Mathematical Problems in Engineering

Volume 2015 (2015), Article ID 686501, 7 pages

http://dx.doi.org/10.1155/2015/686501

## Using a Novel Grey System Model to Forecast Natural Gas Consumption in China

^{1}College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China^{2}Department of Mathematics and Physical, Handan College, Handan 056005, China

Received 14 April 2014; Revised 24 July 2014; Accepted 24 July 2014

Academic Editor: Massimo Scalia

Copyright © 2015 Lifeng Wu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Accurate prediction of the future energy needs is crucial for energy management. This work presents a novel grey forecasting model that integrates the principle of new information priority into accumulated generation. This grey model can better reflect the priority of the new information theoretically. The results of two practical examples demonstrate that this grey model provides very remarkable short-term predication performance compared with traditional grey forecasting model for limited data set forecasting. It is applied to Chinese gas consumption forecasting to show its superiority and applicability.

#### 1. Introduction

Energy has an influencing role in achieving economic and social progress. Forecasting energy constitutes a vital part of energy policy of a country, especially for a developing country like China whose economy is in a stage of energy transition: from low efficiency solid fuels to oil, gas, and electric power [1]. This has motivated many researchers to focus their research on energy forecasting. For example, Jian et al. used bayesian combination model to forecast energy demand of China [2]. Ji predicted petroleum consumption in China by comparing three models [3]. Meng and Niu analysed and predicted annual electricity consumption of China [4]. Zhang et al. forecasted Chinese transport energy demand based on partial least squares regression [5]. Ünler proposed swarm intelligence to improve energy demand forecasting [6]. A large number of studies on energy consumption forecasting using grey model and improved grey model are reported, such as Meng et al. [7], Bianco et al. [8], Li et al. [9], Niu et al. [10], Pao and Tsai [11], and Wang et al. [12].

Although the first-order grey model with one variable (GM(1,1)) had been widely adopted, its predicting performance still could be improved. In this paper, based on the principle of new information priority, we consider the priority of the th component and the th component, respectively, and the th component is more prior than the th component. Similarly, the nd component is more prior than the st component [13]. Two case studies show the effectiveness of the proposed modeling method, which is particularly suitable for limited sample forecasting.

The rest of the paper proceeds as follows: an overview of the relevant grey models and a new GM(1,1) model with the principle of new information priority of grey system are present in Section 2. The advantage of the grey model proposed in this paper over the other grey models is proved by two real cases in China in Section 3. The prediction concerning natural gas consumption in China will be conducted in Section 4. Some conclusions are discussed in final section.

#### 2. Methodology

##### 2.1. Grey Model Based on Autoregressive Method

Assume , where stands for a data sequence. The equation is called the autoregressive GM(1,1) model (ARGM(1,1)). Use the ordinary least squares method to estimate the parameters as follows: where

Theorem 1. *Assume that , are the same as (1). Set ; then recursive function is given by
*

*Proof. *Substitute , into (1); then

Let ; then

We also obtain a nonhomogenous exponential model as follows:

Because grey autoregressive method of GM(1,1) is formulated by using the original data rather than the accumulated generation data, it does not need to inverse accumulated generating. We can see that (1) is an exponential model and (7) is a nonhomogenous exponential model. This method is called the ARGM(1,1).

*2.2. The GM(1,1) Model with the Principle of New Information Priority via Weighted Least Squares Method*

*In this section, by weighted least squares method, the coefficients of (1) can be obtained as follows:
*

*Then we obtain a nonhomogenous exponential model as follows:
*

* can reflect the principle of new information priority, so (9) also pays more attention to the new error and embodies the principle of new information priority. We call this method WLSGM(1,1).*

*2.3. The GM(1,1) Model with the Principle of New Information Priority*

*Assume , where stands for a data sequence. The original data of (1) is
*

*The data with the principle of new information priority is
which is called the treatment of new information priority. The equation
is referred to as grey nonhomogenous exponential model with the principle of new information priority (abbreviated as NIGM(1,1)).*

*Theorem 2. Assume that is certain. Actually, if the error is , then
*

Via the treatment of new information priority, the mean of the error is where is the same as (11). Use the ordinary least squares method to estimate the parameters as follows: where

The variable of is , where

*Proof. *Via the treatment of new information priority, (11) becomes

Obviously,

Use the ordinary least squares method to estimate the parameters as follows:

Substituting
into (21), we obtain

Then

Actually, by
and , we obtain

The more the sample is, the less the attention we pay to the error from new information and vice versa.

We can obtain

By
thus

In most cases, we pay attention to the and and overlook ; thus we denote (27) as

So

*Let ; then the components from to all contain . The components from to all contain . The components from to all contain . The components from to all contain . Analogizing successively, the components and both contain . Only contains . So
pay more attention to the variable of the new information in the modelling process. The modeling procedure of NIGM(1,1) can be concluded as follows.*

*Step 1*. An original nonnegative series is given.

*Step 2*. and which are the same as Theorem 2 can be obtained via the treatment of new information priority.

*Step 3*. Least squares estimation of and according to Theorem 2 is as follow.

*Step 4*. We obtain a nonhomogenous exponential model as follows:

*Step 5*. In order to solve the effect of the initial condition, we assume

*Use the ordinary least squares method to estimate the parameters
*

*where
*

*thus, we obtain
*

*which is a nonhomogenous exponential model.*

*3. Results*

*3. Results*

*In this section, the advantage of the NIGM(1,1) model over the other grey models is demonstrated by two real case studies of energy consumption. Mean absolute percentage error compares the real and forecasted values to evaluate the precision.*

*Case 1 (natural gas consumption forecasting example in China [14]). *This example is from the literature [14], in order to compare the result of the literature [14] with the result of the proposed model. The sample data is the same as the literature [14]. Using the data from 1995 to 2006 to construct NIGM(1,1),

Then the value from 2007 to 2008 (out-of-sample) is predicted. Actual values and the forecasting values of five compared models are presented in Table 1. As can be seen from Table 1, NIGM(1,1) yielded the lowest MAPE compared with the other models during the period from 1995 to 2008.