African economic development depends on energy consumption, the importance of accurate energy demand forecasts is self-evident for countries or regions [
2]. However, now there is limited research in the field of African energy. Even if there are few studies, almost all of them are about Southern Africa or North Africa. Meanwhile, due to limited data from Middle Africa, this paper is different from the previous ones in terms of methods and provides four small sample forecasting models. Next, one part will review the research on energy in Africa. Then, another part will introduce the features of the four models.
2.1. African Energy Research
In terms of energy research, there are many studies about Southern Africa, and North Africa that that also focus on the Middle East, or some African counties. Willem et al. developed two regression-based methods for Southern Africa to calibrate the ECHAM4.5 GCM output [
12]. And then, he used Southern African DJF forecast skill that was evaluated over a 22-year period to forecast the rainfall in early November [
13]. Collins et al. proposed nonlinear primary component analysis (NLPCA) derived from a neural network to evaluate to identify primary synoptic features [
14]. These Southern African studies provided support for local development in Southern Africa. As for North Africa, Singh et al. produced aerosol optical depth by unified model (NCUM) to forecast the dust of North Africa [
15]. Abdul el al. explained how to assess and carry out site selection for solar and wind plants and studied renewable energy development goals in countries in the Middle East and North Africa [
16]. Ben et al. used Granger causality tests and panel co-integration techniques to research the dynamic causal relationship between agricultural value added, renewable energy consumption, and real GDP [
17]. In addition, there was also research on individual countries. For example, Ramakrishnan applied data envelopment analysis of energy consumption and CO
2 emissions in 17 countries in the Middle East and North Africa [
18]. Then, there were some energy studies on South Africa. Roula et al. created a new Engle–Granger method for joint integration and error correction models to predict South Africa’s total electricity demand by 2030 [
19]. Thopil et al. predicted water usage within coal-based electricity generation by baseline assumptions and methodology, which found South Africa’s electricity generation was 20 years in the case of scarce water resources. However, there was almost no research specifically on Middle Africa. Therefore, some studies need to be done for Middle Africa.
2.2. Development of Four Methods
In this part, metabolic grey model (MGM), modified exponential curve method (MECM), autoregressive integrated moving average model (ARIMA), and BP neural network model (BP) are illustrated. Among those forecasting methods, a recent study shows that in the field of energy prediction, the top three most popular models are: Regression-based formulations, time series models and neural networks. We have established four models based on four theories: the grey theory, regression analysis theory, trend extrapolation theory, and neural network theory, and these theories cover both nonlinear and linear methods. The forecasting models used in the energy field are diverse. Each of them has their own strengths. Due to a common their feature, namely suitability for small sample prediction, four models that are totally different can be used to predict energy demand in the next 14 years in Middle Africa to provide four small sample prediction methods. Next, we will introduce the development of these four models separately.
Grey model was improved and applied by many scholars in many aspects, since Professor Deng, a famous Chinese scholar, founded the grey system theory in 1982 [
20]. It is also widely used in energy forecasting field. Wu et al. established the grey model to forecast the energy supply in 2010–2020 in Shandong Province of China [
21]. Kumar et al. developed a rolling grey model to forecast Indian crude oil consumption [
22]. Improved grey model has higher prediction accuracy than traditional grey models [
23]. In this paper, we put forward a metabolic grey model (MGM) to improve the accuracy by the rolling process. In the traditional grey model, only data from the previous four years are used to predict. The more backward the prediction data is, the less convincing the data will be. The MGM is based on the method of data substitution to improve the grey model. It uses five years data to predict the next year’s data, the latter will be pushed to the end. The continuously updated data can be fully utilized, and its accuracy can be greatly improved.
The modified exponential curve method (MECM) indicates that the development of the matter is exponential or near-exponential. Its application range is exponentially changing over a period of time, and the growth trend will slow down and stagnate as time goes by. This model is mostly used for the prediction of subgrade settlements. Zhou et al. used the Taylor expansion modified exponential curve method to predict subgrade settlement [
24]. Its characteristics are consistent with the rapid development of Middle Africa, suggesting that the method can be applied to energy consumption predictions, in theory.
ARIMA model [
25], can reflect the structure and characteristics of time series more essentially and then achieve the optimal prediction of minimum variance, which is different from the time series method that depends on different constraints [
26,
27]. This model has been widely used in public transport [
28], health care [
29] and other aspects of evaluation [
30]. It is also used in the field of energy consumption. Bhutto et al. estimated gasoline consumption in the Pakistani transport sector in the past ten years by using the ARIMA method [
31]. Wang et al. used a novel ARIMA model to forecast China’s dependency on foreign oil and it will exceed 80% by 2030 [
32]. ARIMA model in energy prediction is potential.
BP neural network proposed by scientists led by Rumelhart and McClelland is a feedforward neural network implemented by a back-propagation algorithm [
33], which is characterized by distributed storage and parallel cooperative processing of information, and its hidden layer can solve non-linear problems. Neural networks were usually used to find problems in electricity system configurations to prevent losses [
34]. In addition, it can be used as an input for data generation for the scenario approach theory mentioned [
35] for the case of energy system scheduling. BP neural network has great prospects in the field of energy prediction.
In terms of energy forecasting, previous scholars have put several methods together to predict. Yuan et al. used GM (1, 1) model and ARIMA model to predict China’s main energy consumption [
36]. Cristina et al. presented ARIMA model and autoregressive neural network (NAR) model for energy consumption forecast [
37]. Abdollah et al. proposed three forecasting models including autoregressive integrated moving average, the wavelet transform and artificial neural network, for short-term forecasting [
38]. They used one, two [
39] or even three models to predict energy problems, and this paper used four completely different types of predictive models. For comparison, it is difficult to find which model is more accurate, therefore we chose four models to forecast the same data.
The research on Middle Africa is rare, on the other hand, its resources play an important role in the world and its development should be of concern. Another reason is that the energy consumption data of Middle Africa used in this paper include three characteristics as follows:
- (1)
Energy demand prediction only depends on single raw data.
- (2)
The target of prediction is to show the energy demand in the next ten years, and these models can meet the need of long-term prediction.
- (3)
It is limited data, belonging to a small sample.
According to these characteristics, we chose four models-improved GM, modified exponential curve, linear ARIMA and non-linear BP. Four models provide a multifaceted comparison and show the possibility of prediction from multi-angle. At last, a small sample study is the core of this paper, therefore we can get the ideal results by selecting an appropriate method to predict appropriate data. The method system we have established solved the limitations, further improved prediction accuracy, and provided a methodological reference.