Optimizing Taiwan’s Renewable Energy Mix: A Regression and Principal Component Analysis Approach Under Climate Change Challenges

Abstract

Amid rising global energy demand and Taiwan’s transition toward a non-nuclear and low-carbon future, identifying an optimal renewable energy (RE) mix has become essential. This study analyzes eight RE sources using a three-model framework—Pearson correlation, Stepwise Regression Analysis (SRA), and Principal Component Analysis (PCA)—based on 60 monthly observations from 2019 to 2023. The results show that geothermal energy (GE) and solar photovoltaics (SP) exhibit strong positive correlations with total RE generation. Both SRA and PCA consistently identify conventional hydropower (CH), SP, and offshore wind power (OSW) as Taiwan’s most effective RE combination, while PCA provides superior predictive performance and reduces multicollinearity. In contrast, OWP, SB, BG, and WTE show limited contribution to overall RE output. Policy recommendations suggest prioritizing SP under resource constraints, and jointly expanding CH, SP, and OSW when resources permit, to achieve a balanced and sustainable RE structure.

1. Introduction

As the global population continues to increase, we face ever-increasing energy demands. Moreover, the gradual depletion of fossil fuels has forced us to turn to more sustainable and environmentally friendly energy sources [1]. To address the challenges of global warming and carbon neutrality, our needs are more urgent, which further highlights our urgent need to reduce carbon emissions and transform them into clean energy [2]. Therefore, meeting the growing energy demand is not only an economic challenge but also an environmental issue that needs to be solved. To ensure that future energy needs can be met sustainably, we need to make unremitting efforts to find and develop renewable energy (RE) sources while improving energy efficiency to avoid exacerbating the occurrence of climate disasters [3].

In addition, more and more people have opposed the operation of Taiwan’s nuclear power plant after the Fukushima event in March 2011. As a result, the Taiwanese government plans to shut down all of its nuclear power plants by 2025 (2021) [4], which is the reason for the phase-out of nuclear power.

The basic violation of nuclear power generation to eco-sustainers is the high associated costs of backend disposal [5]. In conclusion, a shift towards safer and more sustainable energy sources is urgently needed. In response to energy security and greenhouse gas-emission reduction issues, the expansion of RE supply and use, as well as the rapid development of the RE industry, are critical elements in Taiwan’s energy policy [6]. In consequence, a rapid shift to safer and more sustainable energy resources is necessary.

In 2009, via the amended Renewable Energy Development Act (REDA), Taiwan introduced a series of policy measures to realize the concept and goals of sustainable energy. The goal of REDA was to reduce energy consumption, enhance the environment, and stimulate economic development [7]. The law explicitly states that renewable energy refers to the energy obtained from nature, which is transformed into a usable form through appropriate technologies and which comes from sustainable or renewable sources. The main reason to encourage renewable energy is that it is considered a clean, endless, and sustainable energy source. Renewable energy is more abundant and cheaper than fossil fuels, which makes it more advantageous. Despite solar and wind energy being infinite and clean, their intermittent and variable nature limits their power generation and power capacity [8].

Nevertheless, RE sources have limitations corresponding to production and capacity. More specifically, the electricity costs that are higher for RE compared to those for current fossil fuels create an obstacle to the smooth development of RE in Taiwan. The Bureau of Energy (BOE) (2023) [9] states that in 2022, the maximum amount of electricity generation was still from coal at 42.07%. This is followed by gas with 38.81%, whereas RE has contributed only 8.27% to the total electricity generation. Likewise, nuclear energy contributes 8.24% to the electricity generation, while oil contributes 1.54%. Finally, pumped storage hydro contributes 1.06% to electricity generation, according to Figure 1. Furthermore, RE has shown a year-on-year growth of 36.59% in electricity generation. However, it only contributes 8.27% to the overall electricity generation, which signals that there are some constraints.

As Taiwan has limited resources and technological background, achieving the target of raising the share of RE generation to 20% by 2025 is a considerable challenge. Also, Taiwan has a long history of a low electricity pricing policy and greatly relies on centralized thermal power generation. This has made it hard to promote and expand renewable energy [10].

This study uses 2019–2023 energy-related statistics to conduct a systematic analysis to explore the future development paths of Taiwan’s renewable energy. Since the existing literature is ambiguous in providing clear interpretation or recommendations regarding Taiwan’s renewable energy development patterns, the present research adopts a three-stage analysis framework.

Initially, correlation analysis is conducted to investigate the relationships between the various types of renewable energy and the total power generation. Next, we use a sequential relation analysis (SRA) model to obtain the optimal combination of renewable energy. The principal component analysis (PCA) model for data integration and dimensional analysis, which extracts the principal components with the largest variances, shows the latent relationship among renewable energy variables. Also, it verifies the most efficient configuration of RE sources.

The main aim of this paper is to find out the appropriate combinations of RE sources in Taiwan, to help the government and relevant decision-makers to design effective renewable energy policies, and to support the drive to move towards sustainable energy development.

Thus, our research seeks answers to the following:

Q1: How do different types of RE sources contribute to Taiwan’s total electricity generation during the period of 2019–2023?

Q2: What are the correlations among various RE sources, and how do they collectively influence total RE generation within the same period?

Q3: What constitutes the optimal combination of RE sources for electricity generation in Taiwan, considering their respective impacts on total RE generation and alignment with national energy policy goals?

Q4: What strategic implications can be derived from the identified optimal RE configuration to support Taiwan’s transition toward sustainable energy development by 2025 and beyond?

The remainder of this paper is organized as follows. Section 2 outlines Taiwan’s energy policy framework. Section 3 reviews the relevant literature. Section 4 specifies the data sources and methodology. Section 5 provides the data and analysis of the findings, whereas Section 6 contains the conclusion and summary.

2. Taiwan Energy Policy

Taiwan’s carbon neutrality movement has gathered momentum in recent years. The Renewable Energy Development Act (REDA), modified in 2009, defines renewable energy as any kind of energy that can be generated from a natural source through the use of technology in such a way that energy can be derived from these sources and will not be depleted. Overall, the REDA serves to meet renewable energy targets.

As stated in the Energy Bureau’s published program announcement for 2019, Taiwan’s clean energy market development work has been operating in six areas of renewable energy, including hydropower, geothermal, solar photovoltaic, wind, biomass, and waste-to-energy. Through these efforts, we are establishing a clean and diverse energy structure that supports the transition to a green energy system and achieves a national goal of net-zero emissions.

Taiwan has sufficient rainfall each year for conventional hydropower. Further, it is estimated that the potential for conventional hydropower that can generate standard electricity in Taiwan is 25,700 gigawatts. Taiwan is located at the boundary of the Philippine Sea and Eurasian plates. This feature provides conditions that favor geothermal development. Solar PV makes use of high solar irradiation in Taiwan, while wind energy is a feasible alternative to fossil fuels through onshore and offshore sources. The biomass energy is mainly obtained from urban organic waste, wood waste, and biogas generated from livestock in solid and gaseous forms. In the end, waste-to-energy technologies transform municipal solid waste into electricity, further diversifying the renewable energy portfolio [11].

Based on the ideals discussed above, Taiwan is now vigorously promoting the development of clean energy, which it considers one of six major forms of renewable energy—hydropower, geothermal, solar photovoltaic, wind, biomass, and waste-to-energy, leading to its core goal of sustainable development. This initiative aims to create a clean and mixed energy system, promote the transformation to green energy, and ultimately achieve the national vision of net-zero emissions.

3. Literature Review

Energy is not only an important engine for production and infrastructure in the economic development of a country, but also an important determinant of the quality of human life and societal progress [12]. Nonetheless, fossil fuels have been used to great lengths for quite some time, which is now impacting the environment adversely. The rising emissions of GHG cause global warming and extreme climate events [8,13].

The Paris Climate Change Conference is likely to extend the negotiations of the Kyoto Protocol until the end of 2015. Thus, the international community will have a greater understanding of climate change threats [8]. Consequently, nations came to the dire realization that a shift to better and greener energy sources is the way forward. As a result, RE or sustainable energy has become an important approach that can solve environmental problems [13,14,15,16,17]. Countries have promoted the research and use of RE to achieve an energy shift and reduce environmental damage.

Moreover, RE is regarded as a clean and limitless energy source and has several benefits over traditional fossil fuels. Renewable sources such as solar and wind energy are free and abundant and are not geographically confined. This reduces dependence on natural resources that cannot be replenished over time. Despite the significant potential of RE to provide sustainable power, the production of which is dependent on weather conditions, factors such as sunlight and wind variability impose certain restrictions on the ultimate reliability of RE [8].

High cost could be a barrier for RE, which has environmental benefits, but comes at high electricity costs. Evidence suggests that RE has greater production costs than what is primarily utilized for fossil fuels [18,19,20,21]. This means that, even though arguments for RE can be made based on good environmental and sustainable development initiatives, if technology and economics are improved any further, it would make them competitive and more affordable.

Due to the lack of additional pollutants produced during the energy conversion process, RE sources (that are more environmentally friendly) include solar energy, wind energy, geothermal energy, hydro energy, tidal energy, biomass energy, etc., which are now global RE sources currently in development [22,23]. As a result, the industry, government, and academia value studies related to renewable energy.

Studies currently underway on RE use big data, multicriteria decision analysis, and literature review extensively. For example, Shin et al. (2015) [24] have used big data analysis techniques, such as text mining and multiterm topic modeling, on newspaper articles related to RE published in Korea in the last ten years. The aim of this study was to identify the principal issues, global trends in RE research, and the development potential of RE. As such, the research results based on information and communication technologies are anticipated to find active application in the RE sector.

Campos-Guzmán et al. (2019) [25] employed multicriteria decision-making methods to evaluate the sustainability of renewable energy (RE) technologies. Estévez et al. (2021) [26] conducted multicriteria decision analyses to study trends in RE and suggested the enhancement of the methods of participation of experts and the involvement of more stakeholders in shaping RE initiatives and policies.

Additionally, according to Arshad and Hussain (2022) [27], they utilized machine learning techniques to forecast RE systems by modeling wind energy in RE systems. Other studies have mostly used literature metric analysis to examine RE-related issues. Hayati et al. (2023) [28] use comparative evaluation on government incentive policy on RE power plant development to create an appropriate policy to optimize renewable resource use. The outcomes from these studies should be influential towards policy direction to overcome resource adequacy in their particular countries.

Over the last 35 years, there has been strong support in the state of Idaho (USA) for an increase in renewable electricity production, and that public support has especially acknowledged the important role of solar and wind energy [29]. Mentel et al. (2023) [30] performed a comprehensive metric analysis of the literature to reveal the scale, structure, and dynamics of innovative research in the green and RE domain. The primary objective of this paper was to find the subject matter and literature trends in RE.

In Taiwan, most research on RE pertained to the study of its policies and developmental trends. For instance, the works of Hsu (1994) [31] and Liu et al. (2005) [32]. On the other hand, some of the literature examines Taiwan’s energy supply and demand structure, along with some environmentally related issues, providing analyses and policy recommendations covering sustainable development policies [33,34].

Lee and Chang (2018) [8] used the multiple criteria decision-making (MCDM) method to rank various RE sources and made specific suggestions for the development of RE in Taiwan. The researcher recommended developing hydropower as the first alternative energy source, followed by other energy sources: solar, wind, biomass, and geothermal energy. In their analysis of Taiwan’s power system in 2025, Hong and Magararu (2021) [35] expect future RE generation to make up 17.26% of total electricity generation.

On the contrary, the SRA model is a statistical approach used in various fields. It involves the assessment of the connection between variables in terms of time or level. This methodology can be used in a variety of data contexts, such as industry analysis and software testing [36]. Yan et al. (2007) [37] underlined the importance of regression testing in software development, particularly regarding database applications. Gallet and Braun (2001) [38] introduce new test procedures for gradual shifts in simple regression when applied to the Phillips curve. In a research article published by Boukezzoula et al. (2018) [36], the SRA model was used to find the relationship between element analyses and industrial properties of anthracite coal in China. Liu et al. (2023) [39] and Luo et al. (2023) [40] demonstrate the SRA model’s ability to find important influencing factors in a system. One will come across further examples in the coming sections. As a whole, these studies provide insights into the application and benefits of the SRA model.

While regression analysis enables one to study the relationship between the variables, it does have certain limitations. For instance, multicollinearity, sensitivity to outliers, and restrictive assumptions (linearity, homoscedasticity, and normally distributed errors) might render the results less stable and less interpretable [41,42]. Traditional regression methods also struggle to identify nonlinear relationships and can only prove correlation, not causation. Thus, this study uses a PCA-based model approach to reduce dimension, eliminate multicollinearity, and integrate variables to identify the optimal mix of renewable energy development. The PCA model has been widely used in energy efficiency analysis, wind power performance evaluation, and multi-renewable energy strategy formulation. In all cases, the decisions are more reliable.

The literature review above shows that prolonged and high-intensity exploitation of non-RE sources has adverse effects, such as environmental pollution, global warming, irreversible depletion, etc. This highlights the demand and importance of RE sources. However, few studies have been conducted with quantitative analyses to find the best mix for the development of RE sources.

Consequently, this research will carry out a correlation analysis to assist in establishing the RE sources that have a good potential for development. Next, a regression analysis will be performed to determine the optimal development model.

Ultimately, a method powered by the PCA model is used to reduce the dimension, synthesize the data, and produce the best combination for the renewable energy development trend.

4. Methodology

This study sequentially utilizes correlation analysis, the SRA method, and PCA-based data integration. Initially, correlation analysis is performed to remove variables with negative or weak correlations, ensuring that the remaining variables are both representative and reliable for further analysis. Then, the SRA method is applied to determine the best combination of renewable energy development trends, creating a decision model based on the refined dataset. Lastly, the PCA-based data integration technique is used to reduce dimensionality and combine data from various sources by extracting principal components that capture the most important variance and uncover potential relationships among variables. The following sections detail the steps involved in each of these three methods.

4.1. Pearson’s Product–Moment Correlation Coefficient

We employed correlation analysis, a statistical method that evaluates a potential linear relationship between two continuous variables. The correlation coefficient serves as an indicator of the strength of the presumed linear association between the data mining methodology and the variables under consideration. The fundamental model configurations are presented in Equation (1) [43,44,45,46]:

$$\mathbf{r}={\displaystyle \frac{\sum _{i=1}^n(x_i-x)(y_i-y)}{\sqrt{[}\sum _{i=1}^n{\left(x_i-\overline{x}\right)}^2][{\left(y_i-\overline{y}\right)}^2]}}$$

(1)

Based on the calculation of the correlation coefficient using Equation (1), values between 0.90 and 1.00 (or −0.90 to −1.00) signify a very strong positive or negative relationship, respectively. Coefficients from 0.70 to 0.90 (or −0.70 to −0.90) indicate a high correlation. A moderate correlation is seen with values ranging from 0.50 to 0.70 (or −0.50 to −0.70), while a low correlation corresponds to coefficients between 0.30 and 0.50 (or −0.30 to −0.50). Values between 0.00 and 0.30 (or 0.00 to −0.30) suggest a negligible correlation between the variables.

4.2. SRA Method

4.2.1. SRA Method Definition

Multiobjective optimization plays a crucial role in establishing quantitative relationships among different combinations to identify the best solutions. Its main importance lies in uncovering the interactions and trade-offs between various objectives to achieve overall efficiency. Since most variables are quantitative, analytical techniques like regression analysis are especially effective for building predictive models, which improve the understanding of how combinations perform. These methods enable precise estimation of relationships among variables, providing a strong foundation for developing more effective strategies in renewable energy advancement [47,48,49].

The construction of a multiple linear regression (MLR) model helps to investigate the impact of several independent variables (x₁, x₂,…, x_k) on one dependent variable (y). The SRA method is an extension of the linear regression model based on Pearson correlation coefficients. The final multiple regression model takes the following form through a gradual process of adding or removing variables (Equation (2)):

y = α + β₁x₁ + β₂x₂ + β₃x₃ + β₄x₄ + … + β_kx_k + e_j

(2)

where

• y = Dependent variable
• α = The intercept
• β′s = Regression coefficients of the variables x₁…, x_k
• x’s = Independent variables
• e_j = Random error

4.2.2. The SRA Method Approach Involves a Sequence of Six Steps

The SRA model identifies the key variables (x_i) that significantly influence total renewable energy output (y) through six sequential steps, as described below:

1.

Model initialization: Start with either an empty model or a full model including all candidate variables.

2.

Variable evaluation: Examine the p-value of each independent variable sequentially to determine whether it meets the criterion for inclusion.

3.

Variable entry: Include variables with a p-value less than 0.05 in the model.

4.

Variable removal check: After adding a new variable, check all variables currently in the model; those with a p-value greater than 0.10 are removed.

5.

Iteration: Repeat the entry and removal steps until no additional variables meet the criteria for inclusion or removal.

6.

Final model: Retain only the variables (x_i) that have a significant impact on total renewable energy output (y).

This procedure ensures that the SRA model systematically identifies the most influential variables while maintaining clarity and statistical validity.

4.3. PCA-Based Method for Data Integration

This approach uses the PCA model to integrate and examine data from multiple sources. By transforming the original dataset into a set of principal components, the method reduces dimensionality while preserving the most significant variance and minimizing information loss. Focusing on these components allows for efficient integration of heterogeneous datasets and facilitates the detection of latent patterns and correlations that may be obscured in the original high-dimensional data [50]. The implementation of the PCA-based model approach consists of six sequential steps:

• Data standardization

Each variable is standardized to have zero mean and unit variance to eliminate scale differences among variables (Equation (3)):

$${\mathrm{z}}_{(\mathrm{ij})}=({\mathrm{x}}_{(\mathrm{ij})}-{\overline{\mathrm{x}}}_{\mathrm{j}})/{\mathrm{s}}_{\mathrm{j}}$$

(3)

where x_(ij) is the value of the j^th variable for the i^th observation, ${\overline{\mathrm{x}}}_{\mathrm{j}}$ is the mean, and s_j is the standard deviation of variable j.

2.

Covariance Matrix Calculation

The covariance matrix C is constructed to capture the linear relationships between standardized variables (Equation (4)):

C = (1/(n − 1)) × Z^TZ

(4)

where Z is the standardized data matrix, and n is the number of observations.

3.

Eigen Decomposition

The eigenvalues and eigenvectors of the covariance matrix are computed as follows (Equation (5)):

C v_i = λ_i v_i

(5)

where λ_i represents the eigenvalue corresponding to eigenvector v_i. The eigenvalues indicate the amount of variance explained by each principal component.

4.

Principal component selection

The top k eigenvectors corresponding to the largest eigenvalues are selected to form the principal component matrix V_k (Equation (6)):

V_k = [v₁, v₂, …, v_k]

(6)

These components represent the directions of maximum variance in the dataset.

5.

Dimensionality reduction

The original standardized data are projected onto the selected components to obtain the reduced feature set (Equation (7)):

Y = Z V_k

(7)

where Y is the transformed dataset in a k-dimensional space.

6.

Model development and evaluation

The reduced dataset Y can be used for subsequent modeling, clustering, or prediction tasks, improving computational efficiency while preserving essential data information [50].

To assess the suitability of the PCA model for dimensionality reduction, the Kaiser–Meyer–Olkin (KMO) measure of sampling adequacy and Bartlett’s test of sphericity were conducted [51,52,53]. The computed KMO value of 0.81 indicates that the sample is adequate for PCA. Furthermore, Bartlett’s test of sphericity yielded a p-value less than 0.001, demonstrating that the variables are significantly correlated. Collectively, these results confirm that the PCA model is appropriate for reducing the multidimensionality of the dataset employed in this study.

5. Empirical Results and Analysis

This part of the discussion undertakes an analysis to understand what is the best combination of trends in RE development. Accordingly, this section is divided into four parts. The first portion illustrates what the variables are and how the global RE predictive modeling works, the second part presents the correlation analysis, the third part applies the SRA model, and, finally, the fourth part employs a PCA-based model approach to validate the best combination of RE development trends. The details are as follows:

5.1. Variable Description and Prediction Models

5.1.1. Variable Description

As per the TPCSR (2021) [4], the RE power generation of Taiwan can be classified into five major categories, including hydropower, geothermal, solar photovoltaic, wind, and biomass and waste.

The wind category is further subdivided into onshore and offshore wind power, and biomass is subdivided into solid biomass and biogas. Consequently, it identifies a total of eight types of renewable energy. Information on each of these types can be found in the list below:

• Conventional hydropower: Electricity is generated through traditional hydropower systems that harness energy from flowing water, typically using dams or similar structures. (Unit: Thousand Degrees (MWh))
• Geothermal: Energy derived from the Earth’s internal heat, commonly used for electricity generation or heating purposes. (Unit: Thousand Degrees (MWh))
• Solar Photovoltaic: Electricity is generated through the direct conversion of sunlight into electrical power via solar panels. (Unit: Thousand Degrees (MWh))
• Onshore Wind Power: Electricity generated from wind turbines installed on land. (Unit: Thousand Degrees (MWh))
• Offshore Wind Power: Electricity generated from wind turbines located in offshore areas, typically in oceans or large bodies of water. (Unit: Thousand Degrees (MWh))
• Solid Biomass: Energy derived from solid organic materials, such as wood chips, pellets, or waste wood, which serve as environmentally friendly energy sources. (Unit: Thousand Degrees (MWh))
• Biogas: Energy produced through the anaerobic decomposition of organic matter, often used for power generation. (Unit: Thousand Degrees (MWh))
• Waste-to-Energy: Electricity generated through the incineration or conversion of waste materials into usable energy. (Unit: Thousand Degrees (MWh))

Before the empirical model was constructed, an exhaustive compilation of preliminary assessment factors was conducted. In this context, the present study draws upon the TPCSR (2023) to identify the impact variables employed in the GRA methodology. The variables used in the analysis are defined as follows:

• Total RE (Y₁): Total electricity generation from all renewable energy sources. (Unit: Thousand Degrees (MWh))
• Conventional hydropower (CH) (x₁): Electricity generated from traditional hydropower methods. (Unit: Thousand Degrees (MWh))
• Geothermal (GE) (x₂): Energy derived from the Earth’s internal heat. (Unit: Thousand Degrees (MWh))
• Solar Photovoltaic (SP) (x₃): Energy produced by converting sunlight into electricity. (Unit: Thousand Degrees (MWh))
• Onshore Wind Power (OWP) (x₄): Energy generated from wind turbines located on land. (Unit: Thousand Degrees (MWh))
• Offshore Wind Power (OSW) (x₅): Energy generated from wind turbines situated offshore. (Unit: Thousand Degrees (MWh))
• Solid Biomass (SB) (x₆): Energy produced from solid biomass sources such as wood particles and waste wood. (Unit: Thousand Degrees (MWh))
• Biogas (BG) (x₇): Energy produced from organic matter decomposition. (Unit: Thousand Degrees (MWh))
• Waste-to-Energy (WTE) (x₈): Energy generated through waste incineration or conversion processes. (Unit: Thousand Degrees (MWh))

5.1.2. Prediction Models

The optimal group prediction model for RE power generation in Equation (8) is explained as follows:

Y_j =α + β₁x₁ + β₂x₂ + β₃x₃ + β₄x₄ + β₅x₅ + β₆x₆ + β₇x₇ + β₈x₈ + e_j

(8)

where

• Y_j = Total power generation from RE.
• α = The intercept.
• β′s =Regression coefficients of the variables x₁ …, x₈.
• x’s = Independent variables: Eight types of RE (e.g., CH, GE, SP, OWP, OSW, SB, BG, and WTE).
• e_j = random error.

5.1.3. Data Collection and Descriptive Statistics (2019–2023)

The descriptive statistical analysis of 60 monthly data points from 2019 to 2023 is presented in

Table 1. Descriptive statistics of the RE variables (2019–2023).

Variable	N	Min	Max	Mean	SE	SD
Y1	60	953,753.92200	2,827,060.93200	1,645,664.3711668	467,127.79284437	218,208,374,847.656
$x_1$	60	138,709.287	882,769.886	363,968.92607	192,162.495399	36,926,424,638.142
$x_2$	60	0.00000	2922.45800	998.5724502	951.37094928	905,106.683
$x_3$	60	200,887.791	1,362,788.166	694,126.21395	311,099.382290	96,782,825,661.517
$x_4$	60	23,812.36413	358,570.24822	150,565.6231385	80,691.87551091	6,511,178,773.469
$x_5$	60	0.00000	744,853.21800	120,895.2172833	163,908.42620669	26,865,972,181.554
$x_6$	60	5682.359	48,259.687	16,548.17025	5968.542011	35,623,493.738
$x_7$	60	2017.648794	19,078.209996	12,257.35913743	3795.143838748	14,403,116.757
$x_8$	60	243,541.792	347,485.926	298,561.64805	24,051.254343	578,462,835.487

Source of data: Compiled by the present study.

below. Table 1 summarizes the descriptive statistics of total renewable energy generation (Y₁) and eight individuals RE sources, including conventional hydropower (CH, x₁), geothermal energy (GE, x₂), solar photovoltaics (SP, x₃), onshore wind power (OWP, x₄), offshore wind power (OSW, x₅), solid biomass (SB, x₆), BG (x₇), and waste-to-energy (WTE, x₈). The dataset consists of 60 monthly observations from 2019 to 2023.

In detail, the total RE generation (Y₁) has a mean of 1,645,664.37 MWh, with a minimum of 953,753.92 MWh and a maximum of 2,827,060.93 MWh, indicating substantial variability over the period. Among the individual sources, CH (x₁) and SP (x₃) represent the major contributors, with mean values of 363,968.93 MWh and 694,126.21 MWh, respectively, reflecting their central role in Taiwan’s renewable energy mix. OWP (x₄) and OSW (x₅) exhibit moderate generation levels with notable fluctuations, suggesting growth potential in terms of wind energy. SB (x₆) and BG (x₇) contribute smaller but relatively stable outputs, whereas WTE (x₈) maintains a consistent role, with a mean of 298,561.65 MWh.

On the other hand, Table 1 (“Descriptive Statistics of Renewable Energy Variables, 2019–2023”) presents the standard deviation (SD) and standard error (SE) in its last two rows, calculated from 60 monthly observations. SD reflects the variability of each renewable energy source relative to its mean, with higher values indicating greater fluctuations. Notably, solar photovoltaic (SP, X₃) and conventional hydroelectric power (CH, X₁) exhibit higher SDs (96,782,825,661.517 and 36,926,424,638.142, respectively), likely influenced by seasonal factors or policy measures. SE measures the precision of the mean estimate, with smaller values indicating more stable averages; for example, the mean total renewable energy generation (Y₁) is 1,645,664.371 MWh, with an SE of 467,127.793.

Together, SD, SE, and the mean provide insights into central tendency, variability, and the reliability of average estimates. Based on these descriptive statistics, subsequent analyses, including correlation analysis, SRA, and PCA model, are conducted to evaluate the contributions of individual renewable energy sources to total generation and to identify the optimal combination strategy.

5.2. Correlation Analysis

This study provides a comprehensive definition of all variables in Section 5.1.1 and is structured into two main sections regarding correlation analysis. The first section examines the interrelationships among different RE sources, investigating the strength and direction of their mutual correlations. The second section explores the relationship between each RE source and the total RE output, aiming to assess their respective contributions to the overall RE generation capacity.

5.2.1. Interrelationships Between RE Sources

The correlation analysis among RE sources in this study was conducted with the objective of obtaining a deeper understanding of the interrelationship among energy sources and also their impact on energy growth. This study seeks to determine the extent to which different RE sources are interrelated by examining their correlations with the aim of providing better indications for energy policies and developments.

Based on the data shown in

Table 2. Interrelationships between RE sources.

	${\mathit{x}}_1$	${\mathit{x}}_2$	${\mathit{x}}_3$	${\mathit{x}}_4$	${\mathit{x}}_5$	${\mathit{x}}_6$	${\mathit{x}}_7$	${\mathit{x}}_8$
$x_1$	1
$x_2$	0.215	1
$x_3$	0.117	0.740 **	1
$x_4$	−0.268	0.225	−0.242	1
$x_5$	−0.144	0.778 **	0.609 **	0.401	1
$x_6$	−0.197	−0.086	−0.282	0.378	0.25	1
$x_7$	−0.219	−0.031	0.094	0.432	0.076	0.025	1
$x_8$	0.003	−0.209	−0.053	−0.306	−0.386	−0.462 *	−0.161	1

* p  <  0.05, ** p  <  0.01. Source of data: Compiled by the present study.

, according to CH, there is no significant relationship with other RE sources. GE and OWP share a significant positive correlation, indicated by r = 0.778 and p = 0.01. OWP is also characterized by a high and significantly positive correlation with SP power (r = 0.609, p = 0.01), with no other RE sources showing any significant correlation. OSW does not demonstrate any significant correlations with any of the other RE sources.

A significant negative correlation was observed between SB and WTE (r = −0.462, p = 0.05), which shows the opposite. Likewise, BG (x₇) significantly and negatively relates to SB (r = −0.462, p = 0.05) while WTE does not significantly relate to the others.

In this study, SB refers to energy generated from solid organic materials such as wood chips, pellets, and waste wood, whereas WTE is produced through the combustion or conversion of municipal waste. Both are classified under Taiwan’s “Biomass and Waste” renewable category.

The observed negative correlation between SB and WTE may indicate a potential substitution effect in resource allocation or policy priorities. Periodic increases in waste availability or policy emphasis on WTE could reduce the availability or support for SB feedstocks, while shared constraints—such as seasonal supply patterns or logistics—may also contribute to their inverse relationship.

5.2.2. Analyzing the Correlation Between Diverse RE Sources and Total RE

For further analysis, the relationships between individual RE sources and total RE generation, including CH, GE, SP, OWP, OSW, SB, BG, and WTE, were examined. The correlation coefficients are presented in

Table 3. Relationships between diverse RE sources and total RE generation.

	${\mathit{Y}}_1$	${\mathit{x}}_1$	${\mathit{x}}_2$	${\mathit{x}}_3$	${\mathit{x}}_4$	${\mathit{x}}_5$	${\mathit{x}}_6$	${\mathit{x}}_7$	${\mathit{x}}_8$
$Y_1$	1	0.43	0.85 **	0.89 **	−0.04	0.673 **	−0.19	0.07	−0.13

** p  <  0.01. Source of data: Compiled by the present study.

:

Table 3 presents the correlation coefficients between total RE generation and the eight individual RE sources. The results reveal distinct patterns of relationships among the RE sources and total RE outputs.

GE and SP exhibit strong positive correlations with total RE generation (r = 0.85 **, r = 0.89 **, p < 0.01), indicating that increases in these two energy sources are closely associated with overall RE growth. This suggests that GE and SP are key drivers of Taiwan’s total RE capacity and likely reflect government policies or investment priorities that favor these technologies.

CH and OSW display moderate positive correlations with total RE generation (r = 0.43 and r = 0.673 **, respectively). While not as influential as GE or SP sources are, these sources still contribute meaningfully to the overall RE output. The moderate correlation for CH may reflect the limited expansion potential of conventional hydropower due to geographical and environmental constraints, whereas OSW’s moderate contribution could be related to ongoing development in offshore wind projects.

In contrast, OWP, SB, BG, and WTE do not exhibit significant correlations with total RE generation. This finding indicates that variations in these sources have a limited impact on the overall RE output. For OWP, the lack of significance may be due to its current installed capacity being relatively small compared with that of offshore wind. Similarly, SB, BG, and WTE might be constrained by technological, logistical, or policy factors that limit their scale relative to other RE sources.

Overall, the analysis highlights that GE and SP are the primary contributors to total RE generation, with CH and OSW providing moderate support. The remaining sources (OWP, SB, BG, WTE) have weaker or nonsignificant contributions. These findings provide important insights for energy planning and policy-making, suggesting that strategic investment in high-impact RE sources could optimize total RE generation while balancing the development of secondary sources.

5.3. SRA Method Analysis

Bardy et al. (2015) [54] indicate that the correlation just indicates statistical similarity. However, it does not prove cause and effect. It is difficult to say that two variables are for certain causing one another if they are correlated. Analysis of correlation may lead to incorrect inferences of cause and effect due to external variables not currently analyzed that may impact correlation. In addition, biases related to sample size and selection can cause us to misinterpret correlations. A small or non-representative sample may cause us to come to wrong conclusions. Correlation presumes linear relationships and, as such, will not fully reflect nonlinear relationships or discrete relationships. It may not be determined which came first, and other factors may distort the connection.

Because of the limitations in correlation analysis as mentioned before, the present study also conducts a stepwise regression analysis to ascertain the best combination for renewable energy development. We use correlation analysis before the regression analysis to remove the variables that have negative correlations. We also remove variables that have insignificant effects so that the predictive accuracy can be successfully improved.

Through this step, the model can be improved by eliminating variables with weak correlation or insignificant nature, thus helping to produce a more compact and useful predictive model.

As the results of correlation analysis show in Table 3, CH (x₁), GE (x₂), SP (x₃), and OSW (x₅) are positively associated with total RE generation. The variables GE (x2), SP (x3), and OSW (x₅) are statistically significant among the others. Consequently, the analysis using stepwise regression (SRA) will further be implemented to investigate four RE sources, namely, CH (x₁), GE (x₂), SP (x₃), and OSW (x₅), to determine optimal combination trends in total RE generation.

Table 4. SRA method analysis results.

Model		Unstandardized Coefficients		Standardized Coefficients	t	Sig.	Collinearity Statistics
		B	Std. Error	Beta			Tolerance	VIF
1	Constant	2,402,885.6	307,461.1		7.81	0.000
	X3	1.161	0.139	0.897	8.37	0.000	1.00	1.00
2	Constant	1,637,296.2	269,133.4		6.08	0.000
	X3	1.111	0.095	0.858	11.67	0.000	0.98	1.01
	X1	0.786	0.173	0.333	4.53	0.000	0.98	1.01
3	Constant	598,648.02	142,569.6		4.19	0.000
	X3	1.191	0.036	0.920	33.13	0.000	0.93	1.06
	X1	0.952	0.066	0.404	14.44	0.000	0.92	1.08
	X5	1.565	0.154	0.290	10.14	0.000	0.88	1.13

Source of data: Compiled by the present study.

presents the regression analysis conducted for the excluded variable, GE (x₂), from the previous regression of total RE across the three models. GE (x₂) was removed from the regression models due to its correlation with other independent variables, which creates multicollinearity problems that can distort estimations of the regression coefficients. By temporarily removing x₂, we can observe how other variables affect total RE more reliably. This improves the estimation stability of the model. The subsequent analyses then assessed the contribution of x₂ to total RE generation. The results for each model are presented below:

5.3.1. SRA Results of Model 1

The research findings (Table 4) indicate that for the constant term, the coefficient (B) is 2,402,885.607, with a standard error of 307,461.120 and a t-value of 7.815 (p < 0.001). In the case of SP, the coefficient (B) is 1.161, the standard error is 0.139, the standardized coefficient (Beta) is 0.897, and the t value is 8.377 (p < 0.001).

Furthermore, the R-squared (R2) value is 0.805, indicating that the model explains 80.5% of the variability in the dependent variable. The adjusted R-squared (adjusted R2) is 0.794, providing a more accurate assessment of the model’s fit by considering the degrees of freedom. Concerning collinearity, the variance inflation factor (VIF) is 1.000, indicating a relatively low level of multicollinearity among the explanatory variables.

Finally, the equation for Model 1, derived from the research findings (Table 4), can be written as follows (Equation (9)):

$$Y_1=\mathrm{2,402,885.607}+1.161\times x_3$$

(9)

5.3.2. SRA Results of Model 2

According to the research findings (Table 4), the analysis of Model 2 is as follows:

The regression results show that the intercept is statistically significant (B = 1,637,296.248, SE = 269,133.476, t = 6.084, p < 0.001). SP has a strong positive effect on total RE generation (B = 1.111, SE = 0.095, Beta = 0.858, t = 11.674, p < 0.001), whereas CH also contributes positively (B = 0.786, SE = 0.173, Beta = 0.333, t = 4.536, p < 0.001), although to a lesser extent. The model explains a substantial proportion of the variance in total RE generation, with R² = 0.915 and adjusted R² = 0.904. Collinearity diagnostics indicate minimal multicollinearity among predictors (tolerance = 0.986, variance inflation factor (VIF) = 1.01), confirming the robustness of the estimates.

Finally, the equation for Model 2, derived from the research findings (Table 4), can be written as follows (Equation (10)):

$$Y_1=1,637,296.248+0.786\times x_1+1.111\times x_3$$

(10)

Overall, these results indicate that Model 2 is statistically effective, with each explanatory variable significantly influencing the model, and the model performs well in terms of collinearity.

5.3.3. SRA Results of Model 3

According to the research findings (Table 4), the analysis of Model 3 is as follows:

The regression results show that the intercept is statistically significant (B = 598,648.022, SE = 142,569.602, t = 4.199, p < 0.001). The SP has a strong positive effect on total RE generation (B = 1.191, SE = 0.036, Beta = 0.920, t = 33.137, p < 0.001), whereas CH also contributes positively (B = 0.952, SE = 0.066, Beta = 0.404, t = 14.443, p < 0.001). OSW also has a statistically significant positive impact (B = 1.565, SE = 0.154, Beta = 0.290, t = 10.141, p < 0.001). The model demonstrates an excellent fit, with R² = 0.989 and adjusted R² = 0.987, indicating that approximately 98.9% of the variance in total RE generation is explained by the independent variables. Collinearity diagnostics reveal minimal multicollinearity among the predictors, with a tolerance of 0.987 and a VIF of 1.014, confirming the robustness of the estimated coefficients.

Finally, the equation for Model 3, derived from the research findings (Table 4), can be written as follows (Equation (11)):

$$Y_1=\mathrm{1,637,296.248}+0.786\times x_1+1.111\times x_3$$

(11)

In summary, Model 3 is statistically significant, and each explanatory variable significantly influences the model. The model performs well in terms of multicollinearity.

Based on the analysis results, out of four RE sources—CH (x₁), GE (x₂), SP (x₃), and OSW (x₅)—the combination of CH, SP, and OWP is the best and most efficient mix for power generation (i.e., total RE generation (Y₁)). It follows that, in situations that limit the resources to adopt SPs, priority should be given to these SPs. This is owing to their contribution to the optimal combination. In other cases, when there are ample resources available, it is better to develop CHs, SPs, and OSWs concurrently for greater renewable energy uptake. It enhances the overall efficiency of the system, meets the energy requirement, and protects the environment. This shows that strategic planning plays a useful role in achieving the efficient use of resources and sustainable development.

5.4. PCA-Based Methods

Since the PCA model can condense quantitative data into a smaller number of underlying components that are commonly used for weight determination, this study further applied PCA to identify the optimal combination of factors for RE development. The analytical results are presented below:

5.4.1. Suitability Test and Purpose

Before applying the PCA model, the adequacy of the dataset was evaluated using the KMO measure and Bartlett’s test of sphericity. As presented in

Table 5. KMO and Bartlett’s tests for PCA suitability.

Test	Statistic	df	p Value	Interpretation
KMO Measure of Sampling Adequacy	0.673	–	–	Acceptable for PCA
Bartlett’s Test of Sphericity	Approx. Chi-Square = 582.565	28	0.000	Significant (p < 0.05), suitable for PCA

Source of data: Compiled by the present study.

, the KMO value was 0.673, suggesting that the data are suitable for PCA, as values between 0.6 and 0.7 are generally considered acceptable for factor analysis. Bartlett’s test of sphericity produced an approximate chi-square value of 582.565 with 28 degrees of freedom (p < 0.001), confirming that the correlation matrix significantly differs from an identity matrix and that the dataset is appropriate for PCA.

As shown in

Table 6. PCA results.

Component	Eigenvalue	Variance Explained (%)
Component 1	3.142	39.27
Component 2	1.566	19.58
Component 3	1.023	12.78

Source of data: Compiled by the present study.

, three principal components were extracted. Component 1 had the highest eigenvalue (3.142), explaining 39.27% of the total variance, followed by Component 2 and Component 3, which accounted for 19.58% and 12.78%, respectively. Collectively, these three components explain a substantial portion of the total variance, indicating that the selected variables effectively capture the key patterns underlying RE development.

Given that the PCA model effectively reduces multidimensional quantitative data into a smaller set of underlying components and is frequently employed for weight determination, this study utilized PCA to identify the optimal combination of factors for RE development. Three principal components were extracted, with eigenvalues of 3.142, 1.566, and 1.023 (see Table 6), accounting for 39.27%, 19.58%, and 12.78% of the total variance, respectively (see

Table 7. PCA model composite score coefficients and weights for RE sources.

RE Source	PC1	PC2	PC3	Composite Score Coefficient	Weight
CH	0.1023	0.5668	0.2700	0.2592	10.64%
GE	0.5071	0.0175	0.3062	0.3375	13.85%
SP	0.5272	0.1309	0.0837	0.3398	13.95%
OWP	0.1017	0.6337	0.1405	0.2540	10.43%
OSW	0.4638	0.1483	0.3761	0.3619	14.86%
SB	0.2960	0.4320	0.2434	0.3238	13.29%
BG	0.2964	0.1324	0.3248	0.2567	10.54%
WTE	0.2313	0.1834	0.7074	0.3032	12.45%

Source of data: Compiled by the present study.

and Figure 2).

5.4.2. Composite Score Coefficients and Weights

The composite score coefficients and weights for each RE source indicate their relative contributions to total RE generation. As shown in Table 6, OSW has the highest composite score coefficient (0.3619) and weight (14.86%), followed by SP (0.3398; 13.95%) and GE (0.3375; 13.85%), indicating that these three sources are the leading contributors to total RE generation. SB (0.3238; 13.29%) also has a notable contribution, whereas WTE (0.3032; 12.45%) and CH (0.2592; 10.64%) contribute moderately. OWP (0.2540; 10.43%) and BG (0.2567; 10.54%) contribute relatively less.

5.4.3. Implications for the Optimal RE Mix

These results highlight that the optimal renewable energy mix should prioritize OSW, SP, and GE while incorporating other sources to achieve a balanced, efficient, and sustainable RE generation strategy. The PCA findings complement the stepwise regression analysis, providing a comprehensive perspective on the contributions of all RE sources and supporting informed decision-making for strategic energy development.

5.5. Comparison of the SRA Regression and PCA Results

Both stepwise SRA and PCA reveal complementary insights into contributions of RE sources to total RE generation, but differ in some salient ways. First, there is the difference in stress on and the ranking of sources.

Using SRA results, it is the case that SP contributes a dominant share to the total RE, followed by the OWP and CH. All three of these resources are statistically significant and positive in terms of total RE generation, which means they are impact factors under limited-resource and abundant-resource conditions. The SRA model does not include GE as a consideration due to multicollinearity constraints. It seemed not to contribute much to the regression model.

In contrast, the PCA results show the relative variance contribution of all eight RE sources, the top three being OSW, SP, and GE. Moreover, OSW has the highest composite score coefficient and weight. The difference is due to the fact that PCA captures all variables and their linear combinations that account for maximum variance. Meanwhile, SRA captures the effect of selected variables on total RE generation while controlling multicollinearity. In addition to the influence of other sources, PCA extends other contributions, such as that of SB and WTE, which are less significant than OSW, SP, or GE but are still non-negligible in the collective total RE generation mix.

6. Conclusions

This section presents recommendations for Taiwan’s renewable energy development, divided into two parts: policy recommendations and policy recommendations with strategic implications. The former focuses on concrete development priorities and resource allocation directions, while the latter further elaborates on the potential impacts of these recommendations on energy security, sustainable development, and policy objectives. Finally, this section also outlines the limitations of this study in terms of data and methodology, providing readers with a clearer understanding of the scope and constraints of the research findings.

6.1. Concluding Remarks and Strategic Implications

6.1.1. Concluding Remarks

Q1 on the contribution of different RE sources to total RE generation (2019–2023):

According to this study, it is observed that SP, GE, and OSW are the foremost contributors to Taiwan’s RE structure. The contributions of CH and other sources, including OWP, SB, BG, and WTE, are either moderate or limited. GE and SP are identified as key drivers of total RE growth.

Q2 on the possibility of correlations among RE sources:

According to the analysis, OWP has a significant positive correlation with GE. Furthermore, the analysis reveals that SP has a significant positive correlation with OSW. On the other hand, it was found that SB has a significant negative correlation with WTE. Furthermore, BG has a significant negative correlation with SB. CH shows limited correlations with other RE sources. In general, GE and SP are the main drivers of total RE generation, and CH and OSW have moderate support, while the rest have weak or negligible impact.

Q3 on the optimal combination of RE sources:

Based upon the stepwise SRA model as well as the PCA model, the optimal combination is identified to be CH, SP, and OSW. While it is suggested that priority be given to SP with limited resources, when resources are sufficient, it is suggested to develop CH, SP, and OSW simultaneously for a more efficient, balanced, and sustainable RE strategy.

Q4 on the strategic implications and sustainable development recommendations:

The combination adds to the diversity and stability of the energy mix, reducing the dependence on a single source. Also, the partnership is in line with Taiwan’s energy policy and the international trend towards low-carbon emissions. Most importantly, it can contribute towards meeting the Sustainable Development Goal. It is strategic to optimize total RE generation efficiency while meeting the energy demand and minimizing environmental impact by focusing on high-impact RE sources. In general, this strategy will support the transition of Taiwan’s sustainable energy development in 2025 and beyond.

6.1.2. Advantages of Pearson, SRA, and PCA and Their Applications in RE Planning and Policy

This study employs Pearson correlation analysis, SRA, and PCA, each demonstrating clear advantages and practical value for renewable energy planning and policy development.

Pearson correlation analysis identifies linear relationships among renewable energy sources and serves as an initial screening tool to remove negatively or weakly correlated variables, thereby improving the representativeness and reliability of subsequent models. SRA helps determine key energy sources that significantly affect total generation and enhances prediction efficiency by eliminating insignificant variables, providing a basis for prioritizing energy development. PCA offers strengths in dimensionality reduction and mitigating multicollinearity, clarifying the underlying structure of different energy sources. In this study, PCA also outperforms SRA in prediction accuracy, making it more suitable for supporting strategic energy decisions.

Overall, combining Pearson, SRA, and PCA enables a more comprehensive quantification of renewable energy impacts and provides solid and reliable references for policy formulation, strengthening the scientific and practical foundation of Taiwan’s renewable energy development.

6.2. Policy Recommendations and Strategic Implications

6.2.1. Policy Recommendations

This study goes on to identify the best combination of RE development in Taiwan. Subsequently, it also provides evidence-based recommendations for policymakers to achieve the goal of energy transition and sustainable development. The SRA model, PCA model, and correlation analysis were used to analyze the data from 2019 to 2023. According to this analysis, CH, SP, and OSW were identified as the main and largest contributors to total RE generation. Accordingly, policymakers are advised to do the following:

• Prioritize high-impact RE sources: Under limited-resource scenarios, SP should receive the highest development priority because of its dominant contribution to total RE generation output.
• Promote integrated development under abundant resources: When resources are sufficient, simultaneous development of CH, SP, and OSW is recommended to achieve a balanced and sustainable energy mix.
• Optimize resource allocation: Focused investment in these primary RE sources ensures the effective utilization of the available resources, while maintaining support for moderate or minor contributors.

6.2.2. Strategic Implications

The implementation of the above policy recommendations has multiple strategic benefits for Taiwan’s energy transition:

• Enhancement of energy security and stability: A diversified RE portfolio reduces the reliance on a single source and stabilizes the electricity supply, mitigating operational or environmental risks associated with individual energy types.
• Alignment between national policy and sustainability goals: The recommended configuration supports Taiwan’s targets for carbon reduction, RE expansion, and energy self-sufficiency, which is consistent with both national and global sustainability agendas.
• Maximizing efficiency and environmental benefits: Prioritizing high-impact sources improves overall energy efficiency, effectively meets electricity demand, and minimizes environmental impacts, contributing to sustainable energy development.

Finally, this combination can enhance energy supply stability and diversity, reduce dependence on a single source, and align with Taiwan’s national energy policies as well as global sustainability goals. Moreover, through strategic resource allocation and prioritization of high-impact renewable energy sources, overall energy efficiency can be improved, energy demand can be effectively met, and environmental impacts can be minimized. The study emphasized that policy implementation should consider the current status and potential changes in Taiwan’s renewable energy environment to ensure the feasibility and effectiveness of the strategy.

On the other hand, the conclusions and recommendations presented here are based on the models constructed, sample data collected, and research methodologies employed in this study. Hence, the current situation and changes in Taiwan’s RE environment must be considered, and any application of our findings must be tailored further to yield more accurate conclusions.

6.3. Limitations

The data used in this study consist of 60 monthly observations from 2019 to 2023. While these data are representative, the time span remains relatively limited and may be insufficient to capture long-term structural changes in Taiwan’s renewable energy generation, policy effects, or annual fluctuations driven by climate variability. Therefore, the optimal energy mix derived in this study primarily reflects short-term trends, and its applicability to long-term forecasting may be constrained.

In addition, this study relies solely on monthly generation records for each renewable energy source and does not incorporate other key explanatory variables that may influence generation performance. These include installed capacity, demand growth, generation costs, equipment retirements, subsidy policies, solar irradiance, wind speed, precipitation, and hydrological inflow. Incorporating such variables into the model would enhance explanatory power and improve the completeness of policy inferences.

Future research is recommended to:

• Extend the temporal coverage to encompass complete policy cycles and a wider range of climate variability, thereby improving the ability to assess long-term structural trends in renewable energy development.
• Incorporate additional explanatory variables, including climate indicators, investment and cost information, installation capacity, policy instruments, and other relevant technical or economic factors, to enhance model robustness and interpretability.
• Apply more advanced analytical methodologies—such as multivariate time-series models, structural equation modeling (SEM), or machine learning techniques—to strengthen forecasting accuracy and increase the reliability of policy and decision-making simulations.