Keywords

JEL Classifications

4.1 Introduction

Renewable energy assets have gained consideration among investors in recent years. Several studies document a growing demand for renewable energies and an increment in clean energy investments in emerging and developed economies (Kaldellis and Zafirakis 2011; Teske et al. 2011; IRENA 2017; REN21 2017). The increasing interest in clean energy equities by investors may be explained by the growth prospects of the sector, which in turn are based on three reasons. First, there is an increasing concern about the natural environment and decarbonizing the energy system, reflected in the Kyoto protocol and the Paris agreement (Schellnhuber et al. 2016; Klein et al. 2017; Grubb et al. 2018). Moreover, there is a need for mitigating energy security issues such as political instability in oil supplying countries or unexpected increments in the oil demand (Lieb-Dóczy et al. 2003; Ang et al. 2015; Bondia et al. 2016). According to the International Energy Agency, energy security is defined as “the uninterrupted availability of energy sources at an affordable price.” Finally, it is important to invest in technological innovation and developing new energy storage technologies to attain a clean energy system (Sagar and van der Zwaan 2006; Wilson and Grubler 2011; Kittner et al. 2017).

Clean energy indices, such as wind and solar energy, are sold in financial markets that share the same dynamics of highly volatile assets. Besides, clean energy returns may exhibit heavy-tailed distributions since financial returns follow fat-tailed distributions (Gabaix 2009). It is important to model the volatility of renewable energy returns for investors since it affects the performance of their portfolios on renewable energy. Many research papers employed generalized auto-regressive conditional heteroskedasticity (GARCH) models of Bollerslev (1986) to model the volatility of renewable energy data (Henriques and Sadorsky 2008; Kumar et al. 2012; Sadorsky 2012; Wang and Wu 2012; Managi and Okimoto 2013; Ahmad et al. 2018; Kocaarslan and Soytas 2019). Nevertheless, to the best of our knowledge, no study has applied generalized auto-regressive score (GAS) models to model renewable energy returns. GAS models are flexible models that are robust to misspecifications of the conditional density (Creal et al. 2013; Harvey 2013).

This chapter contributes to the literature on clean energy returns as follows. First, it searches for optimal models for forecasting the Wilder Hill Clean Energy Index (ECO), the Standard and Poor’s Global Clean Energy Index (SPCLE), the MAC Global Solar Energy Index (SUN), and the European Renewable Energy Index (EURIX). These indices measure the stock market performance of clean energy companies in the world and Europe. This chapter employs 37 flexible and fat-tailed GAS and GARCH models for modeling clean energy returns. No previous study has used GAS models to forecast clean energy returns and risk. Besides, it compares the out-of-sample performance of all models to find the optimal forecast model for clean energy returns. Finally, this chapter performs several backtesting approaches for daily 1%-Value-at-Risk (VaR) forecasts of clean energy returns. It is important to measure correctly VaR to fulfill market risk capital reserves of the Basel Agreements.

Our findings suggest that heavy-tailed distributed GARCH and GAS models are optimal for all renewable energy returns considered. They also have the best out-of-sample forecast performance and the best coverage for 1%-VaR of renewable energy returns. Therefore, fat-tailed distributed models enhance both in-sample and out-of-sample performance of renewable energy returns and risk. These findings illustrate the relevance of modeling the kurtosis for renewable energy returns.

The rest of the chapter proceeds as follows. Section 4.2 outlines the data and the methodology. Section 4.3 presents the empirical results and discussion. Finally, Sect. 4.4 concludes.

4.2 Data and Econometric Methodology

We employ data on 1458 daily observations of the Wilder Hill Clean Energy Index (ECO), the Standard and Poor’s Global Clean Energy Index (SPCLE), the MAC Global Solar Energy Index (SUN), and the European Renewable Energy Index (EURIX). The ECO index is based on US stocks that operate in the promotion and preservation of clean energy. The SPCLE index comprises 30 companies from around the world operating in clean energy-related businesses. The MAC index is made up of US companies involved in the solar energy industry, and the EURIX is built on the largest European renewable energy companies. Our sample period spans from November 14, 2013, to September 18, 2019. We selected this period because of the data availability. We obtained all series from DataStream. Given the closing price \(P_{t}\) of a renewable index at time t, we calculate its logarithm returns as \(r_{t} = 1 0 0\times \ln \left( {P_{t} /P_{t - 1} } \right)\).

Table 4.1 reports descriptive statistics (in percentages) for the daily returns on the renewable energy indices. The clean energy indices are nonstationary at the 5% level, whereas the log-returns are stationary. Besides, all returns are non-normally distributed and volatile, with a standard deviation greater than the mean. All returns are negatively skewed, illustrating the usefulness of heavy-tailed distributed models for the conditional volatility of clean energy returns.

Table 4.1 Summary statistics: Clean energy returns (in %)
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We estimate AR(1)-GARCH(1,1) models of Bollerslev (1986) for the daily returns on renewable energy indices as:

$$r_{t} = c + \varphi_{1} r_{t - 1} + u_{t} ,\;u_{t} = \sigma_{t} \varepsilon_{t} ,$$
(4.1)
$$\sigma_{t}^{2} = \omega + \alpha u_{t - 1}^{2} + \beta \sigma_{t - 1}^{2} ,$$
(4.2)

where \(\left| {\varphi_{1} } \right| < 1\) and \(\varepsilon_{t}\) follow a white noise process. Let \({\text{z}}_{t - 1} = u_{t - 1} \sigma_{t - 1}^{ - 1}\) and \(1 (\cdot )\) be an indicator function. We model different GARCH specifications for the conditional volatility of \(u_{t}\):

$$ {\text{ALL-GARCH}}\left( {1,1} \right) :\sigma_{t}^{\delta } = \omega + \alpha \delta \sigma_{t - 1}^{\delta } \left[ {\left| {z_{t - 1} - b} \right| - \gamma \left( {z_{t - 1} - b} \right)} \right]^{\delta } + \beta \sigma_{t - 1}^{\delta } , $$
(4.3)
$${\text{APARCH}}\left( {1,1} \right) :\,\sigma_{t}^{\delta } = \omega + \alpha \left( {\left| {u_{t - 1} } \right| - \gamma u_{t - 1} } \right)^{\delta } + \beta \sigma_{t - 1}^{\delta } ,$$
(4.4.)
$$\begin{aligned} \begin{array}{*{20}l} {{\text{CGARCH}}\left( {1,1} \right) :} \hfill \\ \end{array} \sigma_{t}^{ 2} & = \xi_{t} + \alpha \left( {u_{t - 1}^{ 2} - \xi_{t - 1} } \right) + \beta \left( {\sigma_{t - 1}^{ 2} - \xi_{t - 1} } \right), \\ \xi_{t} & = \omega + \rho \xi_{t - 1} + \eta \left( {u_{t - 1}^{ 2} - \sigma_{t - 1}^{ 2} } \right), \\ \end{aligned}$$
(4.5)
$$ {\text{E-GARCH}}\left( {1,1} \right) :\,{ \log }\left( {\sigma_{t}^{ 2} } \right) = \omega + \left[ {\alpha z_{t - 1} + \gamma \left( {\left| {z_{t - 1} } \right| - E\left| {z_{t - 1} } \right|} \right)} \right] + \beta { \log }\left( {\sigma_{t - 1}^{ 2} } \right), $$
(4.6)
$${\text{GJRGARCH}}\left( {1,1} \right) :\,\sigma_{t}^{ 2} = \omega + \alpha u_{t - 1}^{ 2} + \gamma u_{t - 1}^{ 2} 1\left( {u_{t - 1} < 0} \right) + \beta \sigma_{t - 1}^{ 2} ,$$
(4.7)
$$ {\text{I-GARCH}}\left( {1,1} \right) :\,\sigma_{t}^{ 2} = \omega + \sigma_{t - 1}^{ 2} + \alpha \left( {u_{t - 1}^{ 2} - \sigma_{t - 1}^{ 2} } \right), 0 < \alpha \le 1, $$
(4.8)
$${\text{NGARCH}}\left( {1,1} \right) :\,\sigma_{t}^{\delta } = \omega + \alpha \left| {u_{t - 1} } \right|^{\delta } + \beta \sigma_{t - 1}^{\delta } ,$$
(4.9)
$$ {\text{T-GARCH}}\left( {1,1} \right) :\,\sigma_{t} = \omega + \alpha \left| {u_{t - 1} } \right| + \gamma \left| {u_{t - 1} } \right|1\left( {u_{t - 1} < 0} \right) + \beta \sigma_{t - 1} , $$
(4.10)

where \(\xi_{t}\) is a permanent component of \(\sigma_{t}^{ 2}\). Equation (4.3) displays the ALL-GARCH model proposed by Hentschel (1995) that encompasses the most important GARCH models. Equation (4.4) describes the Asymmetric Power ARCH (APARCH) model of Ding et al. (1993) that considers long memory for absolute returns, and it estimates the power of heteroscedasticity (\(\delta\)) from the data. Equation (4.5) displays the Component GARCH (CGARCH) model of Engle and Lee (1999) that decomposes the conditional variance of the returns into a permanent and a short-run component. Equation (4.6) shows the Exponential GARCH (E-GARCH) model of Nelson (1991) that specifies an asymmetric impact of negative shocks to \(\sigma_{t}^{2}\). Equation (4.7) presents the Glosten–Jagannathan–Runkle (GJRGARCH) model of Glosten et al. (1993) that represents asymmetric shocks to \(\sigma_{t}^{2}\) by applying an indicator function to negative shocks.

Equation (4.8) illustrates the integrated GARCH (I-GARCH) model of Engle and Bollerslev (1986) that assumes persistency in GARCH models. Equation (4.9) shows the nonlinear GARCH (NGARCH) model of Higgins and Bera (1992) that estimates the power of heteroscedasticity (\(\delta\)) from the data. Finally, Eq. (4.10) displays the threshold GARCH (T-GARCH) model of Zakoian (1994), in which \(\sigma_{t}\) (instead of \(\sigma_{t}^{2}\)) reacts differently to negative and positive shocks. For each model in Eqs. (4.2)–(4.10), the innovations \(\varepsilon_{t}\) follow Gaussian (N), t-Student (t), or skewed t-Student (St) distributions.

We employ GAS models based on time-varying parameters, which are flexible and avoid the problem of incorrect specification. We define the conditional distribution of the returns at time t as \(P\left( {r_{t} ;\varvec{\theta}_{t} } \right)\), given a time-varying vector of parameters \(\theta_{t} \in \varTheta \subseteq {\mathbb{R}}^{N}\) that fully characterizes \(P\left( { \cdot ; \cdot } \right)\) as follows:

$$\varvec{\theta}_{t + 1} = {\mathbf{\rm A}}_{0} + {\mathbf{\rm A}}_{1} \varvec{S}_{t} \left( {\varvec{\theta}_{t} } \right)\frac{{\partial \log P\left( {r_{t} ;\varvec{\theta}_{t} } \right)}}{{\partial\varvec{\theta}_{t} }} + {\mathbf{\rm A}}_{2}\varvec{\theta}_{t} ,$$
(4.11)

where \({\mathbf{\rm A}}_{0} ,\varvec{ }{\mathbf{\rm A}}_{1}\),and \({\mathbf{\rm A}}_{2}\) are matrices of coefficients, and \(\varvec{S}_{t} \left( {\varvec{\theta}_{t} } \right)\) is a positive-definite scaling matrix. Following Creal et al. (2013), we specify \(\varvec{S}_{t} \left( {\varvec{\theta}_{t} } \right)\) as

$$\varvec{S}_{t} \left( {\varvec{\theta}_{t} } \right) = \varvec{I},$$
(4.12)
$$\varvec{S}_{t} \left( {\varvec{\theta}_{t} } \right) = E_{t - 1} \left[ {\frac{{\partial \log P\left( {r_{t} ;\varvec{\theta}_{t} } \right)}}{{\partial\varvec{\theta}_{t} }}\frac{{\partial \log P\left( {r_{t} ;\varvec{\theta}_{t} } \right)}}{{\partial\varvec{\theta}_{t} }}^{'} } \right]^{{ - \frac{1}{2}}} ,$$
(4.13)

where \(\varvec{I}\) is the identity matrix. We denote the specifications for \(\varvec{S}_{t} \left( {\varvec{\theta}_{t} } \right)\) of Eqs. (4.12) and (4.13) as Identity (Id) and Inverse Squared (InvSq), respectively. We employ the following conditional distributions for calculating the score function: asymmetric t-Student with a left-tail (AST1) or two decay parameters (AST), Gaussian, t-Student, and skewed-t-Student.

We estimate all GARCH and GAS models for all renewable energy returns, and we evaluate their Akaike information criterion (AIC), Bayesian information criterion (BIC), and the maximum value of the log-likelihood (LogLik) function. We test for serial correlation on the GARCH residuals by applying the Ljung–Box test on the standardized squared residuals. To test for correct specification of GAS models, we employ the probability integral transform (PIT) test proposed by Diebold et al. (1998) on the estimated conditional distribution of GAS models. We also run 500 one-step-ahead rolling out-of-sample forecasts to analyze the out-of-sample performance of all models. The out-of-sample period spans from September 22, 2017, to September 18, 2019. We compare the root-mean-squared error (RMSE) of the out-of-sample forecasts of all models.

Further, we apply backtests on 1%-Value-at-Risk (VaR) forecasts for each renewable energy index return. We employ the conditional coverage (CC) test of Christoffersen (1998) on the conditional density of the returns \(f\left( {r_{t} |r_{t - 1} ,r_{t - 2} , \ldots ,r_{1} } \right)\) and the dynamic quantile (DQ) test of Engle and Manganelli (2004). We apply the quantile loss measure developed by González-Rivera et al. (2004) to evaluate 1%-VaR forecasts as follows:

$$ QL_{t + 1} \left( { 1 {\text{\%}}}\right) = \left( { 1 {\text{\% }} - e_{t + 1} } \right)\left( {r_{t + 1} - {\text{VaR}}_{t + 1} \left( { 1 {\text{\%}}}\right)} \right), $$

where \(e_{t + 1} = 1\left( {r_{t + 1} < {\text{VaR}}_{t + 1} \left( { 1\% } \right)} \right)\) is a VaR exceedance for a \({\text{VaR}}_{t + 1} \left( { 1 {\text{\%}}}\right)\) forecast at t + 1. We also calculate the ratio between VaR exceedances and the expected values a priori, the Actual over Expected ratio (AE), \(AE = \mathop \sum \nolimits_{j}^{ 5 0 0} e_{t + j} /\left( { 1\% \times 5 0 0} \right)\). VaR forecasts with an AE ratio equal to one are optimal. In addition, we compare the mean and maximum Absolute Deviation (ADmean and ADmax) of the 1%-VaR forecasts among all models, which deliver the expected loss given a VaR exceedance (McAleer and Da Veiga 2008). VaR forecasts with lower ADmean and ADmax are preferred.

4.3 Empirical Analysis

Tables 4.2 and 4.3 report the estimation results of the GARCH models of Eqs. (4.2)–(4.10) and the GAS models of Eqs. (4.11)–(4.13) for ECO returns. The Ljung–Box test shows that all GARCH residuals are serially uncorrelated at the 5% level. On the other hand, the PIT test rejects the correct specification of the GAS-N-Id, GAS-N-InvSq, and GAS-t-InvSq at the 5% level (Table 4.3). The AR(1)-ALLGARCH(1,1), AR(1)-E-GARCH(1,1), and AR(1)-T-GARCH(1,1) with a skewed t-Student distribution have the lowest AIC and BIC for the ECO returns (Table 4.2). The GAS model with a skewed t-Student together with an inverted square score displays the lowest AIC and BIC among all GAS models. Therefore, fat-tailed distributed models display a better in-sample fit for ECO returns. Further, the GAS-t-Id has the lowest out-of-sample RMSE, followed by the AR(1)-CGARCH(1,1)-t and the AR(1)-I-GARCH(1,1)-t.

Table 4.2 GARCH models for ECO returns
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Table 4.3 GAS models for ECO returns
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Table 4.4 presents backtesting measures for daily 1%-VaR forecasts of ECO returns. None of the GARCH models with the lowest AIC and BIC are optimal for 1%-VaR forecasts. For instance, the DQ test rejects that the AR(1)-ALLGARCH(1,1)-St model has a correct specification for 1%-VaR forecasts at the 1% level, although this model has the lowest AIC among all models. Nevertheless, the AR(1)-NGARCH(1,1)-St is the optimal model for 1%-VaR forecasts of ECO returns since it has the best AE and AD mean ratios together with the highest conditional coverage (CC) of 1%-VaR forecasts. The GAS-St-Id and GAS-St-InvSq also display an AE close to the unity and the highest CC of 1%-VaR forecasts. Overall, both the AE and AD mean ratios enhance when we employ fat-tailed distributed modelsfor 1%-VaR forecasts of ECO returns.

Table 4.4 Backtesting measures for daily 1%-VaR forecasts: ECO returns
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Tables 4.5 and 4.6 show the estimation results of the GARCH and GAS models for SPCLE returns. The Ljung–Box test results indicate the residuals are serially correlated for the AR(1)-ALLGARCH(1,1)-St, AR(1)-ALLGARCH(1,1)-t, AR(1)-T-GARCH(1,1)-St, and AR(1)-T-GARCH(1,1)-t at the 5% level. Conversely, all GAS models are correctly specified at the 5% level. The AR(1)-GJRGARCH(1,1) with a skewed t-Student distribution and with a t-Student distribution have the best in-sample fit for the SPCLE returns (Table 4.5). The GAS-t-Id and the GAS-AST1-InvSq present the lowest AIC and BIC among all GAS models. Consistent with the results for ECO returns, fat-tailed distributed models provide a better in-sample fit for SPCLE returns. Further, the AR(1)-CGARCH(1,1)-N, AR(1)-CGARCH(1,1)-t, AR(1)-NGARCH(1,1)-t, and AR(1)-GARCH(1,1)-t have the lowest out-of-sample RMSE.

Table 4.5 GARCH models for SPCLE returns
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Table 4.6 GAS models for SPCLE returns
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Table 4.7 displays backtesting results for one-day-ahead 1%-VaR forecasts of SPCLE returns. Consistent with the backtesting results for ECO returns in Table 4.4, none of the GARCH models with the best in-sample fit is optimal for 1%-VaR forecasts of SPCLE returns. The AR(1)-APARCH(1,1)-St is the optimal model for 1%-VaR forecasts of SPCLE returns since it has the best AE and the highest p-values of the DQ and CC tests. The AR(1)-ALLGARCH(1,1)-N also displays an AE close to the unity and the lowest AD mean ratio. Moreover, the AR(1)-GARCH(1,1)-St, AR(1)-GARCH(1,1)-t, GAS-AST1-Id, GAS-N-Id, and the AR(1)-T-GARCH(1,1)-N also exhibit the optimal AE ratio and the highest conditional coverage for risk forecasts of SPCLE returns.

Table 4.7 Backtesting measures for daily 1%-VaR forecasts: SPCLE returns
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Tables 4.8 and 4.9 present the estimation results for SUN returns. The Ljung–Box test results indicate the residuals are serially correlated for the AR(1)-E-GARCH(1,1)-N and AR(1)-T-GARCH(1,1)-N models at the 5% level. The PIT test rejects the correct specification of the GAS-t-Id and GAS-AST-InvSq at the 5% level. The AR(1)-CGARCH(1,1)-St and AR(1)-NGARCH(1,1)-t have the lowest AIC and BIC, respectively, for the SUN returns (Table 4.8). In addition, the GAS-AST-Id displays the best AIC and BIC among the GAS models. In line with the results for ECO and SPCLE returns, fat-tailed distributed models for the residuals have an optimal in-sample fit for SPCLE returns. Further, the AR(1)-E-GARCH(1,1)-St displays the lowest out-of-sample RMSE among all models.

Table 4.8 GARCH models for SUN returns
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Table 4.9 GAS models for SUN returns
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Table 4.10 shows the results of backtests for daily 1%-VaR forecasts of SUN returns. Consistent with the backtesting analysis of ECO and SPCLE returns in Tables 4.4 and 4.7, none of the GARCH models with the lowest AIC and BIC is optimal for 1%-VaR forecasts of SUN returns. Nevertheless, the AR(1)-E-GARCH(1,1)-St is one of the optimal models for both out-of-sample forecasts of SUN returns and for 1%-VaR forecasts; it has an AE ratio statistically equal to one and the highest conditional coverage rate. In addition, the AR(1)-APARCH(1,1) and the GAS-t-InvSq have the lowest AD mean and AD max ratios for 1%-VaR forecasts, respectively, among the models with an optimal AE ratio. The GAS-t-Id and the AR(1)-NGARCH(1,1)-N models also have an optimal AE together with good AD mean and CC ratios for 1%-VaR forecasts of SUN returns. In consonance with the findings for ECO and SPCLE returns, all backtesting measures enhance when we employ fat-tailed distributed models for 1%-VaR forecasts of SUN returns.

Table 4.10 Backtesting measures for daily 1%-VaR forecasts: SUN returns
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Tables 4.11 and 4.12 show the estimation results for ERIX returns. Table 4.11 indicates that all GARCH residuals are serially uncorrelated at the 5% level. Conversely, the PIT test rejects the correct specification of the GAS-t-Id and GAS-AST-InvSq at the 5% level. The AR(1)-T-GARCH(1,1)-St and AR(1)-T-GARCH(1,1)-t models present the best AIC and BIC, respectively, for the ERIX returns (Table 4.11). Besides, the GAS-AST1-Id and GAS-St-InvSq attain the minimum AIC and BIC among the GAS models for the ERIX returns. Consistent with the results for the other renewable energy returns, fat-tailed distributed models obtain a better in-sample fit for ERIX returns. Yet, the AR(1)-I-GARCH(1,1)-N attains the lowest out-of-sample RMSE for ERIX returns among all models.

Table 4.11 GARCH models for ERIX returns
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Table 4.12 GAS models for ERIX returns
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Table 4.13 shows the results of backtests for daily 1%-VaR forecasts of ERIX returns. The DQ test rejects the correct specification of almost all models at the 1% significance level. In line with the backtesting results for the other renewable energy returns, none of the GARCH models with the lowest AIC and BIC is optimal for 1%-VaR forecasts of ERIX returns. The GAS-N-Id is the optimal model for 1%-VaR forecasts of ERIX returns since it attains the lowest AD mean and AD max ratios together with the highest p-values of the CC and DQ tests. The AR(1)-E-GARCH(1,1)-N and AR(1)-GARCH(1,1)-N also have a similar out-of-sample performance for risk forecasts. However, these models exhibit an AE ratio far from the unity, indicating an excessive number of actual 1%-VaR exceedances over expected ones. Therefore, normally distributed GAS and GARCH models have good performance for 1%-VaR forecasts of ERIX returns, in contrast to our findings for the other renewable energy returns.

Table 4.13 Backtesting measures for daily 1%-VaR forecasts: ERIX returns
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In sum, heavy-tailed distributed GARCH and GAS models have the best in-sample fit for all renewable energy returns. They also exhibit the best out-of-sample forecast performance and the best coverage for 1%-VaR of renewable energy returns. These findings highlight the relevance of modeling the kurtosis for renewable energy returns. For instance, the GAS-t-Id, AR(1)-CGARCH(1,1)-t, and AR(1)-E-GARCH(1,1)-St have the lowest out-of-sample RMSE for ECO, SPCLE, and both SUN and ERIX returns, respectively. In addition, the AR(1)-NGARCH(1,1)-St, AR(1)-APARCH(1,1)-St, AR(1)-E-GARCH(1,1)-St, and GAS-N-Id models are optimal models for 1%-VaR of renewable energy returns. Therefore, fat-tailed GARCH and GAS enhance both in-sample and out-of-sample performance of renewable energy returns and risk. These findings are important for policymakers and investors who invest in the renewable energy sector.

4.4 Conclusions

Clean energy indices, such as wind and solar energy, are sold in financial markets that share the same dynamics of highly volatile assets. Clean energy returns may also exhibit heavy-tailed distributions since financial returns follow fat-tailed distributions (Gabaix 2009). It is important to model the volatility of renewable energy returns for investors since it affects the performance of their portfolios on renewable energy. In this chapter, we search for optimal models for clean energy returns using 37 flexible and fat-tailed GAS and GARCH models. Besides, we compare the out-of-sample performance of all models to find the optimal forecast model for clean energy returns. We also conduct several backtesting approaches for daily 1%-Value-at-Risk (VaR) forecasts of clean energy returns.

Fat-tailed distributed GARCH and GAS models have the best in-sample fit for all renewable energy returns. They also exhibit the best out-of-sample forecast performance and the best coverage for 1%-VaR of renewable energy returns. For instance, the GAS-t-Id, AR(1)-CGARCH(1,1)-t, AR(1)-E-GARCH(1,1)-St have the lowest out-of-sample RMSE for ECO, SPCLE, and both SUN and ERIX returns, respectively. In addition, the AR(1)-NGARCH(1,1)-St, AR(1)-APARCH(1,1)-St, AR(1)-E-GARCH(1,1)-St, and GAS-N-Id models are optimal models for 1%-VaR of renewable energy returns. These findings illustrate the relevance of modeling the kurtosis for renewable energy returns, which are relevant for policymakers and investors who invest in the renewable energy sector.