This is because linear methods cannot be used to detect the complex implicit patterns in time series. This study adopts a hybrid model by incorporating linear and nonlinear methods to predict energy consumption and overcome this problem. However, in accordance with previous studies, no single prediction model is applicable to all scenarios. Therefore, many researchers have introduced hybrid models for predicting time series; such models incorporate both linear and nonlinear models or combine two linear models [5].
Earlier works have also revealed that such hybridization of prediction frameworks not only shows the complementary nature of the frameworks with respect to predictions but also enhances the accuracy of predictions. Thus, models in hybrid forms have become a common practice in forecasting.
However, noise and unknown factors exist in time series. To make the prediction more precise, noise problems should be carefully dealt with. There are several ways to approach noise problems and enhance forecasting performance. One way is to tune the hyperparameter for algorithms such as the support vector regression, SVR.
If a decomposition approach is used, the time series can be split into several stable sequences for prediction. The concept of the proposed model comes from several sources. It has been extensively used to deal with various forecasting issues. Second, based on past research, univariate or single methods used to deal with forecasting problems cannot yield a high forecasting performance when compared to hybrid methods.
Therefore, this study simultaneously uses another nonlinear method, SVR, to enhance the prediction performance. In past decades, SVR has been useful in a wide variety of prediction domains. Therefore, SVR is suitable for this study. Due to computing speed, the authors cannot spend much time searching for the ideal hyperparameters. Consequently, the greedy algorithm grid search will be abandoned. Due to the innovativeness and power of EEMD, recent studies have widely adopted the method in signal processing research.
First, the time series of energy consumption is divided into several intrinsic mode functions IMFs and a residual term. The characteristics of the time series can also be captured in detail. Since the accuracy of the nonlinear time series derived using the ARIMA may be unacceptable, the SVR is utilized based on the nonlinear pattern to further improve prediction performance. In addition, the accuracy of the SVR-based prediction models completely depends on the control parameters, and the parameters should be optimized.
Therefore, the GA is leveraged to derive the optimal parameters. The remaining part of this work is structured as follows. Section 2 reviews the related literature regarding the consumption and forecasting methods of energy. Section 4 describes the background of the empirical study case, the dataset, and the empirical study process. Albeit important, predicting energy consumption is not always simple. Therefore, a robust forecasting model will be necessary.
In the literature on energy prediction, several researchers have completed accurate predictions [2—4,11,12]. Some researchers adopted economic indicators by mixing various energy indicators for predicting energy consumption. Other researchers used only time series data for forecasting. While these forecast methods are different, the prediction results of the two categories of models can serve as solid foundations for further investigations on energy consumption.
Furthermore, to enhance the accuracy of predictions, some authors employed hybrid models. Of such models, linear and nonlinear ones were integrated. The fusion of linear and nonlinear models can overcome the shortage of adopting only one kind of method and provide more accurate results [3,5,13]. In addition to the hybrid methods involving both linear and nonlinear models, some studies have attempted to transform the data by integrating data preprocessing and post-processing procedures [14,15].
By doing so, the forecasting capabilities of the hybrid models with data preprocessing and postprocessing procedures can show superior performance in energy predictions. Further, several studies have proposed machine learning methods for predicting energy consumption. Al-Garni, Zubair, and Nizami [16] used weather factors as explanatory variables of a regression model for predicting the consumption of electric energy in eastern Saudi Arabia.
Azadehet al. Fumo and Biswas [11] employed simple and multiple regression models as well as the quadratic regression model to predict residential energy consumption. Ahmadet al. Ardakani and Ardehali [3] applied regressive methods consisting of linear, quadratic, and ANN models by incorporating an optimization algorithm into the model to achieve better performance in predicting long-term energy consumption. That is, even if the machine learning model outperforms other traditional linear methods, using a single machine learning model to address all time series issues would be problematic and unrealistic.
Many researchers have thus employed hybrid time series forecasting models, which incorporate linear with nonlinear models or combine two kinds of linear models [5]. Previous studies have also revealed that such hybrid frameworks not only complement each other in prediction but also enhance prediction accuracy.
Zhu et al. Azadeh, Ghaderi, Tarverdian, and Saberi [20] also adopted the GA and ANN models to predict energy consumption based on the price, value-add, number of customers, and energy consumption. Further, Yolcuet et al.
They achieved prediction results superior to those of conventional forecasting models. Because of these limitations, more researchers started to adopt SVR in forecasting since it can mitigate the disadvantages of ANN models. SVR is suitable for forecasts based on small datasets. Based on the results of the literature review, hybrid models, including both the SVR and the ANN, have achieved higher prediction accuracies than traditional prediction techniques.
Wang et al. The work demonstrated that the EEMD technique can decompose the nonstationary and time-varying components of times series of crude oil prices. In their methodologies, these works being reviewed attempted to use linear or nonlinear methods to predict energy consumption.
Furthermore, they tried to use the parameter search algorithm in their model to enhance its prediction accuracy. Based on the review results, complex time series can be split by the EEMD into several relatively simple subsystems. The hidden information behind such complex time series can be explored more easily. The framework will be adopted to predict primary energy consumption. Afterward, the optimization approach based on GA will be introduced.
Finally, the analytical process of the proposed hybrid model will be described. When the residue r t becomes a monotonic function or at most has one local extrema point from which no more IMF can be extracted [27], the shifting processes can be terminated. All the IMFs are nearly orthogonal to each other, and all have nearly zero means. Although the EMD has been widely adopted in handling data series, the mode-mixing problem still exists.
The core concept of the EEMD method is to add the white noise into the data processing. White noise can be viewed as a sequence with zero mean value; this sequence does not fall under any distribution. In EEMD, the purpose of this method is to make the original sequence the stable sequence. Hence, this method employs simulation, using the original sequence to generate various sequences of normal distributions—this is the white noise concept. Meanwhile, the sum of the decomposed sequences equals the original sequence.
These decomposed sequences are called IMFs. This way, the mode-mixing problem can be easily solved. Based on previous studies, the number of ensemble members is often set to , and the standard deviation of white noise is set to 0. The model consists of the autoregressive AR and the moving average MA models. The future value of a variable is a linear function of past observations and random errors. This way, the d parameter is determined. Through the parameter estimation Mathematics , 8, and diagnostic checking process, the proper model will be established from all the feasible models.
Meanwhile, hypothesis testing is conducted to examine whether the residual sequence of the model is a white noise. Based on the above procedures, the forecasting model will be determined. The derived model will be appropriate as the training model for predictions. Fitting performance is expected to be enhanced further. Conventional regression methods take advantage of the square error minimization method for modeling the forecasting patterns.
Such a process can be regarded as an empirical risk in accordance with the loss function [29]. Thus, this study aims to predict energy consumption by using integrated methods that incorporate linear and nonlinear methods. Due to issues that arise in time series forecasting, accurate predictions are essential. This is because linear methods cannot be used to detect the complex implicit patterns in time series. This study adopts a hybrid model by incorporating linear and nonlinear methods to predict energy consumption and overcome this problem.
However, in accordance with previous studies, no single prediction model is applicable to all scenarios. Therefore, many researchers have introduced hybrid models for predicting time series; such models incorporate both linear and nonlinear models or combine two linear models [5].
Earlier works have also revealed that such hybridization of prediction frameworks not only shows the complementary nature of the frameworks with respect to predictions but also enhances the accuracy of predictions. Thus, models in hybrid forms have become a common practice in forecasting. However, noise and unknown factors exist in time series.
To make the prediction more precise, noise problems should be carefully dealt with. There are several ways to approach noise problems and enhance forecasting performance. One way is to tune the hyperparameter for algorithms such as the support vector regression, SVR. If a decomposition approach is used, the time series can be split into several stable sequences for prediction. The concept of the proposed model comes from several sources.
It has been extensively used to deal with various forecasting issues. Second, based on past research, univariate or single methods used to deal with forecasting problems cannot yield a high forecasting performance when compared to hybrid methods. Therefore, this study simultaneously uses another nonlinear method, SVR, to enhance the prediction performance. In past decades, SVR has been useful in a wide variety of prediction domains.
Therefore, SVR is suitable for this study. Due to computing speed, the authors cannot spend much time searching for the ideal hyperparameters. Consequently, the greedy algorithm grid search will be abandoned. Due to the innovativeness and power of EEMD, recent studies have widely adopted the method in signal processing research.
First, the time series of energy consumption is divided into several intrinsic mode functions IMFs and a residual term. The characteristics of the time series can also be captured in detail. Since the accuracy of the nonlinear time series derived using the ARIMA may be unacceptable, the SVR is utilized based on the nonlinear pattern to further improve prediction performance. In addition, the accuracy of the SVR-based prediction models completely depends on the control parameters, and the parameters should be optimized.
Therefore, the GA is leveraged to derive the optimal parameters. The remaining part of this work is structured as follows. Section 2 reviews the related literature regarding the consumption and forecasting methods of energy.
Section 4 describes the background of the empirical study case, the dataset, and the empirical study process. Albeit important, predicting energy consumption is not always simple. Therefore, a robust forecasting model will be necessary. In the literature on energy prediction, several researchers have completed accurate predictions [2—4,11,12]. Some researchers adopted economic indicators by mixing various energy indicators for predicting energy consumption.
Other researchers used only time series data for forecasting. While these forecast methods are different, the prediction results of the two categories of models can serve as solid foundations for further investigations on energy consumption. Furthermore, to enhance the accuracy of predictions, some authors employed hybrid models.
Of such models, linear and nonlinear ones were integrated. The fusion of linear and nonlinear models can overcome the shortage of adopting only one kind of method and provide more accurate results [3,5,13]. In addition to the hybrid methods involving both linear and nonlinear models, some studies have attempted to transform the data by integrating data preprocessing and post-processing procedures [14,15]. By doing so, the forecasting capabilities of the hybrid models with data preprocessing and postprocessing procedures can show superior performance in energy predictions.
Further, several studies have proposed machine learning methods for predicting energy consumption. Al-Garni, Zubair, and Nizami [16] used weather factors as explanatory variables of a regression model for predicting the consumption of electric energy in eastern Saudi Arabia. Azadehet al. Fumo and Biswas [11] employed simple and multiple regression models as well as the quadratic regression model to predict residential energy consumption.
Ahmadet al. Ardakani and Ardehali [3] applied regressive methods consisting of linear, quadratic, and ANN models by incorporating an optimization algorithm into the model to achieve better performance in predicting long-term energy consumption. That is, even if the machine learning model outperforms other traditional linear methods, using a single machine learning model to address all time series issues would be problematic and unrealistic.
Many researchers have thus employed hybrid time series forecasting models, which incorporate linear with nonlinear models or combine two kinds of linear models [5]. Previous studies have also revealed that such hybrid frameworks not only complement each other in prediction but also enhance prediction accuracy. Zhu et al. Azadeh, Ghaderi, Tarverdian, and Saberi [20] also adopted the GA and ANN models to predict energy consumption based on the price, value-add, number of customers, and energy consumption.
Further, Yolcuet et al. They achieved prediction results superior to those of conventional forecasting models. Because of these limitations, more researchers started to adopt SVR in forecasting since it can mitigate the disadvantages of ANN models. SVR is suitable for forecasts based on small datasets.
Based on the results of the literature review, hybrid models, including both the SVR and the ANN, have achieved higher prediction accuracies than traditional prediction techniques. Wang et al. The work demonstrated that the EEMD technique can decompose the nonstationary and time-varying components of times series of crude oil prices. In their methodologies, these works being reviewed attempted to use linear or nonlinear methods to predict energy consumption.
Furthermore, they tried to use the parameter search algorithm in their model to enhance its prediction accuracy. Based on the review results, complex time series can be split by the EEMD into several relatively simple subsystems. The hidden information behind such complex time series can be explored more easily. The framework will be adopted to predict primary energy consumption. Afterward, the optimization approach based on GA will be introduced.
Finally, the analytical process of the proposed hybrid model will be described. When the residue r t becomes a monotonic function or at most has one local extrema point from which no more IMF can be extracted [27], the shifting processes can be terminated.
All the IMFs are nearly orthogonal to each other, and all have nearly zero means. Although the EMD has been widely adopted in handling data series, the mode-mixing problem still exists. The core concept of the EEMD method is to add the white noise into the data processing. White noise can be viewed as a sequence with zero mean value; this sequence does not fall under any distribution.
In EEMD, the purpose of this method is to make the original sequence the stable sequence. Hence, this method employs simulation, using the original sequence to generate various sequences of normal distributions—this is the white noise concept. Meanwhile, the sum of the decomposed sequences equals the original sequence.
These decomposed sequences are called IMFs. This way, the mode-mixing problem can be easily solved. Based on previous studies, the number of ensemble members is often set to , and the standard deviation of white noise is set to 0. The model consists of the autoregressive AR and the moving average MA models. The future value of a variable is a linear function of past observations and random errors.
This way, the d parameter is determined. Through the parameter estimation Mathematics , 8, and diagnostic checking process, the proper model will be established from all the feasible models. Meanwhile, hypothesis testing is conducted to examine whether the residual sequence of the model is a white noise.
Based on the above procedures, the forecasting model will be determined. The derived model will be appropriate as the training model for predictions. Fitting performance is expected to be enhanced further.
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