Clean energy stock returns forecasting using a large number of predictors: which play important roles? Free

The global transition to renewable energy is a significant economic transformation for the 21st century. The clean energy sector has experienced unprecedented investment inflows, driven by mounting concerns over climate change and the environmental degradation associated with traditional energy sources. Over the past five years, annual investments in clean energy have consistently surpassed $300 billion, highlighting the sector’s rapid expansion and growing importance within global financial markets (International Energy Agency [IEA], 2023). This surge in investment reflects the sector’s growth potential and the increasing recognition of renewable energy as a cornerstone of the global economy.

As clean energy stocks (CES) gain prominence as an asset class, understanding the factors driving CES returns is critical for investors, asset managers, and policymakers. Accurately forecasting CES returns is particularly essential because these stocks are influenced by a complex interplay of factors, including evolving climate policies, technological advancements, and shifting macroeconomic conditions. Recognizing these dynamics not only provides insights into market trends but also enables more effective resource allocation, enhances market stability by reducing volatility, and supports policymakers in designing targeted strategies for the energy transition.

Despite the rapid growth of the clean energy sector, forecasting CES returns is challenging. CES volatility is driven by a complex set of factors, including macroeconomic conditions, technical market indicators, climate policies, and global commodity prices. The heightened volatility and uncertainty inherent in CES make it even more important for market participants and decision-makers to identify and understand the drivers of CES returns. Significant research on asset return forecasting has examined the forecasting of returns in traditional financial markets, such as equities, bonds, and commodities (Baumeister et al., 2022; Ghosh and Jana, 2024; Hamilton, 1983; Liang et al., 2020; Luo and Zhang, 2024); however, few studies have specifically focused on the unique drivers of CES returns.

This study is designed to fill this research gap. The clean energy sector operates fundamentally differently than traditional markets. Exogenous predictors play a central role in influencing CES returns; these include climate policy uncertainty, environmental regulations, and renewable energy subsidies. However, existing forecasting models do not yet adequately explore these predictors. This study addresses this gap by focusing on the unique predictors of CES returns that are not captured by traditional asset classes.

Forecasting with a large number of predictors increases the risk of overfitting. To mitigate this, the study uses different econometric techniques such as LASSO, Group LASSO, and Quantile Regression. These methods effectively manage high-dimensional datasets, as demonstrated in forecasting studies on oil prices (Zhang et al., 2019) and cryptocurrency volatility (Wang et al., 2023). Applying these robust methodologies improves forecasting accuracy while minimizing model complexity.

Another study driver lies in the underexplored role of technical indicators in forecasting CES returns. Traditional financial variables have been extensively studied; however, technical indicators have not been adequately incorporated into CES forecasting models; these include moving averages, momentum indicators, and volume-based strategies. Given the volatile and dynamic nature of the clean energy market, technical indicators may provide valuable insights into changes in short-term CES returns. This study explores the utility of these indicators in improving CES return predictions.

Climate-related predictors significantly influence clean energy markets; these include climate policy uncertainty, energy consumption trends, and environmental regulations (Ren et al., 2022). These predictors have not yet been sufficiently integrated into asset return forecasting models. This study incorporates both financial and non-financial predictors, providing a more comprehensive approach to forecasting CES returns and capturing the unique dynamics of the clean energy sector.

In summary, this paper fills an existing research gap by systematically identifying and analyzing the factors that most effectively predict CES returns. Specifically, the study addresses several key questions. Which factors have the greatest predictive power for CES returns? How does the relevance of these factors evolve over time? Can grouping different factors improve forecasting accuracy? Additionally, the study explores the impact of both short-term and long-term forecasting horizons on predictor effectiveness.

This paper makes a significant contribution by addressing the growing need for accurate CES return forecasting through a novel approach that integrates both traditional and climate-related predictors. Existing research has largely focused on traditional financial markets and overlooked the unique drivers of CES returns. This study expands on previous work by incorporating these critical climate-related factors into forecasting models, while also employing techniques like LASSO and Group LASSO to enhance prediction accuracy and reduce overfitting. Specifically, the paper makes two key contributions to the field. In one aspect, it constructs a comprehensive forecasting framework that integrates 56 predictors, extending beyond traditional financial variables to include macroeconomic, climate risk, technical, and financial predictors, thereby capturing the diverse influences on CES returns. In another aspect, it systematically examines how these predictor relationships evolve over time across different forecasting horizons, offering deeper insights into their varying significance and improving prediction accuracy.

First, the study introduces a novel approach to forecasting CES returns, addressing research gaps. Previous research has predominantly focused on traditional financial predictors or has used single-model frameworks; however, these approaches do not consider the integrative role of multiple predictors and their temporal variability. In contrast, this study constructs a comprehensive forecasting model by incorporating 56 distinct predictors, spanning macroeconomics, climate risk, technical, and financial predictors. Understanding the contribution of each predictor group is essential for investors, policymakers, and researchers in navigating the complexities of CES market fluctuations. Existing literature has explored the predictive power of certain individual factors, such as climate risk measures (Herrera et al., 2022), and technical indicators (Neely et al., 2014), but comprehensive studies that integrate these dimensions remain scarce. The analysis investigates the predictive power of these diverse predictors across different forecasting horizons, thereby enhancing descriptions of CES return dynamics.

Second, the study explores the role of different predictor groupings, predictor components, rolling windows, and forecasting horizons in improving prediction accuracy. Prior research has often considered these factors in isolation, without assessing their collective impact on CES return forecasting. By analyzing how predictor importance evolves over time and under varying market conditions, we provide empirical insights into the dynamic interactions between CES returns and key predictive factors. Moreover, by leveraging regularization techniques, our study effectively addresses the challenges of overfitting and high-dimensional predictor spaces, ensuring robust and reliable forecasts. These insights contribute to the development of a more adaptive and resilient forecasting framework for CES returns.

The rest of this paper is organized as follows. Section 2 reviews the relationship between CES and other variables. Section 3 describes the data. Section 4 introduces the methodology. Section 5 presents the empirical analysis, and Section 6 concludes the paper.

Macroeconomic factors are key to understanding the dynamics of renewable energy markets. Global economic indicators play a crucial role in shaping investment flows into renewable energy sectors; these include gross domestic product (GDP) growth, inflation, and interest rates (Baumeister et al., 2022; Hamilton, 1983). Wang et al. (2022) showed that global economic activity and uncertainty indices, such as the Chicago Fed National Activity Index (CFNAI) and Consumer Price Index (CPI), effectively predict the volatility of clean energy and natural gas markets. This underscores the interconnectedness between macroeconomic stability and clean energy investments.

Arouri et al. (2016) found that increased U.S. economic policy uncertainty dampens stock returns; this effect is more pronounced during periods of extreme volatility. This highlights the need to incorporate macroeconomic uncertainty measures when forecasting CES returns, as these factors can directly impact investor confidence and market dynamics. Baumeister et al. (2022) also demonstrated the significant predictive value of global economic activity indicators for energy prices. This further emphasizes the role of macroeconomic factors in shaping market outcomes.

With global climate change and increased attention on green investments, academics have explored the influence of climate change on renewable energy markets (Fahmy, 2022). Since the Paris Agreement in 2015, the global energy landscape has significantly transformed, generating new opportunities for developing renewable energy. Many studies have examined the impact of climate change on CES, focusing on both physical and transition risks (Chen et al., 2021; Ding et al., 2022; Herrera et al., 2022).

Climate change affects renewable energy markets through two primary risk areas: physical and transition. Physical risks involve direct effects, such as extreme weather events, which can disrupt energy production and consumption; these risks heighten CES volatility (Dong et al., 2024). These risks are particularly relevant in understanding market stability, as disruptions in energy supply or demand can significantly alter investment decisions and economic stability (Zhou and Lin, 2025). Chen et al. (2021) found that increased investments in clean energy create a positive feedback loop; concerns about climate change drive further investment in clean energy technologies, making these assets crucial for risk mitigation.

Transition risks arise from policy changes, regulatory shifts, and evolving investor sentiment toward green investments. Climate risk awareness surged following the Paris Agreement, driving increased investment in clean energy sectors (Fahmy, 2022). Herrera et al. (2022) highlighted how investor sentiment, driven by climate policy announcements, influences CES volatility. Ghosh and Jana (2024) found that market sentiment and fear indices are strong predictors of clean energy investments, as investor preferences shift towards sustainable assets during periods of economic uncertainty. This sentiment provides valuable predictive power beyond traditional financial variables. Similarly, Khalfaoui et al. (2022) emphasized the importance of climate policy uncertainty (CPU) in transmitting market risk; sectors linked to clean energy and green innovation are particularly sensitive to these uncertainties.

Several studies have highlighted the long-term effects of CPU on renewable energy investments. Husain et al. (2022) found that CPU has strong long-term memory effects: its impact on market reactions can persist over time. He and Zhang (2022) further demonstrated that CPU is a strong predictor for energy sector stock returns; it often outperforms other uncertainty measures and macroeconomic variables in predictive accuracy. These findings collectively underscore CPU’s central role in shaping the renewable energy market landscape, especially during periods of increased policy uncertainty.

Technological advancements and growing public attention to climate issues also influence renewable energy investments. Public sentiment, as captured through media and search engine data, enhances stock market prediction accuracy (Audrino et al., 2020; Gao et al., 2023). Positive sentiment towards sustainable companies is linked to increased returns in clean energy stocks, whereas; negative attention adversely impacts traditional sectors (El Ouadghiri et al., 2021).

Financial and commodity markets are closely linked to CES, and many studies have emphasized their predictive importance. Oil prices, natural gas, and other commodity indices significantly influence clean energy returns. This is because fluctuations in these commodities can change the relative attractiveness of renewable versus traditional energy sources (Campbell et al., 2020; Filis, 2010). The relationship between fossil fuel prices and renewable energy investments is complex, and is often characterized by substitution effects. For example, rising fossil fuel prices can increase interest in renewable energy alternatives.

Financial markets also play a crucial role in CES predictions, particularly with respect to equity indices, green bonds, and volatility indices. Indices like the Morgan Stanley Capital International (MSCI) U.S. Environment, Social, Governance (ESG) Leaders Index are benchmarks for CES performance, providing insights into how broader financial market trends influence this sector. Filis (2010) also noted that financial indicators can serve as leading signals for investment shifts between traditional and renewable energy sectors, particularly during periods of economic volatility.

Based on Sadorsky (2012) and Khalfaoui et al. (2022), this study uses the WilderHill Clean Energy Index (WCEI) as a representative measure for the CES market (see Table 1, Panel A). As of 2024, 73.6% of WCEI companies are U.S.-listed, reflecting the sector’s alignment with the clean energy transition. Therefore, study predictors are based on U.S. macroeconomic or market variables. This study uses monthly data spanning from January 2009 to December 2023, including the post-2008 financial recovery, the 2015 Paris Agreement, and the global shift towards renewable energy investments. This timeframe reflects significant policy changes, technological advancements, and market dynamics, offering a robust foundation for analyzing CES returns. The empirical analysis applies a rolling window length of 60 months. The in-sample period (used for model training and parameter estimation) covers January 2009 to February 2014, and the out-of-sample period (used for testing the model’s predictive performance) extends from March 2014 to December 2023. To maintain consistency with the CES index data, all subsequent predictors are drawn from the January 2009 to December 2023 period.

Many studies have found that technical indicator predictors have statistically and economically significant predictability, both for the in-sample and out-of-sample, outperforming purely fundamental analysis benchmarks (Neely et al., 2014; Yin and Yang, 2016). Based on Wang et al. (2023) and Zhang et al. (2019), this study uses 14 different technical indicator predictors, including:

• (1)

  Moving Average $MA(s,l)$ predictors: MA (1, 9), MA (1, 12), MA (2, 9), MA (2, 12), MA (3, 9), and MA (3, 12). When the short-term (s-month) moving average exceeds the long-term (l-month) moving average, the $MA(s,l)$ value is set as 1; otherwise, it is set as 0. $MA(s,l)$ signals market momentum and trend direction characteristics.

• (2)

  Momentum $MOM(k)$ predictors: MOM (3) and MOM (9). $MOM(k)$ represents the momentum over k months. It measures the rate of change in an asset’s price over a specified period.

• (3)

  On-Balance Volume $OBV(s,l)$ predictors: OBV (1, 9), OBV (1, 12), OBV (2, 9), OBV (2, 12), OBV (3, 9), and OBV (3, 12). When the short-term OBV average exceeds the long-term OBV average, the $OBV(s,l)$ value is set as 1; otherwise, it is set as 0. $OBV(s,l)$ signals buying or selling pressure in the market ^[1].

This study uses 14 macroeconomic variables as potential external predictors, including macroeconomic fundamentals, inflation, and policy uncertainty risk, as shown in Table 1, Panel C. The data sources are also listed in the table.

First, macroeconomic fundamentals provide insights into the broader economic environment that impacts CES. These predictors cover both the supply and demand sides of the economy, and include consumer confidence (CC) and unemployment rate (UNRATE). They reflect the economic cycle’s expansions and contractions, which impact CES performance, as discussed in Section 2.

Second, changes in inflation levels can directly influence asset prices, corporate performance, and consumer demand, even in stable economic conditions. Key inflation indicators in this study include the CPI, Producer Price Index (PPI), and the 10-Year Treasury Constant Maturity Minus 3-Month Treasury Constant Maturity (T10Y3M).

Third, policy uncertainty risk is considered due to its critical role in shaping investor behavior, market stability, and CES resilience to external shocks. The selected predictors, including the U.S. Energy Policy Uncertainty (EPU), Geopolitical Risk Index (GPRH), Trade Policy Uncertainty (TPU), and Monetary Policy Uncertainty (MPU), are widely recognized in the literature for capturing macroeconomic and policy-driven risks (Li et al., 2022; Baker et al., 2016).

As described in Section 2, CES interacts strongly with physical and transition climate risk on theoretical and empirical levels. This study analyzes 14 climate risk predictors, summarized in Table 1, Panel D. The table also includes the data sources.

Climate transition risk is generally measured using word frequency indices from news media to gauge transition risk attention (Yan et al., 2020); this study uses the Climate Policy Uncertainty (CPU) index by Gavriilidis (2021). We also incorporate regional measures, including China Climate Policy Uncertainty (CCPU), Global Climate Policy Uncertainty (GCPU), and North America Climate Policy Uncertainty (NACPU) (Liang et al., 2022; Ma et al., 2024). Specifically, NACPU is derived from CNEFN data on U.S. and Canada CPU; it is constructed using the principal component of the original series. Further, the Transition Risk Index (TRI) provides additional information, providing a broader perspective on transition risks.

Physical risk includes impacts from extreme climate events, particularly frequent occurrences of extreme cold or heat, tornadoes, and droughts. Using Zhang et al. (2023), we calculate the abnormal values for these three types of extreme climate events. These variables serve as predictors of climate physical risk.

In addition to transition and physical risks, public attention to climate change also influences CES (Chen et al., 2023; Lang et al., 2023). This study uses Google Trends data from keyword searches to reflect public attention. Five different topic indices are constructed: broad cognitive level topic, physical risk attention topic, opportunity attention topic, clean energy attention topic, and climate commission topic. Detailed calculation methods for each attention topic index are in the  Supplementary Material.

Financial markets are critical in understanding CES due to their interconnectedness with broader economic and market dynamics, as discussed in Section 2. This paper summarizes these predictors and the associated data sources in Table 1, Panel E.

First, based on Sadorsky (2012) and Lu et al. (2021), natural gas, oil, gasoline, and heating oil are selected as CES predictors, due to their role in determining the cost structure and overall pricing dynamics within the energy sector.

Second, the broader stock market also affects CES. The dynamics of major stock indices can influence investor sentiment and capital allocation toward the clean energy sector. Indices like the S&P 500 Index (SP500) and others provide a benchmark for evaluating the relative performance and risk-return profile of clean energy investments.

Third, market sentiment and fear indices also play a significant role in CES performance. Indices such as the Chicago Board Options Exchange (CBOE) Volatility Index (VIX) reflect overall commodity price movements and green project financing dynamics, and help measure risk sentiment in financial markets. This directly affects the required risk premiums for investing in CES.

The selection of predictors in this study is based on their theoretical and empirical relevance to CES returns. Technical indicators predictors, such as MA and OBV, are widely used in asset pricing models to capture short-term price trends and trading volume dynamics, which can signal investor sentiment and momentum effects (Neely et al., 2014). Macroeconomic predictors, including CFNAI and TPU, reflect broader economic trends and policy-related risks (Ghosh and Jana, 2024), which are crucial for understanding capital flows into clean energy investments. Climate risk predictors such as TRI capture transition and physical risks that influence CES valuations through regulatory uncertainty and environmental impacts (Herrera et al., 2022). Financial predictors, including volatility indices (VIX, OVX) provide insights into market conditions and investor sentiment (Khalfaoui et al., 2022), complementing the understanding of CES returns. Together, these predictors offer a comprehensive framework for understanding CES returns.

Regularization techniques are crucial in high-dimensional forecasting as they mitigate multicollinearity and overfitting. Traditional models like OLS become unstable with numerous predictors, leading to unreliable estimates (Tibshirani, 1996), whereas penalized regression methods such as LASSO and Elastic Net impose constraints on coefficients, reducing variance and improving robustness (Zou and Hastie, 2005). Empirical studies confirm their effectiveness, with Wang et al. (2022) demonstrating that LASSO enhances return predictability in clean energy markets by selecting relevant predictors and addressing multicollinearity, while Zhang et al. (2019) show that shrinkage techniques improve out-of-sample forecasting by eliminating redundant variables and capturing key features. These findings support the necessity of penalization techniques in our approach.

Basic shrinkage models, such as PLS and PCR, are foundational tools for reducing dimensionality and addressing multicollinearity in high-dimensional datasets. They simplify predictor variables into principal components or latent factors, providing interpretable structures while preserving key information.

Based on the data described in Section 3, the basic prediction procedure to determine CES returns $rt+1$ at $t+1$ is:

where the $βiTech$⁠, $βiMacro$⁠, $βiClimate$ and $βiFin$ represent the 56 coefficients. The $fi,tTech$⁠, $fi,tMacro$⁠, $fi,tClimate$ and $fi,tFin$ are the 56 predictors. Due to problems such as multicollinearity, the coefficient estimates in Equation (1) are not able to identify key predictors over time. As such, this study applies different dimension reduction methods to identify which predictors are most important for predicting CES.

• (1)

  Model 1: Partial Least Squares (PLS) model

The PLS model is used to identify $K$ principal components $fk,tPLS$⁠, $k=1,2,…,K$ between $rt+1$ and the 56 predictors. This reduces the dimensionality of predictors. Subsequently, the PLS model regresses $rt+1$ on $fk,tPLS$⁠, as follows:

where $fk,tPLS$⁠, $k=1,2,…,K$ incorporate the correlation information among $rt+1$⁠, $fi,tTech$⁠, $fi,tMacro$⁠, $fi,tClimate$ and $fi,tFin$⁠. The canonical components $fk,tPLS$⁠, $k=1,2,…,K$ are mutually orthogonal. We set $K=5$ for this study.

• (2)

  Model 2: Principal Component Regression (PCR) model

The PCR model is used to estimate and shrink the coefficients of predictors in Equation (1). It is expressed as:

where $fk,tPCA$⁠, $k=1,2,…,K$ denotes the principal component, and $K$ represents the first $K$ principal components with the highest cumulative explained variance. This variable is set to $K=5$⁠.

This study considers three popular regularization models: the LASSO model (Zhang et al., 2019), the adaptive LASSO of Zou (2006), and the elastic net (EN) of Zou and Hastie (2005). Each model modifies the baseline regression model of Equation (1) by adding penalties to manage sparsity and correlated predictors.

• (3)

  Model 3: LASSO model

The LASSO model relies on the $l1−$ penalties functions to estimate and shrink the parameters $β$ in Equation (1). The LASSO estimator $βˆλLASSO$ is then defined as:

where $T$ denotes the sample size of observations, and $λ∈R$ the regularization parameter that controls the level of penalty applied to predictor coefficients. By adjusting $λ$⁠, the LASSO model shrinks some coefficient estimates to zero. This effectively reveals a subset of relevant key predictors.

• (4)

  Model 4: Adaptive LASSO model

The adaptive LASSO model extends the standard LASSO by incorporating adaptive weights for each predictor in the $l1−$ penalty term. This allows different coefficients to experience different degrees of penalization. This mitigates the over-penalization problem in LASSO and improves variable selection accuracy. In this study’s forecasting model, the parameter estimates for adaptive LASSO are calculated as:

where $wi=1/|βˆiRidge|,i=1,2,…,56$ is an initial estimate weight, obtained using the Ridge estimation in Equation (1).

• (5)

  Model 5: Elastic Net model

The Elastic Net (EN) is a regularization method that linearly combines both $l1−$ and $l2−$ penalties. This approach improves forecasting performance, particularly when addressing highly correlated predictors (Zou and Hastie, 2005). The parameter estimates for Enet are calculated as:

where $μ$ is the tuning parameter that balances the contribution of the $l1−$ and $l2−$ penalties. This study sets $μ=0.5$⁠, enabling the model to effectively handle correlated predictors.

This study applies several widely used predictor selection methods, in conjunction with quantile regression techniques (Ren et al., 2022). These include Quantile LASSO, Quantile Adaptive LASSO, and Quantile Elastic Net. Generally, the median of $rt+1$⁠, $rt+1(50%)$ is used to estimate $rt+1$⁠. Equation (1) is rewritten as follows:

• (6)

  Model 6: Quantile LASSO

First, we consider the Quantile LASSO (QLASSO) model, which extends the LASSO model to the quantile regression framework. This model uses $βˆλ(50%)∈R56$ to estimate $β$ in Equation (1). Equation (4) is then rewritten as follows:

• (7)

  Model 7: Quantile Adaptive LASSO

We also apply the quantile adaptive LASSO (Q-ALASSO), which applies adaptive weights to the $l1−$ penalty in quantile regression. This allows different penalties for different predictors to improve accuracy, as follows:

where we set $wi$ the same as in Equation (5).

• (8)

  Model 8: Quantile Elastic Net

We estimate the quantile elastic net (Q-EN) model to obtain $βˆλQEN∈R56$ to estimate $β$ in Equation (1):

where $μ=0.5$⁠, similar to Equation (6).

The distinction and adoption of quantile-based regularization models arise from their ability to address limitations of classical regularization methods. Classical regularization models focus on average effects and perform well in stable markets. However, they may overlook important predictor influences under extreme conditions. Quantile-based models analyze conditional quantiles capturing predictor impacts across the entire distribution of returns. This makes them particularly effective in handling heteroscedasticity and tail dynamics, which are crucial for understanding the volatility and risks inherent in CES markets.

Single forecasting methods often have difficulty maintaining high predictive performance over the long term in dynamic markets. In contrast, combination methods improve predictive accuracy. The combined forecast at time $t$ is expressed using the weighted average of the N individual forecasts, shown as follows:

where $rˆtc$ is the combination forecast at month $t+1$ and $rˆi,t+1$ is the individual forecast for the i-th model at month $t+1$⁠. The term $ωi,t+1$ denotes the weight assigned to the i-th forecast at time $t+1$⁠. Based on Rapach et al. (2010) and Zhang et al. (2019), three combination methods are used: Model 9: Mean combination, Model 10: Median combination, and Model 11: Trimmed mean (T-Mean) combination.

This subsection examines which prediction model in Section 4, achieves the most accurate prediction under a one-step-ahead forecasting scenario using a large set of predictors. This analysis also helps identify the most effective model for extracting the functional characteristics of the predictors. Tables 2-4 present the out-of-sample $R2$ predictive performance of different models with rolling window lengths of 60, 72, and 84 months. The table notes explain the metrics; further clarifications are in Ren et al. (2022) and Campbell and Thompson (2008).

Across all three window lengths, the Q-EN model (a quantile regularization model) consistently delivers the best forecast performance compared to other models, achieving a positive $R2$ and higher scores relative to both AR(1) and RW benchmarks. Specifically, under the 60-month AR(1) benchmark, Q-EN yields an $R2$ of 0.632 for $OORMSPE2$ and 1.909 for $OORMAPE2$⁠. These significantly outperform other models for both metrics. Similarly, under the 72-month window, Q-EN achieves an $R2$ of 1.832 for $OORMSPE2$ and 2.161 for $OORMAPE2$⁠. This further demonstrates the model’s superior predictive accuracy. At the 84-month window, the model continues to show robust performance, with an $R2$ of 1.773 for $OORMSPE2$ and 2.320 for $OORMAPE2$⁠; this reflects an ongoing advantage over other competing models. These results indicate that Q-EN effectively captures out-of-sample predictability, and reduces forecast errors when considering both mean-squared prediction error and mean absolute error.

When comparing other forecasting models, basic shrinkage models (PLS and PCR) have the lowest predictive performance, with negative values across all metrics and benchmarks. This indicates they are less effective prediction models. The regularization models are also limited in their predictive effectiveness, though EN performs slightly better than the others. The EN’s score is closer to zero than other models in this group; however, it falls short of achieving significant predictive accuracy compared to the benchmark.

In contrast, quantile regularization models generally demonstrate stronger predictive performance. As noted above, Q-EN consistently outperforms the other quantile models, yielding positive and higher $R2$ values across all benchmarks and time windows. Of the model combination models, the median forecast model occasionally reaches positive $R2$ values; this indicates that it outperforms the baseline in these instances. However, Q-Lasso and Q-ALasso generally show negative $R2$ values, indicating they do not provide better predictions than individual benchmarks.

In summary, in contrast with other models showing generally lower predictive ability, the quantile-based methods, particularly Q-EN, effectively increase forecasting accuracy, especially when leveraging median robustness and adaptive elastic net regularization.

Figures 1 and 2 show the cumulative out-of-sample $OORMSPE2$ for different forecasting models over a 60-month rolling window, comparing the models to the AR(1) and RW benchmarks.

The plots show that Q-EN consistently shows stable and better forecasting performance compared to the benchmarks. In both the AR(1) and RW comparisons, Q-EN maintains the highest cumulative $OORMSPE2$ for most of the forecasting period. This demonstrates its consistently better predictive performance compared to other models. The Q-EN curve has a relatively flat slope after the initial adjustment phase, indicating sustained predictive accuracy over time.

Additionally, all models fluctuate in their cumulative $OORMSPE2$ compared to the benchmark models around early 2020, a period with significant volatility. This period, highlighted by vertical bars in the figure, corresponds to the outbreak of the COVID-19 pandemic. This caused abnormal shifts in CES returns and reduced predictability. This is also when the National Bureau of Economic Research (NBER) officially declared the onset of a recession.

The previous section evaluated the predictive accuracy and performance of different models under out-of-sample conditions. It identified the Q-EN model as being most accurate across different forecasting windows. This section further examines the importance of the 56 predictors, to understand their contributions in forecasting CES returns. The discussion focuses on overall and time-varying pick-up rates (degree of importance in predicting CES) to provide insights into their forecasting roles.

The predictability of CES returns stems from macroeconomic mechanisms, such as CFNAI and TPU, which reflect economic trends and uncertainty, and climate risk predictors like TRI, capturing policy impacts and extreme events. Indicator predictors, such as OBV, are effective for short-term trends driven by market activity. These drivers collectively explain CES predictability under varying conditions. Figure 3 shows that macroeconomic predictors dominate the pick-up rate, with UNRATE ranking the highest at 25.64%, followed by GPRH at 20.86%, and TPU at 20.80%. These predictors capture key aspects of labor market dynamics, geopolitical risks, and trade policy uncertainty. This aligns with Baumeister et al. (2022), who demonstrated that macroeconomic indicators, such as unemployment rates and economic activity indices, are robust predictors of energy-related market performance.Among the technical indicator predictors, OBV(3,12) has the highest pick-up rate, at 16.93%. This reflects the influence of market volatility. TRI leads the climate predictors at 14.56%. This highlights the importance of climate transition factors. The SP500 is the top-ranked predictor in the financial assets group at 15.92%; this highlights the role of broader market movement.

When comparing predictor groups, macroeconomic predictors have the highest average pick-up rates, reaffirming their critically influential role in forecasting CES returns. Financial predictors rank second. These are followed by climate risk predictors, which show increasing relevance, particularly those related to the energy transition. Technical indicator predictors have lower pick-up rates.

Figure 4 provides a detailed view of the time-varying pick-up rate of predictors throughout the out-of-sample period, showing distinct patterns across groups. The macroeconomic predictors UNRATE, USDX, and TPU maintain consistently high pick-up rates. During periods of increased uncertainty, predictors like GPRH and EPU become more important. This reflects their ability to capture external shocks and sentiment.

Climate risk predictors, including TRI and Ab_TEMP, show significant variability, with higher pick-up rates during climate policy shifts or extreme weather events. For example, TRI increases as green energy policy changes, while Ab_DRT aligns with severe energy production disruptions due to weather.

In the technical indicator predictors group, $OBV(s,l)$ and $MOM(k)$ are consistently relevant during periods of high market volatility, indicating their role in capturing short-term market dynamics. However, their intermittent importance reflects their sensitivity to specific market conditions, rather than broader economic trends. Financial predictors, such as SP500 and WTI, also vary across time, often becoming significant during periods of financial turbulence. The low, but growing, pick-up rate of ESG signals the increasing integration of sustainability metrics into clean energy investment decisions.

To further explore these dynamics, predictor importance is considered across distinct time periods. From 2016 to 2018, the macroeconomic predictors UNRATE and TPU are most important, driven by the global economic recovery and trade policy uncertainty during this period. Relatively stable markets limit the importance of the technical indicator predictors $OBV(s,l)$ and $MOM(k)$⁠. In 2019 and 2020, escalating geopolitical risks, including U.S.-China trade disputes and the COVID-19 pandemic, increase the importance of GPRH, TPU, and UNRATE in CES predictions. Climate risk predictors such as TRI also gain importance, reflecting shifts in energy policies and rising public awareness of climate issues.

From 2021 to 2022, the global post-pandemic recovery and accelerated green energy transitions increase the influence of the climate predictors TRI and Ab_DRT. Concurrently, market volatility increases the relevance of technical indicator predictors, particularly $OBV(s,l)$ and $MOM(k)$⁠. In 2023, the stabilization of the clean energy sector results in a more balanced distribution of predictor pick-up rates. Macroeconomic predictors USDX and INDPRO, and climate risk predictors TRI and Ab_TEMP, maintain their consistent level of importance. This reflects a long-term focus on economic and climate-related trends.

In summary, this time-based analysis highlights how predictors respond to global economic shifts, policy changes, and climate dynamics. Macroeconomic predictors are consistently most important, overall and in time-varying contexts, with respect to predicting CES returns, particularly during economic fluctuations. Climate risk and financial predictors play notable but secondary roles. Climate risk predictors are more important during sustainability transitions, while technical and financial predictors influence forecasts during period of market volatility. This underscores the importance of integrating diverse predictors and accounting for temporal dynamics to improve forecasting accuracy.

This subsection investigates the group-level performance of the 56 predictors, to assess the overall importance of each predictor group (macroeconomic, climate risk, technical, and financial predictors) in forecasting CES returns. Group regularization models are used; these apply a uniform penalty to the coefficients of predictors within the same group. This approach ensures that predictors within a group influence the model consistently. This helps identify the collective importance of a group of predictors.

The Group LASSO (Yuan and Lin, 2006) extends the LASSO model to enable variable selection for grouped predictors. In this study, the predictors fall into four groups. The parameter vector in Equation (1) has a group structure ${g1,g2,g3,g4}$⁠, subject to the following: $⋃i=14gi={1,2,…,N}$ and $gi$ are disjoint. The Group LASSO estimator is formulated as:

where $βgj$ are the parameters in the $gj$-th group. The multiplier $mj$ is used to balance cases where the groups have very different sizes (different number of variables). We set $mj=Tj$⁠, where $Tj$ is the number of parameters in the j-th group.

This study also considers the group SCAD model. The parametric estimator in the penalized regression with the group SCAD is:

where $Pλ$ is the group SCAD penalty, defined as:

The Quantile Group LASSO (Group-QLASSO) model addresses situations where predictors are naturally grouped together. The estimator is defined as:

Table 5 presents the predictive performance of the group-based models in terms of $OORMSPE2$ and $OORMAPE2$ percentages across different forecast horizons and rolling window lengths. We also report the predictor group pick-up rates across multiple forecast horizons, highlighting the relative contribution of each group when predicting CES returns.

In the 60-month rolling window, the Group-QLasso model excels in the 1-step ahead forecast; this model achieves the highest $OORMSPE2$ (46.038) and $OORMAPE2$ (23.308) values. This highlights its strength in capturing short-term dynamics. For 2-step ahead predictions, the Group-Lasso model achieves the highest $OORMSPE2$ (49.258) and $OORMAPE2$ (26.006) values, followed closely by Group-SCAD. In the 3-step ahead forecast, the Group-Lasso model remains the top forecasting performer, further demonstrating its robustness in medium-term forecasting.

In the 72-month rolling window, the Group-QLasso model performs best again in the 1-step horizon. For 2-step and 3-step forecasts, the Group-SCAD is better in its predictions compared to Group-Lasso and Group-QLasso. It particularly excels in the 3-step horizon, with the highest $OORMSPE2$ (50.321) and $OORMAPE2$ (26.094) values. The Group-Lasso model is also strong; it ranks second in these longer horizons, but maintains consistent prediction performance. In the 84-month rolling window, the Group-QLasso model remains the best in the 1-step horizon. The Group-Lasso model shows strength in the 2-step horizon (48.176 $OORMSPE2$⁠, 24.778 $OORMAPE2$⁠) and remains competitive in the 3-step forecast.

Overall, the analysis reveals that the three models have clear differentiated predictive strengths. The Group-QLasso model is particularly effective for short-term forecasts across all rolling windows; this makes it the preferred choice for immediate predictions. The Group-Lasso model consistently excels in multi-step horizons, particularly in medium-term forecasts. This showcases its robustness across conditions. Group-SCAD, while not preferred in shorter horizons, delivers strong performance in longer forecasting horizons and rolling windows. These results emphasize the importance of selecting the most effective model based on the forecast horizon and window length.

The predictor group pick-up rates in Table 6 describe the relative importance of each group in forecasting CES returns across different time horizons.

Macroeconomic predictors are consistently most important for accurate predictions, with a pick-up rate of 37.50% for 1-step ahead forecasts. This rate decreases to 15.62% by the 7-step horizon; however, macroeconomic predictors remain the most influential group overall. This finding highlights their critical role in short-term forecasts, explained by the direct and immediate impact of economic conditions on market behavior. Studies like Arouri et al. (2016) highlight the lasting impact of macroeconomic uncertainty on renewable energy investments, which supports the empirical findings here.

Climate risk predictors are second most important, with a 34.38% pick-up rate for 1-step ahead forecasts. Their importance gradually decreases as the forecast horizon lengthens. These results align with the structural and long-term nature of climate-related factors. These factors are less responsive to short-term market fluctuations but remain moderately relevant over longer horizons.

Financial predictors decline in importance as the forecast horizon increases. They contribute significantly to 1-step ahead forecasts (30.21%), but have a minimal level of importance for 7-step ahead forecasts (4.17%). This verifies that their short-term focus is driven by external shocks, such as oil price changes or financial crises.

Finally, technical indicator predictors are sporadically important, with relatively low pick-up rates across all horizons. Their contributions peak at 16.67% for 1-step ahead forecasts, but fall to 0% for 7-step forecasts. This indicates their contextual dependence, influenced primarily by short-term market momentum and volatility.

In summary, macroeconomic and climate risk predictors are key to CES forecasting: macroeconomic predictors are most important over short-term horizons and climate risk predictors decline in importance over time. Technical and financial predictors have limited, short-term relevance. As with the previous model-based analysis, these results emphasize the need to align predictor groups with forecasting horizons.

This subsection focuses on analyzing the time-based trends associated with predictors, to evaluate their contributions to CES return forecasting. Decomposing predictors into short-term, medium-term, and long-term components shows how these components work and perform in predicting CES returns. This approach highlights the most impactful time-based components of predictors and provides deeper insights into how different trends influence CES forecasting.

This analysis focuses on macroeconomic and climate predictors, due to their higher rates of importance. Wavelet decomposition, a technique that separates a signal into components at different frequency levels, is used here to capture the multi-scale nature of predictor impacts (Dai et al., 2025; Miao et al., 2022; Xue et al., 2024; Zhang et al., 2025). Each predictor is decomposed into four components:

where $ϕj,k,t$ denotes the father wavelet function and $ψj,k,t$ denotes the mother wavelet function, expressed as:

where $J$ denotes the maximum level of decomposition; this level is set to 3. Additionally, the father and mother wavelet functions satisfy the following:

Then, the coefficients of the high frequency $Dj,k$ and low frequency $Sj,k$ have the following form:

This generates four decomposed components: $D1,t$ (short-term cycles, 1–2 months), $D2,t$ (medium-term cycles, 2–4 months), $D3,t$ (long-term cycles, 4–8 months), and $S3,t$ (longer-term trend components, over 8 months).

Table 7 shows the predictive performance of these macroeconomic and climate risk predictor components over three forecasting horizons: 60, 72, and 84 months. The results indicate that the D1 component contributes less to accurate predictions. The Group-QLasso model shows the most consistent performance, particularly for the 84-month horizon. In contrast, the Group-SCAD model does not work effectively with D1, overall and especially for longer horizons. This is shown by the negative $OORMSPE2$ values. This indicates that Group-SCAD may be less effective in capturing short-term dynamics.

The D2 component has the most robust predictive power across all models. The Group-SCAD model performs best at the 84-month horizon, followed by the Group-Lasso model. The Group-QLasso model is effective, but is somewhat less effective for D2. This indicates it is more suitable for short-term rather than medium-term forecasting. The significant impact of D2 components likely reflects their ability to capture market transitions and investor sentiment. Macroeconomic predictors like UNRATE and TPU show medium-term effects, aligning with Baumeister et al. (2022) on energy markets. Climate risk predictors also peak in this period due to their relevance during policy and regulatory changes, as noted by Herrera et al. (2022). These findings suggest that the 2–4 months window optimally captures predictors with a balance of short-term responsiveness and longer-term trends, enhancing predictive performance across models.

For the D3 component, the Group-SCAD model again outperforms other models. The Group-Lasso model shows more volatility, including negative $OORMSPE2$ values at the 60-month horizon. Finally, the S3 component contributes the least to prediction accuracy, with both Group-Lasso and Group-SCAD models showing mixed results across horizons. The Group-QLasso model maintains relatively stable performance, especially at the 84-month horizon. However, overall, the S3 component is less useful.

Figure 5 illustrates the importance of macroeconomic and climate predictors, particularly the macroeconomic variables. Among the macroeconomic predictors, CFNAI (53.12%) and INDPRO (24.38%) have the highest relevance for forecasting, and are significantly more important than climate predictors. Several climate-related predictors have values of zero, with limited individual utility for predicting CES returns. This result aligns with findings above, emphasizing the higher stability and relevance of macroeconomic predictors in forecasting CES returns.

Moreover, the time-based varying rates of the D2 components, as shown in Figure 6, further highlight the importance of macroeconomic predictors. Variables such as CFNAI, INDPRO, and CPI are persistently important over time, indicating their robust predictive contribution across different forecasting periods. Macroeconomic predictors consistently provide valuable information, particularly in capturing medium-term cycles. In contrast, climate predictors are less consistent in their importance, reflecting their more volatile and unstable contributions to predicting CES returns. This variation further supports the conclusion that macroeconomic predictors play a more dominant and stable role, while climate predictors have more limited and sporadic utility.

In conclusion, the wavelet decomposition method highlights the significant contribution of D2 components in forecasting CES returns, particularly for macroeconomic predictors. Components D1 and D3 also have predictive value, but their effectiveness depends on the forecasting method and the horizon. Medium-term components provide a more consistent and stable contribution, especially when considering the robust performance of the macroeconomic predictors CFNAI and INDPRO.

The consistently higher relevance and stable time-varying contributions of macroeconomic predictors emphasize their significant role in forecasting CES returns. These predictors provide valuable information across different time horizons, particularly in the medium term. Climate risk predictors play a role, but their impact on prediction is more sporadic and has less stable utility. Thus, medium-term macroeconomic predictors should be prioritized to accurately forecast CES returns.

Additional analyses are conducted to assess the robustness of the findings and to explore further implications. Specifically, we conduct multi-horizon forecasting and investigate the role of predictors compared to autoregressive components in improving forecast accuracy.

Multi-horizon forecasting examines predictive performance over different timeframes, including two-, three-, five-, and seven-step ahead forecasts. This approach describes and evaluates how our models perform when extended beyond short-term predictions. This helps further assess the model’s stability and predictive capability over multiple horizons. Tables 8 and 9 present the multi-step data for each model.

Each model is compared against AR(1) and RW across the different forecast horizons. The table shows that quantile-based methods consistently have lower forecast errors across multiple horizons, particularly for longer forecasting periods such as five and seven-steps ahead. The Q-EN model has the most robust predictive performance; this indicates its effectiveness in capturing complex dynamics over extended time horizons. The traditional models PLS and PCR do not perform as well; they are limited in multi-horizon scenarios.

This subsection explores the relative contribution of this study’s predictors, compared to autoregressive components in improving forecast accuracy. Specifically, we investigate the degree to which including external predictors increases predictive performance beyond the baseline AR model.

To evaluate predictor impact, we compare the forecasting results of models that incorporate external predictors (e.g. including macroeconomic, inflation, and policy uncertainty indicators) against models that rely only on autoregressive terms. The results show that incorporating external predictors significantly improves forecast accuracy across different models and horizons. Specifically, the quantile regularization models show the most significant improvement in predictions. This indicates that these predictors capture critical external information that autoregressive terms do not effectively account for on their own.

In particular, provide crucial information to help anticipate shifts in CES performance, especially during periods of economic instability. The comparison shows that models relying purely on autoregressive terms tend to underperform, particularly when market conditions change rapidly. This emphasizes the importance of including diverse external predictors.

The analysis highlights the value of combining traditional autoregressive terms with well-chosen external predictors for more accurate and robust forecasts. The empirical evidence shows that external predictors play a vital role in predicting CES returns, outperforming the baseline AR(1) model alone.

This study provides a comprehensive framework for forecasting CES returns using diverse predictors, including technical, macroeconomic, climate risk, and financial factors. Different shrinkage models are used to systematically analyze the role and effectiveness of individual predictors, group-level predictors, and their trend components in CES forecasting. This study approach addresses key research questions about their predictive power, time-varying relevance, and group-level contributions.

The findings provide clear economic insights into CES returns. Macroeconomic predictors, such as CFNAI, capture economic cycles and guide investment decisions during uncertainty. Climate predictors, like TRI, highlight sustainability’s growing role in shaping market responses to policy changes. Technical and financial predictors, though short-term, help investors navigate market volatility. These results connect CES forecasting with broader financial theories and offer actionable guidance for navigating the complexities of clean energy markets. Key results are as follows.

First, at the individual level, macroeconomic predictors are the most influential for predicting CES returns; they consistently demonstrate high relevance across different forecasting models and periods. Unemployment rates and geopolitical risk indices play a critical role, particularly during periods of increased uncertainty. Climate risk predictors are temporally variable, reflecting the dynamic impacts of policy shifts and public sentiment. Technical and financial predictors are relevant primarily during volatile market conditions.

Second, at the group level, macroeconomic predictors are the main contributors to forecasting accuracy when analyzed collectively. Applying group shrinkage models shows that macroeconomic predictors consistently outperform other predictors in both short- and long-term horizons. Climate risk predictors are more important during periods of increased focus on sustainability and energy transitions. Technical and financial predictors are less stable, but provide valuable insights during periods of market disruption.

Third, analyzing trend components shows that medium-term dynamics play a key role in forecasting CES. These components, particularly among macroeconomic predictors, contribute the most to predictive accuracy. This highlights their importance in capturing the underlying trends at work with CES returns. While short-term and long-term components provide useful information, their effectiveness depends on specific market conditions and forecasting methods.

These findings are valuable for both investors and policymakers. Investors can use the time-varying relevance of predictors to make better decisions. During economic uncertainty, focusing on predictors like UNRATE and GPR can improve CES return forecasts. When sustainability or energy transitions are prioritized, climate risk predictors become more significant. Policymakers can tailor policies to align with key predictors at different times, optimizing their response to economic shifts or sustainability goals, thereby improving effectiveness in the clean energy sector.

Overall, this study addresses key questions about which predictors have the greatest power for forecasting CES returns, how their relevance evolves over time, and whether grouping and decomposing predictors improves forecasting accuracy. These findings emphasize the critical role of macroeconomic predictors, the value of group-level analysis, and the importance of medium-term trend components in improving predictions of CES returns. These insights offer valuable guidance for investors and policymakers navigating the complexities of the clean energy sector amidst rapid economic and environmental change. This study is limited by its use of monthly data and focus on the WilderHill Index, which may reduce generalizability. Future research could explore higher-frequency data or other regional markets to uncover new dynamics and further optimize forecasting methods for improved accuracy, particularly by incorporating advanced machine learning techniques to capture non-linear relationships in CES returns.

Funding: This research is financially supported by the National Social Science Fund of China (Grant No. 21&ZD110) and the National Natural Science Foundation of China (Grant No. 52270183).