Mathematical Problems in Engineering

Volume 2018, Article ID 5194810, 13 pages

https://doi.org/10.1155/2018/5194810

## Energy Demand Forecasting: Combining Cointegration Analysis and Artificial Intelligence Algorithm

School of Economics, Southwestern University of Finance and Economics, Chengdu 611130, China

Correspondence should be addressed to Junbing Huang; nc.ude.tib@23410702

Received 6 October 2017; Accepted 6 December 2017; Published 10 January 2018

Academic Editor: Benjamin Ivorra

Copyright © 2018 Junbing Huang 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

Energy is vital for the sustainable development of China. Accurate forecasts of annual energy demand are essential to schedule energy supply and provide valuable suggestions for developing related industries. In the existing literature on energy use prediction, the artificial intelligence-based (AI-based) model has received considerable attention. However, few econometric and statistical evidences exist that can prove the reliability of the current AI-based model, an area that still needs to be addressed. In this study, a new energy demand forecasting framework is presented at first. On the basis of historical annual data of electricity usage over the period of 1985–2015, the coefficients of linear and quadratic forms of the AI-based model are optimized by combining an adaptive genetic algorithm and a cointegration analysis shown as an example. Prediction results of the proposed model indicate that the annual growth rate of electricity demand in China will slow down. However, China will continue to demand about 13 trillion kilowatt hours in 2030 because of population growth, economic growth, and urbanization. In addition, the model has greater accuracy and reliability compared with other single optimization methods.

#### 1. Introduction

Energy, which is a vital input for the economic and social development of any economy, has gained special attention. Combined with globalization and industrialization, global energy demand has been increasing continually for decades and is expected to rise approximately 30% from 2015 to 2035 in accordance with the worldwide economic growth [1]. Therefore, energy demand projection should be developed because accurate energy demand forecasts aid policy makers in improving the schedule of energy supply and providing valuable suggestions for planning energy supply system operations.

Given the importance of accurate energy forecasts, extant studies using different estimation methods have been undertaken since the 1970s. In general, these early studies can be classified into two major categories: econometric [2–9] and machine learning (ML) methods [10–23]. The artificial intelligence (AI) energy forecasting model, which is a class of ML method, has gained popularity in recent years because of its superiority in time series processing and its capability to deal with noise data. Several tools, such as artificial neural networks (ANN), genetic algorithm (GA), ant colony optimization (ACO), and particle swarm optimization, are commonly employed in the model [10–17]. Compared with the conventional econometric energy forecasting method, the AI-based model frequently demonstrates higher prediction accuracy in terms of mean absolute error (MAE), mean square error (MSE), mean absolute percentage error (MAPE), and root mean square error (RMSE) [16, 17]. According to economic theories, the model is feasible for predicting future energy demand by using the historical relationship when the periodical characteristics between energy demand and its explanatory variables will not change in the long term. However, the current AI-based method is referred to as the “black-box” because it predicts energy demand without knowing the internal relationship between energy demand and its affecting factors [23]. In addition, few econometric and statistical evidences are found that can prove the relationship between energy demand and its factors. This relationship may change in the long run based on the current AI-based model.

This study aims to present a more scientific AI-based energy demand forecasting framework that ensures the reliability of predicted results. The electricity demand of China is forecasted as an example to show the process of implementing this framework. In addition, the predicted results are beneficial for policy makers to perform appropriate measures to bridge the electricity gap and arrange the supply of electricity demand.

The rest of the paper is organized as follows. Section 2 conducts a detailed literature review on the recent developments of energy demand forecasting. Section 3 presents the new framework. Section 4 predicts the electricity demand in China for 2016–2030 under three scenarios. The final section summarizes the main conclusions and presents the policy implications.

#### 2. Literature Review

Energy estimation modeling has attracted wide spread interest among current practitioners and academicians. The commonly used econometric techniques include cointegration analysis, autoregressive integrated moving average (ARIMA) model, partial least square regression (PLSR), and vector error correction model. The ML method mainly refers to the AI model, support vector regression (SVR) method, and Grey forecasting method. Their details are described in the following sections.

##### 2.1. Econometric Method

Cointegration analysis can establish a long-run relationship among variables, and the forecasting results are reliably shown through tests ranging from unit root to cointegration analysis [2, 3]. Early studies such as Chan and Lee [24] and Lin [2] forecasted the total energy and electricity demands in China, respectively. They conducted a series of tests ranging from unit root test to cointegration test to guarantee that a cointegration relationship exists between energy demand and its factors (i.e., the nexus will not change in the medium and long term). The ARIMA model is presented as an appropriate method for long-term projections [4–8, 25]. This model depends on three parameters, including order of moving average, order of differencing, and order of autoregressive scheme. However, ARIMA cannot be employed with missing and nonstationary data; otherwise, the original data should be first transformed by differencing. Recently, Cabral et al. [7] considered the spatiotemporal dynamics in the conventional ARIMA model. Their results confirmed that the new spatiotemporal model improves the electricity demand forecasts in Brazil and is paramount to achieving the goals of the Brazilian electricity sector for a secured electricity supply. Contrary to the ARIMA model, PLSR is a popular statistical tool that can deal with data, especially missing or highly correlated data [26]. However, PLSR was recently discussed in the field of energy demand estimation [26, 27]. For instance, Zhang et al. [26] employed the PLSR model to estimate the transportation energy demand in China on the basis of GDP, urbanization rate, passenger turnover, and freight turnover. Their results demonstrate that the transport energy demand for 2020 will reach a level of 4.3313 billion tons of coal equivalent (BTCE) and 4.6826 BTCE under different scenarios.

##### 2.2. ML Method

Any optimization technique requires information on future scenarios and a search for the best solutions against a test criterion. In this case, ML techniques are superior and are frequently used to solve these two problems. The ML models include several tools, such as the AI, SVR, and Grey forecasting methods. To motivate our research, we focused particularly on the AI-based model.

The concept of SVR is developed from the computation of a linear regression function in a high-dimensional feature space where the input data are mapped via a nonlinear function, which can be found in Vapnik [28] and Vapnik et al. [29]. Dong et al. [19] were the first to employ SVR to predict the monthly energy use of buildings in tropical regions. Local weather data, including monthly average outdoor dry-bulb temperature, relative humidity, and global solar radiation, are selected as the factors affecting energy demand. Their results demonstrate that the relative error rate is less than 4%. Wang et al. [30] applied SVR for predicting hourly electricity use in residences and compared the results with other AI-based methods. They report that SVR improves the prediction accuracy.

Energy Grey forecasting model adopts the essential part of Grey system theory. In energy demand forecasting [18], the basic Grey model (GM (1,1)) was employed. Recently, Kang and Zhao [31] combined the moving average method and Markov model with GM to improve the accuracy of forecasting results. The improved Grey forecasting model demonstrates better performance compared with the conventional GM (1, 1). Xu et al. [32] combine GM and the Autoregressive and moving average model. The result indicates that the improved energy forecasting model has excellent accuracy and a high level of reliability for the case study of Guangdong Province.

AI-based prediction method predicts energy use according to its correlated variables, such as population growth, economic growth, and economic structure [2–6, 15–17]. For instance, Haldenbilen and Ceylan [10] proposed an AI model based on GA using population, GDP, and vehicle-km as affecting factors to forecast the transport energy demand in Turkey. Recently, Günay [23] modeled an electricity demand function for Turkey using the data on population, GDP per capita, inflation percentage, unemployment percentage, average summer temperature, and average winter temperature. Then, ANN is employed to determine the optimal weights that can maximize the accuracy of the function. The aforementioned algorithms can be called the single AI-based method. To eliminate several essential limitations in these algorithms, researchers also propose hybrid methods that integrate at least two AI algorithms, such as the GA-ANN [33] and PSO-GA models [12–16], to improve the prediction accuracy. The hybrid combination of a single AI algorithm shows greater performance compared with other methods.

The current AI-based prediction method is generally composed of four main steps: data collection, data preprocessing, model training, and model testing. With the superiority in time series processing, the AI-based model displays a good performance in predicting future energy demands. However, a spurious regression problem occurs in a wide range of time series analysis in econometrics owing to its nonstationarity. The current AI-based model cannot avoid this problem. If the selected variables do not satisfy the basic requirements of constructing a cointegration relationship over the sample period, the AI-based forecasting models cannot be employed to make energy demand projections because the nexus between energy demand and its factors will change in the medium and long term. Therefore, the mechanism for predicting energy demand should be reformulated.

#### 3. Methodology

##### 3.1. Introduction to AI-Based Energy Demand Model

In the precedent AI-based models, the commonly employed independent variables were around population, GDP, urbanization, industrialization, energy price, and energy mix. Three forms of the estimation models, including linear, quadratic, and exponential forms, were then adopted for data training [10, 11, 15–17], which can be expressed as follows: where models (1), (2), and (3) are the linear, quadratic, and exponential forms, respectively. In each model, is the th energy demand-affecting factor, is the number of energy demand-affecting factors, and and are corresponding weights.

The “fittest” weights are finally searched through different AI tools, such as GA, ACO, and hybrid algorithms, based on the fitness function employed to monitor the forecasting accuracy, which aims to minimize the sum of squared error between the actual and estimated values shown as follows:where and denote the actual and predicted energy demand values, respectively. is the number of observations.

After obtaining the optimal weights, the model was applied to forecast the future energy demand under different scenarios. Compared with the traditional econometric energy demand forecasting model, the proposed AI-based model frequently demonstrates higher prediction accuracy. However, according to economic theory, these periodical characteristics of economic variables will not change in the medium and long term when an economy remains in a consistent state. Consequently, their historical relationship between energy demand and factors in the sampling period should be entirely stable. When this relationship was satisfied, it could be used for forecasting energy demand. However, the current AI-based energy demand forecasting model does not determine this historical relationship through econometric and statistical analysis. This condition can be recognized as a “black-box” without knowing the internal relationship between energy demand and its affecting factors [33]. Accordingly, this model cannot be adopted for energy demand prediction when the historical relationship estimated through the AI-based model will change over time. Therefore, the improved AI-based model framework should be presented to improve the reliability.

##### 3.2. Improved AI-Based Model

As indicated in the abovementioned conventional AI-based model, the AI tool is directly applied to obtain the optimal weights for the model after preprocessing the original data. Then, the model is employed to forecast future energy demand. However, the prediction results are not reliable when the variables cannot build a stable and long-run relationship or when the parameters will change over time. Therefore, the model stability tests should be performed before proceeding to obtain the fittest weights through the AI tools. The cointegration analysis is widely employed as a key econometric method to forecast mid- and long-run energy demand because it can establish a long-run relationship among variables [3]. Cointegration theory and operations are employed to determine whether a long-run relationship exists between energy demand and its factors. To compare with the precedent AI-based model, our new framework for energy demand forecasting is shown in Figure 1(b) and the original framework described in previous literature is presented in Figure 1(a). As shown in Figure 1, if the energy demand and its factors cannot satisfy the cointegration relationship over the sample period, then this model cannot be adopted to predict future energy demand based on the current AI-based model because the stable relationship between them does not exist in the medium and long term.