Models of Electricity Price Forecasting: Bibliometric Research

Abstract

Electricity Price Forecasting (EPF) influences the sale conditions in the energy sector. Proper models of electricity price prognosis can be decisive for choice between energy sources as a start point of transformation toward renewable energy sources. This article aims to present and compare various EPF models scientific publications. Adopted in this study procedure, the EPF publications models are compared into two main categories: the most popular and the most accurate. The adopted method is a bibliometric study as a variation of Systematic Literature Review (SLR) with specified automated queries supported by the VOSviewer bibliometric maps exploration. The subject of this research is the exploration of EPF models in two databases, Web of Science and Scopus, and their content comparison. As a result, the SLR research queries were classified into two groups, the most cited and most accurate models. Queries characteristics were explained, along with the graphical presentation of the results. Future promising research avenues can be dedicated to the most accurate EPF model formulation proved by statistical testing of its significance and accuracy.

1. Introduction

The energy sector is the core of each country’s economy and influences all other economic sectors [1,2]. This sector impacts economic growth [3,4] and development [5,6]. In the energy sector, there is an ongoing transition from fossil fuels to renewable or nuclear energy [7,8]. The transformation processes have been challenging the “traditionally monopolistic and government-controlled power sectors” [9]. This change also influences energy prices [10,11] and Electricity Price Forecasting (EPF) procedures [9,12] and models [13,14]. On the other hand, the mathematical models that predict what electricity prices will be in the future are important not only for the electricity produces [15,16] but also for their clients [17,18]. Electrical energy producers are involved in domestic economies because energy sources affect the prices of energy goods and services [19,20].

The EPF in the energy sector influences energy companies’ stocks [8] and their business management [21,22] and strategic decisions [19,23], because electricity is also traded under market rules [15,21]. The energy sector companies generate, transfer, distribute, and retail electricity [19]. The conditions under which they operate can be described as a dynamic equilibrium between supply and demand [24] due to the changes caused by the weather and business activity [25]. On the other hand, electricity is a very special commodity, because it is “economically non-storable, and power system stability requires a constant balance between production and consumption” [9]. Electricity price is hard to forecast because of the unanticipated price dynamics [26,27] and specific characteristics of the market [28,29]. The development of the methods represented in citation dynamics, or the number of newly published papers, indicates the importance of the subject and is the reason for this research.

In the literature related to the EPF, the forecasting models are based on the specific statistical methods chosen for the energy sector [30]. The choice of the EPF model and its results can support the decision-making process in day-ahead trading, the transition towards new preferred business technologies [22], renewable energy sources [31,32], electromobility [33,34], and regional investment directions [35]. Although the forecasting methods are numerous, they have encouraged researchers to intensify their studies to develop more accurate forecasting techniques [36]. Finally, there is a research gap related to the comprehensive comparison of the EPF models’ bibliometric relations, their development, and their accuracy [37]. There is also a growing importance of transforming the economy [38,39] and economic growth model into one “that includes the environmental as well as the social dimension and establishing a relationship between the environment and development” [40]. Such a change is possible only if the EPF models are classified or their risks are recognized and assessed [41]. The accuracy of the EPF influences the volume of the generated electricity [42,43] and reduces the operational risk in business [44,45]. Therefore, the subject of EPF is important because the choice of the model has fundamental input on energy companies’ strategic decision-making [3,46].

The aim of this article is to present and compare various EPF models in two categories: the most popular (often cited), and the most accurate procedures. The models presented in this scientific paper literature review of EPF models cover identified research gaps in the indicated categories. This research is an attempt to determine which EPF approaches are the most popular and accurate procedures [9]. The adopted method in this research is a bibliometric study as a variation of Systematic Literature Review (SLR) [47,48] based on the databases’ research queries [49,50] and developed in bibliometric maps with the use of the VOSviewer program (version 1.6.18) [51]. The method used in this research is to perform bibliometric analysis to produce a network visualization of keyword maps for the queries [52,53].

This paper is based on the structure of the obtained data from two original queries, and the database’s scope and results. The queries used in this research allowed this study to explore Scopus and Web of Science databases. This study provides data analysis by utilizing mapping tools and providing analysis of the research gap [22]. Then, the scientific contribution of this paper is to demonstrate the bibliometric data analysis related to the identified EPF two groups’ procedures. Therefore, this paper presents and compares various EPF model-related publications into two groups: the most popular and the most accurate [54,55].

The paper is organized in a classical arrangement and has an IMRaD structure. After already being presented in this section introduction, the method section is explained in detail. The detailed method explanation in this article is accompanied further by the obtained calculations and presentation of results. Based on the proposed methods, the results of the Systematic Literature Review (SLR) are analyzed, presented, and discussed. Then, conclusions are presented, along with the theoretical and managerial implications, in the last part of this article. The possible research avenues are also addressed.

2. Method

The subjects of the research were scientific publications collected in bibliographic databases WoS and Scopus. These scientific databases are multidisciplinary [56]. A bibliographic database is an organized digital collection of references to published scientific literature, including journal articles, conference proceedings, patents, books, etc. Scientific databases generally contain very rich subject descriptions in the form of keywords, subject classification terms, or abstracts [56]. Information related to a bibliographic record is called bibliographic metadata, and this can be explored with visualization tools. The method adopted in this paper is a bibliometric study variation of SLR [57] to explore EPF models related to publications based on the queries in scientific databases. The SLR has its own procedure, which is not presented in detail in this paper [58]. There is also a classical review method dedicated to the selected papers’ overall presentation. The papers were distinguished in the SLR and VOSviewer (version 1.6.18) analyses [59]. In the variation of the SLR method, the two original queries were formulated by authors based on the keywords to create a comprehensive and similar query syntax for each explored database. The use of similar keywords may have influenced the results of the study when two databases are compared. The keyword “business management” in the Web of Science query was added automatically by search filters. Next, keyword “business management” in the Web of Science was emphasized directly in the syntax of Query 2. Scopus query has a similar keyword “limit-to (SUBJAREA, “BUSI”)” and it was created from the refined results sidebar after the query was executed to achieve similarity of queries. The inspiration for the two queries was the publication of R. Weron [9], which is based on a similar bibliometric approach [60]. Therefore, in this paper, the main method is supported by the bibliometric analysis performed in VOSviewer for the Web of Science (WoS) and Scopus databases. The choice of these two databases has its limitations, most notably the fact that some of the newer journals are not indexed in these systems. There is no fixed classification in research in terms of the EPF technique details or in terms of the planning time horizon duration in the researched EPF models. The adopted approach in performed SLR is an explorative one. For the Scopus search, original Query 1 was constructed as follows:

(TITLE-ABS-KEY (((forecasting) AND (electricity AND spot OR electricity AND day-ahead OR electricity AND price)) OR ((price AND forecasting OR price AND prediction OR forecasting AND price OR predicting AND price OR forecasting AND spikes) AND (electricity AND spot AND price OR electricity AND price OR electricity AND market OR day-ahead AND market OR power AND market OR sales OR energy AND sectors)))) AND (limit-to (srctype, “j”) OR limit-to (srctype, “p”)) AND (limit-to (doctype, “ar”) OR limit-to (doctype, “cp”)) AND (limit-to (subjarea, “COMP”) OR limit-to (subjarea, “ECON”) OR limit-to (SUBJAREA, “BUSI”) OR limit-to (subjarea, “SOCI”)) AND (limit-to (pubyear, 2021) OR limit-to (pubyear, 2020) OR limit-to (pubyear, 2019) OR limit-to (pubyear, 2018) OR limit-to (pubyear, 2017) OR limit-to (pubyear, 2016) OR limit-to (pubyear, 2015) OR limit-to (pubyear, 2014)) AND (limit-to (Language, “English”))

(1)

The original standard Query 2 for the Web of Science exploration was formulated as:

TS = (((“forecasting”) AND (“electricity spot” OR “electricity day-ahead” OR “electricity prices” OR “sales”)) OR ((“price forecasting” OR “price prediction” OR “forecasting” “price” OR “predicting price” OR “forecasting spikes”) AND (“electricity spot price” OR “electricity price” OR “electricity market” OR “day-ahead market” OR “power market” OR “energy sectors”)) AND (“business management”))

(2)

There are differences in the formulated queries. The queries have a syntax that corresponds with the database on which they are used. Moreover, queries differ in the explicit year, publication type, and category filters in the query. The WoS search panel allows filtering by refining results, which do not differ from examined queries. The Query 2 limitations are chosen from the left panel of the WoS and are equivalent to the Query 1 filters. To determine which models are accurate, the word “accurate” was added to the end of the query for the studied databases. This modification was the basis for the new queries dedicated to the exploration of the most accurate EPF models in the Scopus and WoS databases. Double underlined “AND” in Queries 1 and 2 indicates the position where the keyword was added (before filtering to year, publication, and category). For Query 1, according to the syntax, the following was added after double underlined the “AND” element of syntax: (accurate and precise), so this part of Query 1 has the form: AND (accurate OR precise). In the case of WoS exploration with Query 2, the “accurate” or “precise” search phrases were set after “forecasting” but before the underlined “AND” because only there yielded satisfactory results. After the modifications, Query 1 output yielded 198 document results and Query 2 hit 85 document results, respectively. The most cited scientific publications were visible in both databases when the filter “most cited” was applied to the results of Queries 1 and 2, respectively. The results of this procedure are gathered in Supplementary Materials File S1. Due to the ongoing research in the discipline, the newest publications were not distinguished from each database with the use of original Queries 1 and 2, respectively. The newest publications can be selected with the use of the publication date filter in Scopus and WoS on the basis proposed in this study for the two queries. However, heat maps or overlay visualizations as bibliometric maps in VOSviewer were also generated to illustrate the direction and development of scientific publications about the most cited and accurate EPF models.

To extend the SLR method, the VOSviewer program was used. The results obtained from Queries 1 and 2 from the studied time intervals were downloaded each time a set of files, for the Scopus database in .csv format, and WoS, a .txt file, and during export, all fields on the publication were marked. For Scopus, the following fields were selected for export: citation information, bibliographic information, abstract, keywords, funding details, and other information. On the other hand, in the WoS database, the following fields were marked for export: author, title, source, abstract, keyword, addresses, cited references, use of funding, and others. Further analyses were carried out on the most recent data. The exported data were used for analyses in VOSviewer, and the results are shown in bibliometric maps. The choice of the number of keywords co-occurrences determines the result obtained in its graphical presentation and bibliometric map clarity, as suggested by L. Waltman and N. Van Eyck [59]. Therefore, a minimum number of 5 keywords co-occurrences was set for each bibliometric map, if not indicated by another number of co-occurrences for a specific map. Additionally, there is a comparison between bibliometric analysis results performed at different time points. This procedure aims to present the dynamics of the scientific interest in the EPF, also visible in bibliometric maps revealing the subject trends. The VOSviewer allows researchers to define the research gaps covered by published papers and indicate the directions of scientific development. The exploration of the scientific databases leads to the comparison of two categories of the queries results. First were highly cited papers (hoping that they are ‘the influential ones’) and therefore cover the most popular models listed in Supplementary Materials File S1. Second, the most accurate procedures are listed in Supplementary Materials File S2 and presented in the article text. The newest EPF models are rarely cited, but they are opening new and promising research avenues.

3. Results

This section is divided into two subsections that reflect the two method approaches. The first subsection contains a bibliometric analysis of the popularity of EPF-related publications and those that are claimed to be the most accurate or precise [9]. This approach is gaining popularity in bibliometric analysis with the use of queries and VOSviewer software [61]. The second subsection consists of an overview of the selected scientific publications identified as the most cited and accurate EPF models in the first subsection [62].

3.1. Bibliometric Analysis Results

Queries 1 and 2 were used for studying each database at different time points. The number of the obtained results of each query is presented in

Table 1. Queries dynamics results in indicated time points.

Query	10 December 2021	10 May 2022	10 July 2022
1 (Scopus)	766	798	851
2 (WoS)	377	435	443

Source: Authors elaboration.

. The observed changes indicate the huge dynamics in the topic of EPF and its popularity. There are existing research gaps covered by researchers in multiple papers within seven months.

Although the WoS has fewer records representing the indexed scientific publications than Scopus (Table 1), the syntaxes of formulated Queries 1 and 2 differ. The results do differ quantitatively, as the collections of publications indexed by WoS and Scopus are not the same, but they do not differ qualitatively. However, the Scopus search engine is more user-friendly and allows for more refined queries. The results presented in the Supplementary Materials File S1 section prove that among the ten most cited papers indexed in WoS, some go beyond the energy or EPF models. There are some of the most cited papers related to the fashion, food, and movie industries. Due to this observation, these papers were excluded from further research with the VOSviewer program. However, from Scopus analysis, the most popular model (Table S1 in Supplementary Materials File S1) for EPF is “A moving-average filter-based hybrid ARIMA-ANN model for forecasting time series” [63]. On the other hand, in the same Query 1 results, there is the highest growth (111%) of citations related to the paper titled “Energy markets volatility modeling using GARCH“ [64]. In the WoS, the most popular is the paper “An empirical comparison of alternative schemes for combining electricity spot price forecasts” [65], as proved by Query 2 (Table S2 in Supplementary Materials File S1).

The number of publications aggregated by year in the WoS and Scopus databases is displayed in Figure 1. A primary database, Queries 1 and 2, was used to generate tabular results, and the graph was created using a Python tool. Figure 1 presents the results of Queries 1 and 2 in the period 2014–2021. The year 2022 is not presented in Figure 1. The WoS contains a lower number of scientific publications than Scopus, but on this basis, it is not clear if it contains the same documents. Contrary to other publications, there is no certainty that the WoS is a sub-collection of Scopus (differences in results collected in Supplementary Materials File S1). Figure 1 shows numbers for scientific books, book chapters, journal articles, and conference papers.

Figure 2 and Figure 3 show a bibliometric map of co-occurrences of keywords related to EPF forecasting models in the energy sector. A file was selected in the VOSviewer program, which was prepared from the queries performed on the Scopus and WoS databases. A 5 minimum number of keywords co-occurrences was set for each bibliometric map (Figures 2–4 and 6 except for Figures 5 and Figure 7). In the final dialogue box in the VOSviewer program, the keywords selected that are related to forecasting models and keywords duplicates were removed.

Although the EPF subject was explored by Query 1 in Scopus and Query 2 in Wos, the keyword “electricity price forecasting” is not present in Figure 2 and Figure 3. The keywords which were selected and used by the VOSviewer program are gathered in

Table 2. Clusters of keywords co-occurrences visible in Figure 2 for Scopus.

Cluster	Color	Keywords
1	Red	Bayesian networks; clustering; fuzzy neural networks; wavelet transforms; genetic algorithms; Monte Carlo methods; neural networks
2	Green	convolutional neural networks; deep learning; long short-term memory; multilayer neural networks; recurrent neural networks; reinforcement learning
3	Blue	feedforward neural networks; linear regression; arima; support vector machine; hybrid model; garch
4	Yellow	adaptive boosting; decision trees; ensemble learning; gradient boosting
5	Purple	extreme learning machine; machine learning

Source: Authors elaboration.

. Keywords are separated by semicolons. In Table 2 there are clusters identified by colors, as in Figure 2. Despite the original writing form (for example ARIMA or GARCH models), the keywords in Table 2 are written in small letters as in the VOSviewer program. The order of clusters presented in Table 2 is caused by the number of keywords identified by the VOSviewer.

The identified clusters are related to the different areas of the scientific interest of the analyzed scientific publications’ authors. First is the red cluster, related to the mathematical aspects of EPF models. The second cluster is marked in green and is related to deep learning, and this is additionally represented in Table 2. In Figure 2, there is also a third cluster with seven keywords, and this cluster is related to the classical statistical models. The fourth cluster (yellow color) consists of keywords combined with analyses of data used for EPF model formulation. The final identified by the VOSviewer cluster revolves around machine learning with two similar keywords.

Figure 3 presents the graphical results of Query 2 used for the WoS exploration. In Figure 3, the minimum 5 co-occurrences of keywords are represented as nodes in the network. The edges of the network represent the explored co-occurrences between keywords in data obtained from WoS [66]. The keywords used in the WoS Query 2 were collected in

Table 3. Clusters of keywords co-occurrences as visible in Figure 3 for WoS.

Cluster	Color	Keywords
1	Red	machine learning; regression; deep learning; support vector machines
2	Green	selection; lasso; quantile regression; arima
3	Blue	artificial intelligence; neural networks; classification
4	Yellow	genetic algorithms; support vector regression; extreme learning-machine

Source: Authors’ elaboration.

and are separated by semicolons. The keywords are written in small letters in Table 3, despite their original writing due to the VOSviewer procedures.

In Table 3 there are 4 clusters automatically identified and ordered by the VOSviewer program. The first cluster is marked in color red in Figure 3 and consists of co-occurring keywords related to machine learning models of EPF. The second cluster keywords revolve around procedures and models related to the EPF. Another group of scientific publications gathered in the third blue cluster crate paper dedicated to artificial intelligence. The last cluster, colored in yellow in Figure 3, consists of a mix of EPF procedures.

Figure 2 (results from Query 1) and Figure 3 (results from Query 2) bibliometric maps represent the number proportions presented in Table 1 and Figure 1. There is a significantly lower number of the bibliometric map nodes in Figure 3, which represent keywords identified by VOSviewer algorithms. There are, however, the common points of both bibliometric maps visible in yellow keywords (Figure 2 and Figure 3) related to EPF models: LSTM, deep learning, and regression models.

After the identification of the most popular EPF method in scientific works and their areas in two researched databases, the used original queries were modified to find the most accurate EPF models. Although the EPF models and procedures were explored by Query 1 in Scopus and Query 2 in Wos, the keyword “electricity price forecasting” is not present in Figure 4 and Figure 5. There are co-occurring keywords, along with the EPF’s most accurate models.

Figure 4 presents the graphical results of data gathered with Query 1 in the Scopus database exploration. In Figure 4, the minimum 5 co-occurrences of keywords are represented as nodes in the network. The edges of the network represent the explored co-occurrences between keywords in data obtained from WoS. Their connection represents the common areas represented by the repetition of some keywords in clusters distinguished automatically by the VOSviewer program. The keywords extracted from Scopus by modified Query 1 were collected in

Table 4. Clusters of keywords co-occurrences as presented in Figure 4.

Cluster	Color	Keywords
1	Red	neural networks; fuzzy neural networks; wavelet transforms; multilayer neural networks; genetic algorithms
2	Green	decision trees; support vector machines; clustering; adaptive boosting
3	Blue	long short-term memory; deep learning
4	Yellow	arima; hybrid model
5	Purple	machine learning; extreme learning machines

Source: Authors’ elaboration.

. The keywords are written again in small letters, despite their original writing.

In Table 4 there are 5 clusters identified and ordered automatically by the VOSviewer [67]. The first cluster is marked in color red in Figure 4 and consists of co-occurring keywords related to neural networks and their modifications related to models of EPF [16,68]. Second cluster keywords revolve around procedures and models related to the EPF such as clustering and decision tree models. Another group of scientific publications gathered in the third blue cluster is dedicated to deep learning. The fourth cluster, colored in yellow in Figure 4, consists of hybrid EPF model procedures. The last cluster in Table 4 consists of the keywords “machine learning” and “extreme learning machines”, which are used to calculate the most accurate EPF models.

Figure 5 presents the bibliometric map of keyword co-occurrences with a minimum number of thresholds equaling 1. During the creation of a bibliometric map, the same methodology as in the Figures described earlier was applied. The uniqueness of this map comes from the vast number of clusters and their combinations. Two clusters (green, yellow, and red) were observed to be interconnected. The remaining clusters are connected by a minimum of 2 keywords between them or are so far apart that the keywords do not strictly form clusters, as there is one keyword in the cluster defined by the VOSviewer software. Therefore, only the interconnected three nodes are further described in

Table 5. Selected clusters of keywords co-occurrences presented in Figure 5.

Cluster	Color	Keywords
1	Red	machine learning; xgboost; sarima; ga-bp algorithm
2	Green	arima; hybrid model; neural networks; lasso
3	Yellow	classification; decision trees

Source: Authors elaboration.

.

In Table 5 there are presented only interconnected clusters from Figure 5. The rest of the clusters are nodes with no connections. The designed minimum cluster size was established for 2 keywords. Only red and green clusters aggregate more than 2 keywords (Table 5). The most accurate EPF models identified in the WoS database are gathered in the red cluster and are connected with the following keywords: machine learning; xgboost; sarima; ga-bp algorithm. The second cluster, colored green, consists of hybrid EPF models. The third yellow cluster is similar to the results gathered in Table 4, and cluster 2 is related to the decision trees and classification procedures.

Keywords identified in bibliometric procedures with the use of original and modified Queries 1 and 2 are collected in

Table 6. Common results of the performed analyses of publications related to the EPF models.

Most Cited Scientific Publications	Most Accurate Scientific Publications
extreme machine learning; machine learning; arima; neural networks	arima; hybrid model; decision trees

Source: Authors elaboration.

. Common keywords are present in different numbered and colored clusters when the results of original queries are compared. The hybrid models are a narrow group of methods and are a subset of machine learning. These keywords are distributed without any pattern between Table 2 and Table 3. In modified query results, the whole colored and numbered clusters are exchanged between Table 4 and Table 5. For example, the yellow 4th cluster from Table 4 and part of the 2nd green cluster in Table 5.

There are more differences between Table 4 and Table 5. Therefore, there is a small number of common keywords in Table 6. Another reason for the observed differences between Table 4 and Table 5 is the different thresholds of a minimum number of co-occurring keywords, 5 and 1 keyword respectively. This indicates that the Scopus database contains more details than WoS in areas related to the EPF models [68,69]. That was proved by the disconnected points in the bibliometric map in Figure 5 instead of the network in Figure 4 (Scopus’ results).

The trend of EPF models is presented in Figure 6 and Figure 7. The overlay visualization map indicates which methods have been developed over time and which are still in use. The years are represented by various color ranges. In blue, green, and yellow, the topics studied over the studied years of 2014–2021 are depicted. Darker colors are used to mark the older publications, while light colors represent the newest publications.

In Figure 6, there is a clear shift from fundamental or classical statistical EPF methods (purple and dark blue) to decision trees and their derivatives (green and light green) to keywords associated with the most recent (yellow) EPF models: LSTM, deep learning [70], and convolutional neural networks. Additionally, there are strong relations between neural networks and machine learning, which are presented as a wider edge between these two nodes in Figure 6, also visible in dynamic analysis in the VOSviewer software. Trend analysis does not provide information about groups or categories of methods to calculate EPF models as shown in Figure 2, Figure 3, Figure 4 and Figure 5. However, it is possible to name 3 main groups in Figure 6 and Figure 7, due to the years and colors: blue (2016–2017), green (2018–2019), and yellow (2020–2021).

In Figure 7, there is movement in the interest of authors from ARIMA to LSTM. This change is visible in Figure 7: differences between the oldest blue and the newest yellow keyword in the presented time. There is a distinguished group of keywords on the far-right side of Figure 7, and those are extreme machine learning, support vector regression, and genetic algorithms. Those keywords represent the oldest directions of scientific publications dedicated to EPF models. There are also combined methods of EPF in the upper-left corner of Figure 7. Classification and clustering methods are represented on the lower-left side of the same bibliometric map.

The trend of EPF models presented in Figure 6 and Figure 7 indicates that there are classical and new methods of EPF model formulation. An interesting observation is that hybrid models for EPF are intermediaries in both databases. The trend in publications goes towards machine learning in both explored databases. Both figures present different numbers of nodes (keywords) and edges (relations, co-occurrences) as results of standard Queries 1 and 2 for Scopus and WoS, respectively. The common elements for both Figures are the newest EPF models: ARIMA, LSTM, deep learning models (Scopus), and regression models (WoS). There are also visible differences between Figure 6 and Figure 7. Scopus analysis shows in Figure 6 that the dominant node of the bibliometric map is made by EPF models based on neural networks. As a result of the WoS analysis, the machine learning as EPF model is visible as the network’s largest node (Figure 7).

3.2. Overview of the Most Cited and Most Accurate Publications of EPF Models

The result of the use of Query 1 in the Scopus database is the most cited scientific article, which describes a hybrid model between linear and nonlinear time series forecasting models proposed by Babu and Reddy [21]. This paper explores the linear autoregressive Integrated Moving Average (ARIMA) [71] and nonlinear Artificial Neural Network (ANN) models to develop a new hybrid ARIMA–ANN model for the prediction of time series data [72]. ARIMA models assume that current data is a linear function of previous data points and past errors before fitting a linear equation to the data. Moreover, ARIMA requires that the data be made stationary. In the related works [72,73] in the hybrid methods, the input data were collected as the sum of linear and nonlinear components. The given data, however, is not divided into linear and nonlinear components; instead, a linear ARIMA model is fitted directly to the data, and the resulting error sequence is applied to the nonlinear component. Therefore, the linear aspect of the ARIMA model is used in both these hybrid models [63].

The most cited paper from Query 2 in WoS is “An empirical comparison of alternative schemes for combining electricity spot price forecasts” [65]. The main findings of this article indicate the added value of combining the projections of separate methods to derive more accurate forecasts. Nevertheless, the performance is not uniform across the markets and periods investigated. Specifically, equally weighted pooling of forecasts emerges as a simple yet effective strategy when compared to alternative systems that rely on estimated combination weights, but only when no predictor regularly outperforms its competition. Constrained least squares regression (CLS) [12] provides a balance between robustness against such well-performing individual approaches and relatively accurate forecasts, which are, on average, more accurate than those derived from the individual predictors. Some well-known forecast averaging strategies, such as ordinary least squares regression (OLS) and Bayesian Model Averaging (BMA), are inappropriate for forecasting day-ahead electricity prices.

The most cited publication from modified Query 1 was “The price prediction for the energy market based on a new method” [74]. The described article is a common part of Query 1 (no. 6 article in Supplementary Materials File S1 Table S1). In the article under review, a feature selection based on mutual information is implemented for day-ahead prediction of energy prices, which is essential for establishing the redundancy and relevance of selected features [74]. Based on a neural network, a combination of wavelet transforms and a hybrid EPF method is presented.

From modified Query 2, the article titled “A novel ensemble deep learning model with dynamic error correction and multi-objective ensemble pruning for time series forecasting” was distinguished [75] and the accurate method was elaborated. Due to high variances and low biases, standalone deep learning methods are not sufficient. In the novel forecasting model, ensemble methods are being used. The main difference between standard learning models is using fewer methods for both statistical and deep learning models. The result of that combination is better robustness in dynamic environments and improving generalization effectiveness. This article with the most cited article in WoS contributed a new framework for time series forecasting [75].

The proposed EPF models require more computation time, memory, and resources during the construction and combination stages of the basic predictors, according to the available literature. To further enhance the computational efficiency and scalability of the model, it is necessary to investigate more efficient construction and ensemble methods for basic predictors [75]. Another study concludes that the proposed hybrid method is over a hundred times more efficient than the bootstrap neural network (BNN) method [76].

4. Discussion and Conclusions

EPF models are important both for energy consumers [77] and producers [34,78]. Therefore, EPF models are an important scientific subject of many publications indexed both in Scopus and WoS. The topic of EPF has saturated the research community in recent years, although the number of citations is still increasing [9,62]. Both theoretical and empirical research provides a vast number and variety of EPF models [79], which results in different organizational performances among energy producers and their strategic decisions [11,80,81]. The bibliometric analyses of the EPF is a rare subject in the literature due to the complexity and number of scientific publications, and this paper covers this research gap.

In this paper, two databases, Scopus and WoS, were explored with the SLR method using Queries 1 and 2. The queries were modified to explore the designed two groups of scientific publications in each database. In this method, the most popular (cited), accurate publications dedicated to the EPF procedures and models were identified. The queries used in the SLR were then extended by the VOSviewer program results. The obtained results of database analyses proved that there was a difference in the query selectivity, although the syntax of the Queries was the same.

There are two groups of EPF models scientific publications. The first group consists of the most popular and most cited papers identified by the original queries. The second group is the most precise or accurate EPF models recognized by modified queries. The second group results were compared between studied databases (Figure 4 and Figure 5) and confirmed by the trend analysis in the presented bibliometric maps (Figure 6 and Figure 7). The wide scope of the WoS database is visible in the obtained results of the SLR query and bibliometric maps representing its assets. The WoS explored with Query 2 unfortunately found that EPF models-related papers cover the movie industry, food industry, and fashion, so those publications have to be excluded from the analysis. On the other hand, publications indexed in WoS are less cited than in Scopus. One of the possible reasons for this difference is the impact of the Mendeley reference manager usage among authors, which is associated with the Scopus database and allows authors to find references related to the EPF models. On the other hand, the WoS is combined with the EndNote reference manager.

Contrary to the other bibliometric analysis publications [9,82], this study does not prove that WoS is a subset of Scopus [9], therefore it is not possible to limit literature review analysis to WoS only [83]. The comparison of citation data in both multidisciplinary databases performed by L. Waltman proved the similarities between both database collections [84]. Additionally presented in this article are numerical and graphical results related to the EPF models that prove there are differences between explored databases, which stand following the results of bibliometric analyses performed by M. Aria and C. Cuccurullo [56,85].

In this paper, Wos and Scopus databases were explored, and those have some significant limitations. These databases require a standard academic subscription, which can be a source of limitations for those who would like to replicate this study. Next to accessibility is the structure of the data available to be exported from databases [86]. WoS is preferable to Scopus in terms of data quality. In Scopus, cited reference items are not standardized, therefore they need to be matched. In WoS, plain text format is preferable to BibTeX in terms of the completeness of the information used in further analyses [85].

There is a limitation of the used methods of SLR related directly to the formulation queries. In the queries, the limitations were primarily caused by explored years 2014–2021. Regarding the queries, a large number of synonyms, and a variety of spellings for certain EPF models or procedures, was the limitation in the queries’ syntax and the results presented by the VOSviewer software. Another limitation of the study is that only the frequency and popularity of particular keywords in scientific publications are presented without the positive or negative meaning. The repeated keywords denoted the primary limitation of bibliometric maps. It is caused mainly by a lack of consensus among researchers, and for instance, there is a keyword defining neural networks that has multiple permutations, including neural networks, neural networks, artificial neural networks, ann, and many other variations. Additionally, the VOSviewer program recognizes or reverts the capital letters of abbreviations to small letters. In this paper, this specific limitation required revising each keyword and removing the keyword duplicates.

The scientific contribution of this paper is the presentation of the existing research in published scientific papers and the proposition of the classification of the EPF models related to scientific publications. Another scientific contribution is the visualization of bibliometric maps of the researched EPF. This research article aimed to present and compare various EPF model publications in two categories: most popular (cited) and accurate procedures. Another scientific contribution is a detailed description of procedures that assure the reproducibility of the paper by the other authors. The novelty of this is based on the usage of combined methods of bibliometric method variation of SLR and bibliometric maps analysis. The visualizations present the relationships between EPF model formulation and performed classification research among scientific publications. Bibliometric maps prove the trends in science and inform other authors about the general progress or research gaps in the explored field of science [87]. The presented complex literature research revealed that linear models of EPF do not accurately capture the asymmetric relationship between energy consumption and energy pricing. There are numerous instances in which predictive methods are specified. The limitation may not be exceptional in this field. In a future study, it is proposed to combine similar keywords.

Researched EPF models, forecasting energy, and energy carriers can be used for considering future financial plans and energy infrastructure development. On the other hand, short-term energy forecasting aims to increase energy schedule efficiency and is another possible future research avenue.