EVIDENCE ON PRICE FORMATION IN FINANCIAL MARKETS: A MULTITEMPORAL ANALYSIS

Background: Although clean energy stocks have become a popular new asset class for market players, relatively little research has been done on risk management strategies for investors in clean energy stock markets. Gold and Silver are examples of precious metals typically considered suitable investments to hedge against uncertainty. Therefore, their demand tends to rise when stock markets decline. Purpose: The study aims to analyse the influence of precious metals (Gold, Silver and Platinum) and green stock indices (Clean Energy Fuels, Nasdaq Clean Edge Green Energy, S&P Global Clean Energy, WilderHill Clean Energy) on price formation during different economic periods between 1 January 2018 and 23 November 2023. Methods: The periods analysed were Tranquil, 2020 pandemic, pre-conflict and Conflict (Russian invasion of Ukraine). To this end, a VAR Granger Causality/Block Exogeneity Wald model was estimated to identify different influence patterns during each period. Results: During the Tranquil period, 15 movements affecting prices were observed, with Silver significantly influencing all its peers, while Gold impacted Platinum, S&P Global, Nasdaq and WilderHill. Platinum was the asset that received the most shocks from its peers. During the 2020 pandemic, there was an increase to 26 movements, with the S&P Global and Nasdaq Clean indices influencing most of their peers. Gold and Platinum continued to be the assets most influenced by their peers. In the pre-conflict period, 11 movements were identified, with the highlight being the mutual influence between Gold, the Nasdaq and WilderHill indices, and Platinum. During this period, Silver and S&P Global only affected the price formation of Platinum and Clean Energy Fuels, respectively. During the Conflict period, 18 movements were observed, highlighting the influence of Platinum and S&P Global on the price formation of various assets. Gold was the asset that received the most shocks from its peers during this period. Conclusion: the results indicate changes in the interactions between assets throughout the different economic contexts, highlighting the importance of understanding these dynamics to make more informed decisions.


INTRODUCTION
Over the last two hundred years, polluting energy resources such as coal, oil and gas have played a key role in economic advancement and industrialisation.However, it has also been responsible for contributing significantly to environmental problems such as climate change, giving rise to growing concern about the viability of this model.Growing global attention to reducing carbon emissions and transitioning to clean energy sources has resulted in substantial investments in renewable technologies such as solar, wind, hydroelectric and geothermal energy.As a result, clean energy has become a crucial sector driving economic growth.To efficiently observe the progress of the clean energy industry, the WilderHill Clean Energy Index was created in 2004.In practical terms, this index tracks the performance of publicly traded companies involved in the study and production of clean technologies such as solar panels, wind turbines and biofuels and is recognised as the sector's leading benchmark and an indispensable tool for investors interested in this booming market (Dias, Horta, et al., 2023;Dias, Teixeira, et al., 2023).
The clean energy sector is currently one of the fastest-growing segments of the energy industry.Recent statistics reveal that between 2009 and 2019, the clean energy sector experienced an annual growth rate of 5 per cent, compared to dirty energy's annual growth rate of 1.7 per cent.As a result, a significant amount of capital is being redirected from conventional energy sources to clean energy.For example, global investments in the clean energy sector grew from $120.1 billion to $363.3 billion between 2009 and 2019.Even during the Covid-19 pandemic, investments in clean energy increased by 2 per cent.This has increased interest among market participants in clean energy stocks (Bloomberg New Energy Finance, 2019).
The emergence of clean energy stocks as a new asset class has attracted considerable attention from investors, professionals and academics.On the other hand, investments in 4 renewable sector stocks are not without risk, which suggests the need to consider suitable hedging assets to eliminate risk.Given that precious metals, notably Gold, are used as effective hedges against adverse movements in international stock market returns, one might wonder about the relationship between clean energy stock indices and precious metals, especially from the perspective of hedging and risk management (Elie et al., 2019).
Portfolio rebalancing in the capital markets is a process of adjusting the asset allocation in a portfolio to align it with the investor's investment targets and risk tolerance.This process is especially important during periods of uncertainty in the global economy, as it helps investors manage risk and maintain a desired level of portfolio diversification.Rebalancing can involve selling assets that have appreciated their value and reallocating the proceeds to underperforming assets to align the portfolio with its target allocation.Doing so helps reduce the risk of the portfolio becoming too heavily weighted in a particular asset class, sector or geographical region (Dias, Chambino et al., 2023;Dias, Chambino et al., 2023).
This study contributes to the body of literature in several ways.Firstly, although clean energy stocks have emerged as a new asset class for market participants, especially for environmentally concerned investors, existing studies pay very little attention to how investors in clean energy stock markets can reduce their risk.Precious metals, such as Gold and Silver, are traditionally considered hedging assets in times of uncertainty.Their demand tends to increase when stock markets fall, offering investors protection.
Based on the literature studied, precious metals can be effective in mitigating the risks of different asset classes, including stocks (Dias and Carvalho, 2020;Dias et al., 2021;Dias and Carvalho, 2021;Teixeira et al., 2022).However, the research on how Gold, Silver and Platinum can be considered hedging assets against green energy indices still lacks robust evidence.
Secondly, this is also the first study to document the impact of the 2020 and 2022 events on the structural dynamics and correlations between precious metals and clean energy.Thirdly, the study follows a time-frequency perspective to investigate the interconnections between precious metals, given that the sample will be subdivided into four sub-periods: the Tranquil This paper is divided into section 2 for the literature review with different sub-sections.
Section 3 provides the data and methodology.The empirical results are discussed in section 4, and section 5 covers the conclusion and the main practical implications.

LITERATURE REVIEW
In recent decades, the transition to a carbon-resilient economy has become a topic of great interest within academia, companies, investors and financial institutions.This transition involves moving from traditional carbon-intensive forms of energy, such as coal and oil, towards cleaner and more sustainable energy sources, such as solar and wind power.The Paris Climate Agreement, signed in 2015, has been one of the main drivers of this transition, as it set a target to limit global warming to less than 2 degrees Celsius above pre-industrial levels to limit global warming to 1.5 degrees Celsius.This aim cannot be achieved without significant reductions in greenhouse gas emissions, mainly from the energy sector.
The United Nations Climate Change Conference (COP26), held in November 2021, was critical in the global effort to deal with climate change.One of the main challenges in this transition is balancing the immediate economic benefits of traditional energy sources with the long-term environmental costs.Many companies and investors are now recognising the potential risks of investing in carbon-intensive industries, as the costs of carbon emissions are likely to rise over time, making these investments less attractive.At the same time, the transition to clean energy presents significant opportunities for companies and investors, particularly in areas such as renewable energy, energy efficiency and low-carbon transport (Ettinger et al., 2023;Tzeremes et al., 2023;van Asselt & Green, 2023).

RELATED STUDIES ABOUT HEDGING ASSETS
The growing interest and investment in the clean energy sector reflects global awareness of climate change and the pressing need to adopt more sustainable practices for the planet's future.As a result, the clean energy stock market has witnessed a significant increase, accompanied by considerable volatility and several associated risks.In this context, hedging assets have emerged as essential tools for investors looking to mitigate the risks associated with investing in clean energy stock indices.Among the most common hedging assets are precious metals, namely Gold.When used strategically, these assets not only reduce the risks associated with investments in clean energy but also provide increased levels of security in the context of strategic portfolio diversification management ( Chen and Wang, 2017;Bulut and Rizvanoghlu, 2020;Caporale and Gil-Alana, 2022;Kakinuma, 2022).Jin et al. (2019) examined three commonly used hedging assets: Bitcoin, Gold and crude oil.The results indicate that the dynamic correlations between the gold and crude oil markets In 2022, the authors Gustafsson et al. (2022) and Erdoğan et al. (2022) studied the relationship between clean energy stock indices and energy metals that are sensitive to the growth in demand for clean energy solutions and make inferences about whether energy metals can act as hedges or safe havens for clean energy stock indices.Gustafsson et al. (2022) show statistically significant non-linear relationships between the markets studied.All energy metals, except cobalt, have a significant positive link with clean energy stock indices, and these associations are maintained during episodes of high volatility.Although none of the energy metals under study acts as a hedge for clean energy stock markets, the results support previous evidence on the hedging properties of precious metals, showing that Gold and Silver serve as hedges for certain clean energy stock indices.Complementary Erdoğan et al. (2022) show that there is a unidirectional causal link from clean energy stock returns to precious metal prices in the centre and left tail of the distribution.On the other hand, there is strong feedback between the variables in the right tail of the distribution.These results show that clean energy stock prices have an advantage in affecting precious metal prices and precious metals cannot be used as hedging assets for investments in clean energy stocks.
More recently, authors Dias, Chambino, et al. (2023) investigated the relationship between energy and precious metals to assess their suitability as safe-haven assets in clean energy investment portfolios during the 2020 and 2022 events.The authors showed a positive association between energy metals (excluding nickel futures) and clean energy indices, suggesting their potential as safe-haven investments for green investors diversifying their portfolios.Furthermore, the study confirms the reliability of precious metals such as Gold, Silver and Platinum as safe havens for clean energy stock indices.Moreover, Dias, Horta, et al. (2023) examined the co-movements between the capital markets of the Netherlands (AEX), France (CAC 40), Germany (DAX 30), the United Kingdom (FTSE 100), Italy (FTSE MIB), Spain (IBEX 35), Russia (IMOEX) and the spot prices of crude oil (WTI), Silver (XAG), Gold (XAU) and Platinum (XPT).The authors demonstrated a significant increase in the number of causal relationships between the market pairs analysed (62 causal relationships out of 110 possibilities), including a relative increase in the influence of commodities on capital markets and capital markets on commodities.These conclusions show that during the events of 2020 and 2022, the capital and commodity markets significantly accentuated their co-movements with each other, indicating that alternative markets such as WTI, XAG, XAU and XPT do not have the attributes of a safe haven for the capital markets in question.In line with this, the authors Dias, Alexandre, et al. (2023b) examined whether cryptocurrencies could be considered a safe haven for investments in sustainable energy indices during the events of 2020 and 2022.
The empirical findings show that clean energy stock indices can offer a viable safe harbour for cryptocurrencies classified as "dirty" due to their excessive energy consumption.However, the precise associations differ depending on the cryptocurrencies analysed.
The recent events of 2020 and 2022 have highlighted the importance of studying the interconnections between clean energy stock indices and hedging assets in order to improve the performance of sustainable energy portfolios and risk mitigation in the face of the recent events, thus strengthening the resilience of investments in a context of climate change and disruptive events.

Countries and their indices
Source: Own elaboration.

METHODOLOGY
This section describes the methodology and the tests used to answer the research question.In the first stage, the sample was characterised by applying a set of descriptive statistical methods.Furthermore, the Jarque and Bera (1980) adherence test was applied to analyse the data distribution of the seven time series and test the assumption of normality, and the quantile graphs were analysed to check the residuals of the time series.In the second stage, the panel unit root tests of Breitung (2000), Levin, Lin, and Chu (2002), and Im et al. (2003) were employed to validate the stationarity of the time series.The Dickey and Fuller (1981) and Phillips and Perron (1988) tests, with Fisher's transformation, were used to validate the results and also the quantile graphs.The Clemente et al. (1998) model will be used to identify the breaks in the structure.The research question, i.e. the existence of movements between precious metals and clean energy indices, will be answered using the Granger causality model (Engle and Granger, 1987;Granger, 1969Granger, , 1981)).The concept of Granger relates to the idea of temporal precedence between variables, that is, considering two variables X t e Y t , and it is said that X t causes Y t , in the Granger sense, if the historical values of X t help predict the future values of Y t .The Granger test allows validation of whether this predictive capacity of the values of X t relative to Y t is statistically significant, defending as a null hypothesis that the exogenous coefficients lagging behind the causality variable are null and therefore do not cause the dependent variable in the Grangerian sense and the alternative hypothesis postulates the existence of causality (Granger, 1969;Sims, 1980).
The VAR Granger Causality or Block Exogenety Wald Test model will be used to analyse the causal relationship between the financial markets in question.It uses the Wald statistic to assess whether the independent (or exogenous) variables contain information that helps explain the dependent variable's behaviour.9 The model can be expressed as follows: Where: is a vector of endogenous variables ( × 1),   a vector of exogenous variables ( × 1),  1   , represent the matrices of lag coefficients to be estimated, and  corresponds to a matrix of coefficients of exogenous variables.  denotes a white noise process, commonly referred to as innovations or shock term, with normal distribution and zero mean.
That said, according to Parzen (1982), statistical modelling proposes methods that are often applied automatically without adjustment.However, an important aspect to consider when estimating a robust autoregressive model is the specification of the number of lags considered in the model.Lütkepohl (1993)  Graphical observation shows that the average returns appear relatively stable, oscillating close to zero.However, a closer look at the data reveals substantial fluctuations, emphasising the pronounced volatility experienced by these markets.This volatility is particularly evident during the first few months of 2020, coinciding with the beginning of the impact of the COVID-19 pandemic on the global economy.

Figure 1
Evolution, in returns, of the clean energy and precious metals stock indices from 1 January 2018 to 23 November 2023. -.5

DIAGNOSTIC
Table 3 shows the summary table of the stationarity tests applied to the time series for the clean energy and precious metals stock indices from 1 January 2018 to 23 November 2023.Breitung (2000), Levin et al. (2002), Im et al. (2003) tests were applied to confirm stationarity and the Dickey and Fuller (1981) and Perron and Phillips (1988) with Fisher Chi-square transformation and Choi (2001) tests were used to validate the results.Stationarity was obtained by performing the logarithmic transformation in first differences to smooth the time series so that the characteristics of white noise could be achieved (mean 0; constant variance), thus validating the assumption of stationarity by rejecting it at a significance level of 1%.

METHODOLOGICAL RESULTS
Table 4 shows the results of the VAR Global only influences the determination of Platinum prices without having any predictive power over the other markets.Clean Energy Fuels does not influence its peers, while Platinum is the market that receives the most shocks from its peers (5 out of a possible 6).These results highlight the complexity of the interactions between the different assets within the clean energy markets and regarding precious metals.Platinum.The results reveal the presence of 18 movements (out of a total of 42 possible) that impact price formation, while in the Pre-conflict sub-period, there were only 11 movements.
The precious metal Platinum influences the price formation of Silver, S&P Global, Nasdaq and Clean Energy Fuels, while the S&P Global index affects the price formation of Gold, Platinum, Nasdaq and WilderHill and does not affect the prices of the other markets.The Clean Energy index influences the price formation of Gold, Silver, Nasdaq and WilderHill, while Nasdaq Clean affects the price formation of Gold, Platinum and WilderHill and has no influence on the prices of the other markets.To a lesser extent, the WilderHill Clean Energy index only affects Gold prices, while the Gold market does not influence the price formation of any markets analysed.In addition, Gold is the asset that receives the most shocks from its peers (4 out of a possible 6).

period from 1
January 2018 to 31 December 2019; the Covid-19 global pandemic period from 1 January 2020 to 31 December 2020; the pre-conflict period from 1 January 2021 to 23 February 2022; and lastly, the war between Russia and Ukraine, which covers the years from 24 February 2022 to 23 November 2023.
Evidence on Price Formation In Financial Markets: A Multitemporal Analysis ___________________________________________________________________________ Rev. Gest.Soc.Ambient.| Miami | v.18.n.9 | p.1-23 | e06304 | 2024.6 are almost positive, while between Bitcoin and Gold, they are almost negative, thus showing the properties of hedging assets.
BenMabrouk et al. (2024) examined the effectiveness of hedging assets between five main segments of Non-Fungible Tokens (NFTs): namely Collectibles, Art, Games, Metaverse and Utility, and other asset classes, namely Bitcoin and US stocks (S&P500).The authors show weak dynamics between NFTs and other assets, indicating that these new digital assets are still relatively decoupled from traditional assets and Bitcoin.3MATERIALS AND METHODS3.1 DATA The data used in the research are the daily index prices of Gold (Gold, Handy & Harman), Silver (Silver, Handy & Harman) and Platinum (London Platinum), as well as sustainable energy stock indices such as Clean Energy Fuels, S&P Global Clean Energy, Wilderhill Clean Energy, and NASDAQ Clean Edge Green Energy, from 1 January 2018 to 23 November 2023.The sample was analysed in four sub-periods to add robustness to the study: the first comprises the years from January 2018 to 31 December 2019, referred to as Tranquil; the second includes the first wave of the Covid-19 pandemic, and comprises the months from 1 January 2020 to 31 December 2020; the third sub-period covers the years from 1 January 2021 to 23 February 2022, referred to as Pre-Conflict; the fourth and final sub-period covers the period from 24 February 2022 to 23 November 2023, referred to as Conflict.The data was obtained through the Thomson Reuters Eikon platform and is represented in local currency to offset exchange rate distortions and possibly bias results.
Figure 1 shows the daily return trends of Gold (Gold, Handy & Harman), Silver (Silver, Handy & Harman) and Platinum (London Platinum), as well as sustainable energy stock indices such as Clean Energy Fuels, S&P Global Clean Energy, Wilderhill Clean Energy, and NASDAQ Clean Edge Green Energy, over the period from 1 January 2018 to 23 November 2023.

Figure 2
Figure2shows the quantile graphs for the gold(Gold, Handy & Harman), silver (Silver, Handy & Harman) and platinum (London Platinum) price indices, as well as for sustainable energy stock indices such as Clean Energy Fuels, S&P Global Clean Energy, Wilderhill Clean Energy and NASDAQ Clean Edge Green Energy, for the period from 1 January 2018 to 23 November 2023.Through the graphical observation of quantiles illustrated in Figure3, it is also possible to infer the normality of the time series data analysed.The normal distribution line is in orange, and the data distribution for each time series is in blue.Comparing the dispersion of the time series data with the normal distribution line reveals that none of the series completely overlap, with a certain amount of asymmetry.

Figure 2
Figure 2 Quantile graphs of returns for the clean energy and precious metals stock indices from 1 January 2018 to 23 November 2023.

Figure 3
Figure 3 shows the summary table of the unit root test with structural breaks of Clemente et al. (1998) applied to the returns of Gold (Gold, Handy & Harman), Silver (Silver, Handy & Harman) and Platinum (London Platinum), as well as sustainable energy stock indices such as Clean Energy Fuels, S&P Global Clean Energy, Wilderhill Clean Energy, and NASDAQ Clean Edge Green Energy, for the period from 1 January 2018 to 23 November 2023.Based on the results, we see that the most significant falls in precious metals and the main clean energy stock index occurred in 2020, as follows: Gold (24/03/2020), Platinum (16/03/2020), Silver (16/03/2020), Wilderhill Clean Energy (24/03/2020).On the other hand, the other green energy indices show their most significant structure breaks in 2021, for example, S&P Global Clean Energy (07/01/2021), NASDAQ Clean Edge Green Energy (07/01/2021), Clean Energy Fuels (08/02/2021).

Figure 3
Figure 3 Clemente's unit root test with structural breaks on returns applied to the time series for the clean energy and precious metals stock indices from 1 January 2018 to 23 November 2023.
Energy and the precious metals stock indices, Gold, Handy & Harman, Silver, Handy & Harman and London Platinum.The results show that 26 movements (out of a possible 42) affect price determination in the markets studied.When examining the results, the S&P Global and Nasdaq Clean indices (5 out of 6 possible) influence the price determination of all their peers, except for the WilderHill Clean Energy index.Similarly, Platinum influences the pricing of Silver, S&P Global, Nasdaq and WilderHill without impacting the other markets.Clean Energy Fuels only influence the prices of Gold, Platinum, S&P Global and Nasdaq.On the other hand, Silver influences the Gold market, Platinum and the Nasdaq index, while WilderHill influences Gold, Platinum and the Clean Energy index without influencing the other markets.Gold influences the price formation of the Nasdaq and WilderHill stock indices, but the shocks to the other markets are not significant.It can be seen that during this period of stress in global markets, Gold and Platinum are the assets that receive the most shocks from their peers (5 out of a possible 6).
Gold, Handy & Harman, Silver, Handy & Harman and London Platinum.The study reveals the presence of 11 movements (out of a possible 42) that influence price formation.Based on the results, Gold and the Nasdaq and WilderHill indices (2 out of 6 possible) have an equal influence on the precious metal Platinum and the Clean Energy index and no influence on the other markets.Platinum influences the S&P Global indices, and Clean EnergyFuels is not significant for the other markets analysed.To a lesser extent, Silver and Clean Energy only influence the price formation of the precise metal Platinum, while the S&P Global index only affects the price formation of Clean Energy Fuels.

Table 2
shows the main descriptive statistics for Gold (Gold, Handy & Harman), Silver (Silver, Handy & Harman) and Platinum (London Platinum), as well as for sustainable energy stock indices such as Clean Energy Fuels, S&P Global Clean Energy, Wilderhill Clean Energy, Evidence on Price Formation In Financial Markets: A Multitemporal Analysis ___________________________________________________________________________ Rev. Gest.Soc.Ambient.| Miami | v.18.n.9 | p.1-23 | e06304 | 2024.11 and NASDAQ Clean Edge Green Energy, for the period from 1 January 2018 to 23 November 2023.Based on the results, it is possible to see that the mean returns are positive, with the exception being the Platinum market (-2.10e-06).The Clean Energy Fuels index (0.0478) has the highest standard deviation, showing that it is the index with the highest levels of volatility.

Table 2
Summary table of statistics for the clean energy and precious metals stock indices from 1January 2018 to23 November 2023.

Table 3
Summary table of the stationarity tests applied to the time series for the clean energy andprecious metals stock indices from 1 January 2018 to23 November 2023.

* Probabilities for Fisher tests are computed using an asymptotic Chi-square distribution. All other tests assume asymptotic normality.
Source: Own elaboration.
Granger Causality/Block Exogeneity Wald test during the Quiet period, relating to the clean energy stock indices Clean Energy Fuels, Nasdaq Clean Edge Green Energy, S&P Global Clean Energy, WilderHill Clean Energy, and the precious metals Gold, Handy & Harman, Silver, Handy & Harman and London Platinum.The results indicate that 15 movements (out of 42) affect price determination.When examining the results, it was found that Silver influences the price determination of all its peers except Clean Energy Fuels.Meanwhile, Gold influences Platinum, S&P Global, Nasdaq and WilderHill but has no impact on Silver and Clean Energy Fuels.WilderHill Clean Energy influences the pricing of Platinum, S&P Global and Nasdaq but does not affect the other markets.Meanwhile, Nasdaq Clean only influences Platinum and WilderHill.To a lesser extent, Platinum only influences the Nasdaq Clean without affecting the other markets.Similarly, S&P

Table 4
Granger causality/Block Exogeneity Wald Tests of the financial markets analysed during the Note: The markets in the column cause the markets in the row.The value in brackets corresponds to the level of lags (in days).The asterisks ***, **, * represent the significance level at 1%, 5% and 10% respectively.Source: Own elaboration.

Table 6
provides the results of the VAR Granger Causality/Block Exogeneity Wald test for the pre-conflict period, focussing on stock indices related to sustainable energy, such as Clean Energy Fuels, Nasdaq Clean Edge Green Energy, S&P Global Clean Energy, WilderHill Clean Energy, and the precious metals

Table 7
shows the results of the VAR Granger Causality/Block Exogeneity Wald test for the Conflict period, focusing on stock indices related to sustainable energy, such as Clean Energy Fuels, Nasdaq Clean Edge Green Energy, S&P Global Clean Energy, WilderHill Clean Energy, and the precious metals Gold, Handy & Harman, Silver, Handy & Harman and London