean values of t and x t , respectively.
Step 2: Input ܽ ො and ܾ into regression equation: (2) And then compute prediction values of all the years.
Step 3: Input x t and ‫ݔ‬ ො ௧ into F statistics: (3) where, , Give significance level α (usually 0.05) and if F>F α (1, n-2), the regression equation can be considered significant, i.e., there is a linear relation between t and x t and it can be used for prediction.Otherwise, the regression equation has no meaning and cannot be used for prediction.

Grey prediction model:
The basic Grey prediction Model is GM (1, 1).It constructs a linear one-order differential equation model for grey exponential time sequences and the corresponding time response function is exponential function.Grey prediction process can generally be divided into grey generation, parameters calculation and model tests.The steps are as follows (Deng, 1990): Step 1: Grey generation: Usually, the original sequence is unlikely to have grey exponential law.So we need to make accumulation operation and weaken the influence of bad data in the original series.The cumulated series is recorded as Y = {y 1 , y 2 , …, y n }, where: (4) Based on the cumulated series, the grey Generation Model GM (1, 1) is:   ARIMA prediction model: ARIMA (p, d and q) model was put forward in 1970s by Box and Jenkins, which is a time series prediction method (Gao, 2006).AR means auto-regressive, MA means moving average, p is auto-regressive item, q is moving average item and d is the difference frequency made to stabilize time The process of ARIMA construction can be seen as Fig. 1.The steps of ARIMA are as followed: ( ) Step 1: Smooth and white noise test of series: Check the autocorrelation function of original sequence X to determine whether it is a stable sequence or not.If X is unstable, we need make difference operation.Repeat this step d times to ensure that Z = ∆ d X is a stable sequence.
Step 2: Model identification: Calculate the autocorrelation function and partial autocorrelation function of Z to determine the parameters p and q.Where, according to the q steps truncation of correlation function to determine the moving average item q; according to the p steps truncation of partial autocorrelation function to determine autoregressive item p.If the autocorrelation function and partial autocorrelation function decay according to exponential law, but they are both not censored, then we should fit ARMA model order from low order to high order.
Step 3: Parameters estimation: Calculate parameters φ 1 , φ 2 , …, φ p and θ 1 , θ 2 , … , θ q and get the ARIMA model: Step 4: Model diagnosis: We can use AIC information criterion, correlation coefficient or fitting error to make model tests.Generally, AIC should be small, the absolute value of correlation coefficient should be close to 1 as possible and the fitting error should be small.Usually, step 1 to step 4 are performed at the same time.

OPTIMAL WEIGHTED COMBINATION PREDICTION OF ENERGY CONSUMPTION STRUCTURE
Combination prediction will combine different prediction models together.It utilizes different information provided by different prediction methods comprehensively and gives combination prediction models in appropriate weighted form (Chen, 2008).Optimal weighted combination method is to construct the objective function based on some optimal criterion and in certain conditions; it will minimize objective function to acquire weighted coefficients of different prediction methods.
Assume that w 1 , w 2 , w 3 are the weights of regression prediction, grey prediction and ARIMA prediction methods respectively and are the prediction values of the t th year by the three methods, we can get the combination prediction value of the t th year is: (10) Use minimization the sum of squared prediction error as the objective function and we can construct optimal weighted combination prediction model as follows: (11) Solve the above mathematical programming model and we can get the optimal solutions of w 1 , w 2 , w 3 .Input them into model ( 10) and then we can use it to predict energy consumption in the future years.
In order to estimate the prediction effects of all the prediction models, we use the followed error indexes: • Mean square error: (12) • Mean absolute error: (13) • Mean absolute percentage error: • Mean square percentage error: (15)

ENERGY CONSUMPTION STRUCTURE PREDICTION OF SHANDONG PROVINCE
Single prediction: The statistics of primary energy consumption structure of Shandong province in 1996-2010 is as shown in Table 1.To make energy consumption structure prediction, we can predict the total primary energy consumption, coal consumption and oil consumption and then get the future trend of energy consumption structure.This study will only describe the modeling process of total energy consumption and the processes of coal consumption and oil consumption prediction are the same with it.It can be seen from Table 1 that the total energy consumption of Shandong province has raised and the trend of it is linear basically.Use linear regression prediction and we get the regression equation is: At the same time, we get F = 133.41>F0.05 (1, 13) = 4.67, which means that the equation is significant and can be used for prediction.Input t = 16, 17, …, 20 and we get the prediction value of total energy consumption in 2011-2015 as shown in Table 2.The prediction values of coal consumption and oil consumption are also shown in Table 2.
Then we use ARIMA method to predict energy consumption.Firstly, we take the natural logarithm of original time series: lnX = log (X).Secondly, we make unit root test and find that after two orders difference, the time series become stable, namely, the difference order d = 2. ADF test result is as shown in Table 4.We can see that t statistic value is less than critical value under confidence level 1%, so it refuses the hypothesis of having unit root.
After two orders difference, we get autocorrelation function and partial autocorrelation function as shown in Fig. 2.
By using Eviews 6.0 to calculate iteratively and comparing AIC and SC, we consider ARIMA (1, 2 and 1) model is the best model.ARIMA model is as follows: where, The prediction model is: And AIC = -2.5685.All the parameters are significant in 5% level and have passed significance test.Residual correlation coefficients and partial correlation coefficients are all in the confidence interval, so they are white noise series.The prediction values of energy consumption in 2011-2015 are shown in Table 5 6.The energy consumption ratios of coal and oil are shown in Fig. 3.We can see that although coal ratio will decrease, but it will still exceed 70% and the average value of it in 2011-2015 will be 73.24%.Oil ratio in energy consumption will rise gradually and the average value of it in 2011-2015 will be 25.27%.Coal and oil ratio in the energy consumption will still exceed 98% and the average value of it in 2011-2015 will be 98.52%.
The results of error indexes of three single prediction models and optimal weighted combination prediction model are as shown in Table 7.We can see that the results of four error indexes are the smallest among four prediction models, which indicate that the combination prediction model is the best prediction model.

CONCLUSION
This study constructs linear regression model, grey prediction model and ARIMA model to predict energy consumption structure of Shandong province of China.Based on the three single prediction models, it constructs the optimal weighted combination prediction model.The prediction results show that the combination prediction model has higher accuracy than the three single prediction models, which can achieve very good prediction effect and provide a new method for prediction of energy consumption structure.
development grey number u = Called endogenous control grey number Step 2: Parameters calculation: Record ܽ ො as parameters vector ܽ ො = [a u] T , where: , We can use least squares method to calculate parameters a and u:

Fig
Fig. 1: Process of ARIMA construction

Fig. 2 :
Fig. 2: Autocorrelation function and partial autocorrelation function of ∆ 2 lnX series Make subtraction operation and we get the prediction model of raw sequence is:

Fig. 3 :
Fig. 3: Predicted coal and oil ratios in energy consumptionCombination prediction: Calculate the prediction errors of total energy consumption of three methods and input them into the optimal weighted combination prediction model, then we get the optimal solution: w 1 = 0.1106, w 2 = 0.2242 and w 3 = 0.6652.The prediction values of energy consumption in 2011-2015 by combination prediction are shown in Table6.The energy consumption ratios of coal and oil are shown in Fig.3.We can see that although coal ratio will decrease, but it will still exceed 70% and the average value of it in 2011-2015 will be 73.24%.Oil ratio in energy consumption will rise gradually and the average value of it in 2011-2015 will be 25.27%.Coal and oil ratio in the energy consumption will still exceed 98% and the average value of it in 2011-2015 will be 98.52%.The results of error indexes of three single prediction models and optimal weighted combination prediction model are as shown in Table7.We can see that the results of four error indexes are the smallest among four prediction models, which indicate that the combination prediction model is the best prediction model.

Step 5: Prediction: If
ARIMA prediction model does not pass model tests, we should return step 2. Otherwise, if it has passed model tests, we can apply it to predict energy consumption in the future years.

Table 1 :
Energy consumption of Shandong province

Table 5 :
Prediction results of energy consumption by ARIMA