Research on time series data prediction can generally be divided into three directions, namely, research on prediction methods based on statistics, research on prediction methods based on machine learning, and research on prediction methods based on hybrid models. Among them, machine learning includes traditional machine learning and deep learning, and hybrid prediction models mainly consist of two parts: signal decomposition of time series data and time series prediction.
Traditional method
In the realm of energy system forecasting, considerable advancements have been made to identify efficacious methodologies suitable for real-world application. Such forecasting models are crucial in mitigating system failure risks and enhancing the reliability of energy systems through the projection of future scenarios [
24].
Historically, an analog methodology was initially employed to project wind speed distributions, representing a nascent step in predictive modeling [
25]. This was superseded by the advent of time series models, which aimed to forecast wind power several hours ahead, thereby facilitating more agile energy management strategies [
26]. For short-term wind speed forecasting, the Kalman filter emerged as a dynamic tool that assimilated new data to refine predictions continually [
27].
Traditional statistical methods have long been used to emulate the characteristics of time series data, such as ARIMA (Auto-Regressive Integrated Moving Average) and AR-ARCH (Auto-Regressive Conditional Heteroskedasticity), both of which have found applications in financial markets for predicting return rates [
28]. The fractional-ARIMA model, which offers predictive capabilities for several days in advance, demonstrated superior accuracy compared to the persistence model in a case study involving a 750 kW wind turbine [
29]. Moreover, the ARIMA model has been effectively adapted to forecast global solar irradiance, with modifications such as the combination of ARIMA and repeated wavelet transform yielding significant improvements in forecasting performance [
30].
In an innovative step, Wang et al. incorporated an extreme learning model with ARIMA, validating its accuracy through various case studies for wind projection [
31]. The synergy between Artificial Neural Networks (ANN) and ARIMA in a hybrid model developed by K R Nair underscored the potential for greater accuracy than when these models operate independently [
32]. The integration of machine learning techniques with ARIMA has been suggested to further enhance the precision and consistency of wind speed forecasts (Liu et al. [
33]). Additionally, Asim et al., introduced an ARIMA-based model designed to improve accuracy and manage the uncertainties inherent in wind speed prediction and carbon emission control [
34,
35].
It is critical to acknowledge that ARIMA-based models exhibit optimal performance with stationary time series data. However, energy-related time series such as solar radiation and wind speed typically manifest seasonality and trends. To address these non-stationary characteristics, the Seasonal ARIMA (SARIMA) model has been employed, with Xianqi Z. demonstrating its high accuracy in predicting thermal energy requirements for district heating systems [
36]. The SARIMA-RVFL (Random Vector Functional Link) model, designed for short-term solar photovoltaic generation predictions, and Wang H. et al.'s application of the SARIMA model for monthly wind velocity forecasting have both shown improved accuracy over traditional ARIMA-based approaches [
37].
ANNs have seen widespread use due to their capacity to resolve complex nonlinear equations, thus enabling predictions across diverse future scenarios. Time series statistical methods coupled with ANNs have been extensively applied in the prediction of solar and wind energy patterns (Shuai Hu et al. [
38]). The implementation of ANN techniques in solar irradiance prediction has yielded more accurate results compared to empirical regression models [
39]. Diverse ANN architectures such as feed-forward propagation (FFBP), adaptive linear element (ADALINE), and radial basis function neural networks (RBFNN) have demonstrated varying levels of forecasting acuity, contingent upon their respective structures and parameterizations [
40]. Feed-forward neural networks (FFNN) have been broadly applied to wind power prediction with satisfactory accuracy [
41].
A novel approach using genetic neural networks (GNN), which apply a genetic algorithm for weight and bias optimization instead of the traditional backpropagation method, has shown promising results in wind velocity prediction [
42,
43]. Enhancing ANN training with particle swarm optimization (PSO) has also been reported to produce superior outcomes compared to conventional training methods [
44]. For instance, a study employing ANN to predict solar irradiance a day ahead in a grid-connected solar photovoltaic plant reported a mean absolute error (MAE) of 3.21% and a mean bias error (MBE) of 8.54% [
45].
Support vector machines (SVMs), which are adept at modeling non-linear data patterns similar to ANN techniques, have exhibited improved prediction performance in multi-layer perception neural networks (Uncuoglu, et al. [
46]). Additionally, wavelet networks—a hybrid of wavelet theory and neural network methodology—have been applied in solar irradiance prediction, with one particular study demonstrating their competitive performance against other neural network techniques [
47]. Both ANNs and SVMs have demonstrated proficiency in capturing and modeling the complex non-linear trends in energy forecasting.
Series decomposition methods for prediction
In the realm of short-term load forecasting (STLF), several methodologies have been employed over the years to enhance prediction accuracy, such as traditional algorithms, Similar Day (SD) selection, Empirical Mode Decomposition (EMD) techniques, artificial intelligence (AI), and an amalgamation of different forecasting models [
48,
49]. Deep Learning-Based Trees Disease Recognition and Classification Using Hyperspectral Data. Computers, Materials & Continua. 77. 681–697.
https://doi.org/10.32604/cmc.2023.037958.). The ever-evolving energy grids have necessitated the incorporation of diverse variables in forecasting models, such as climatic conditions, seasonal holidays, and dynamic pricing structures [
50], revealing the inadequacies of conventional forecasting approaches that often struggle with non-linear dynamics [
51].
The SD selection method relies on the analysis of historical data, pinpointing past days with load patterns that resemble the target day's expected conditions. Attributes like the day of the week and meteorological conditions serve as a basis for prediction (Maxwell et al. [
52]). This method has been refined through the integration of the XGB algorithm to determine attribute significance and calculate distances for optimal SD selection [
53]. Despite its utility, the standalone SD method may not fully encapsulate the intricate nature of electrical load patterns, prompting researchers to suggest its combination with other predictive techniques for improved robustness [
54].
AI and machine learning (ML) technologies are increasingly adopted by electric utility providers to tackle complex load forecasting. Despite significant research efforts, achieving high accuracy in STLF remains a complex endeavor due to the non-stationarity of electrical load data and the prediction of long-term dependencies [
55]. Models such as Long Short-Term Memory (LSTM) networks and their bidirectional variants (BiLSTM) are used to forecast demand-side load across different time horizons (Ullah I, et al. [
56]). Gated Recurrent Unit (GRU) models have found applications in forecasting short-term load for electric vehicle (EV) charging stations and battery state-of-charge predictions [
57,
58]. Comparative assessments of LSTM, BiLSTM, and GRU models indicated the superior performance of BiLSTM in predicting the load for EV fleets, despite the challenges posed by the complexity of aggregate load data [
59].
The EMD method has become a staple in diverse forecasting applications, ranging from energy consumption to renewable energy outputs and commodity prices [
60]. It excels at distilling original datasets into intrinsic mode functions (IMFs), facilitating the analysis of unstable and non-stationary time series data [
61]. Among the variations of EMD, the Complete Ensemble EMD with Adaptive Noise (CEEMDAN) stands out for its efficient spectral separation capabilities at a reduced computational load [
62]. Recent advancements have seen the CEEMDAN method utilized to enhance the input/output data structures for electrical demand forecasting, yielding models with substantially improved accuracy [
63].
The convergence of these advanced methodologies signifies a progressive stride in the field of STLF, highlighting a collective move towards intricate, multi-faceted approaches that address the complex nature of power consumption patterns. Integrating various models and techniques to compensate for individual limitations has become a key strategy in developing more reliable and precise forecasting systems.
In the early stages of research on time series prediction, researchers first used methods based on statistics to complete the task. Nepal B. et al. used an autoregressive moving average model (ARMA) to predict power load [
64]. However, since most time series data have strong non-stationarity, ARMA does not have good predictive performance for non-stationary time series. In order to better handle non-stationary time series data, scholars have improved the ARMA model by adding differential terms to obtain the ARIMA model, which can analyze the periodicity and oscillations of time series data. Saglam M. used the ARIMA model to predict Turkey's energy demand [
65]. Although statistical time series prediction models have achieved good predictive performance, when faced with time series data with increasing volume and complexity, models based on statistics are overwhelmed.
With the emergence of machine learning, researchers have seen new solutions. Brouno et al.
66] used the support vector machine (SVM) method to predict stock trends, while Gupta et al. used SVM to construct a time series prediction model [
67]. The experiments showed that SVM has stronger feature extraction capabilities for nonlinear data compared to prediction models based on statistics and better robustness to noise in data. Ashfaq et al. used the KNN method to predict short-term power load [
68]. KNN is a non-parametric unsupervised learning algorithm which is simple, easy to use and has strong applicability, while [
69] used ANN to predict AQI time series data in the air. ANN is a combination of multiple neurons capable of non-linear output. Compared with classical machine learning methods such as SVM and KNN, it has stronger data fitting ability. Deep learning is an important branch of machine learning. With the increase of data volume and computing power, deep learning has become increasingly prominent. Deep learning can learn more complex data features [
70]. Recurrent neural networks (RNN) can retain previously processed information and pass it to the next time step, making them very suitable for solving time series prediction tasks However, when the input sequence data is long, RNN may encounter the problems of vanishing or exploding gradients. To improve this problem, researchers have improved RNN and obtained the long short-term memory network (LSTM). (Zha et al. [
71]) used the convolutional neural network (CNN) combined with LSTM to predict natural gas production, using CNN to extract data features and further improve the predictive accuracy of the LSTM network. Graph convolutional neural network (GCN) has strong learning ability for data relations. Zhang et al. [
72] predicted traffic flow using a GCN-based model.
In recent years, more and more scholars have started to use hybrid models to complete time series prediction tasks. Hybrid prediction models generally consist of two parts: signal decomposition and signal prediction. Commonly used signal decomposition methods include EMD, EEMD, VMD, etc. Compared with single-structured prediction models, hybrid models often achieve better performance [
73,
74] used EMD to decompose the original sequence data and then used SVM to predict to achieve short-term power load forecasting. Shu et al. [
75] used EMD to decompose the original sequence data, then extracted features using CNN, and finally used LSTM neural network to model the extracted features and obtain predictive results. Experiments have shown that this model performs significantly better than single models. However, EMD lacks rigorous mathematical proof and may produce mode mixing in some cases. EEMD is a method improved from EMD to solve the problem of mode mixing. Wu et al. [
76] used EEMD combined with LSTM to predict oil prices. Yin S. et al. [
77] predicted international financial data using a combination model of VMD, ARIMA, and TEF. However, VMD cannot effectively decompose the non-periodic parts of non-stationary signals.