Shock and Volatility Transmissions Across Global Commodity and Stock Markets Spillovers: Empirical Evidence from Africa

Abstract

This paper investigates the link between commodity price volatility and stock market indices in Nigeria, Ghana, and Côte d’Ivoire, focusing on commodities such as oil, cocoa, and gold over a daily period from 2 January 2020 to 31 December 2021. In order to conduct this study, the BEKK-GARCH process is applied to test the volatility transmission across commodity and stock markets, while focusing on the asymmetry in the conditional variances of these markets. The analysis reveals a 30% increase in volatility spillovers during the COVID-19 period, highlighting significant asymmetry in conditional variances between African stock markets and global commodity markets. Furthermore, the findings demonstrate that conditional variances in stock and commodity markets are asymmetrical. This study advances the literature on volatility transmission by providing novel evidence on asymmetric spillovers between African stock markets and global commodity prices, particularly during COVID-19. It offers insights into the unique role of emerging African markets in global financial interconnectedness.

1. Introduction

With the growing trend of financial globalization, the interrelationships between dynamic returns and the transmission of volatility between capital markets and commodity markets have become more interesting and have generated increased interest in the financial community. The distribution of returns and volatility across markets causes stock adjustments for policymakers. This adjustment aims primarily at preventing the risk of contagion in the event of a crisis (Arouri et al., 2011). The interconnectedness of stock market returns and commodity price movements was strongly analysed, especially after the 2008 global financial crisis.

Volatility transmission is a concept that can be described as the mechanism by which variation or shocks in one market make a particular impact on the volatility of another market (Yang et al., 2022). It is most applicable in the stock and commodity markets because these two are closely related. These commodities can cause inflation or deflation. This affects trade balances, GDP, and stock returns.

Several econometric models have been employed in the analysis of volatility transmission in the literature. Foremost among these is the Baba Engle Kraft Kroner General Autoregressive Conditional Heteroskedasticity (BEKK-GARCH) model (Engle & Kroner, 1995). This model enables forecasting the time-varying conditional covariance and understanding how shocks pass through the markets. Thus, the BEKK-GARCH models are more appropriate for the cross-market analysis, as they are multivariate models, unlike univariate GARCH, which works with single time series (Özdemir & Bilgiç, 2023).

This line of research has developed in light of both large-scale financial crises and changes in the world economy. In analysing volatility transmission, earlier research concentrated more on developed economies, particularly the USA and Europe. However, the rising importance of emerging markets has led to a growing interest in knowledge of how volatility spreads in less developed financial systems (Spulbar et al., 2020). In particular, African markets are quite unique due to their connection with commodity export and their sensitivity to world fluctuations. These markets are generally associated with lower levels of turnover, higher transaction costs, and broader exposure to world prices for commodities. These conditions provide a preferred terrain for volatility transmission research.

In Africa, the inter-channels of volatility between stock and commodity markets play several roles. First, a considerable number of African countries are indebted due to the exportation of a few limited products, for instance, oil, cocoa, and gold among others. Consequently, changes in global commodity prices have direct effects on the revenue balances of these economies (Majumder et al., 2022). Second, the African stock markets tend to be less developed and, therefore, more illiquid and more susceptible to shocks than developed markets. Third, the integration of African markets with global financial markets, driven by the opening of cross-border flows and increased capital movement, has made these markets more vulnerable and more likely to transmit volatility from global markets (Logogye et al., 2024).

Over the last decade, the instabilities of financial markets have been manifested most evidently through global shocks like the COVID-19 pandemic, particularly in emerging and frontier markets (Canuto, 2023). COVID-19 introduced unprecedented levels of market unpredictability, disrupting both commodity prices and stock exchange performance. This context has led to a renewed focus on analysis of the relationship between time-varying volatility of global commodities prices and the African stock markets (Tiwari et al., 2022). To this end, learners have wondered how the pandemic affected volatility connections and whether earlier models can still serve as a means of identifying such changes.

This study contributes to the emerging empirical research work on the dynamic relationship between key financial and commodity markets, especially in the post-COVID-19 period. By applying the asymmetric BEKK-GARCH models, we provide a deeper examination of the degree of the spillover and other time-varying effects across the African selected countries’ equity markets, commodity markets, and international oil markets. We investigate the extent to which the commodity market can provide diversification benefits for investors holding positions in equity and oil markets. We report significant unidirectional return and volatility spillover effects from both the stock market and international oil market to the African commodity markets, providing important practical implications for investors and regulators. It would be beneficial to expand this issue into the African context while adding basic commodities other than oil, such as gold and cocoa, since the empirical results may provide information for the creation of precise models for asset valuation and volatility forecasts between these markets. The focus is also placed on the direction of volatility transmission studied.

To this end, the study seeks to answer key research questions, including whether COVID-19 has impacted volatility spillovers and whether the impact is symmetrical or not across the African stock and global commodity markets. All these factors are relevant in explaining the effects of volatility arising from the pandemic on the African financial system’s stability.

The rest of the paper on our investigation is structured as follows: The relevant literature is included in the next section. In Section 3, econometric methods are presented in order to describe the research plan. The data utilized for the preliminary study are presented in Section 4, and the findings are discussed in Section 5. The conclusion and policy implications are covered in Section 6. Section 7 presents the limitations and scope.

2. Literature Review

2.1. Theoretical Underpinning

The question of volatility transmission between two types of markets has been extensively studied in the literature, with reference only to oil to analyze co-movements between oil and stock markets. Malik and Ewing (2009) analyzed the transmission of volatility and shocks between oil and equity returns in five major market sectors using a bivariate GARCH. The results show evidence of the transmission of shocks and volatility between oil prices and certain market sectors. Choi and Hammoudeh (2010) used data for the period between 1990 and 2006 to focus on the volatility behavior of oil and industrial commodities markets with the stock market. Their results show high and low volatility patterns between the five commodity prices and the S&P 500. For dynamic conditional correlations (DCC; Engle, 2002), the GARCH model shows increasing correlations between all commodities since the 2003 Iraq war and decreasing correlations with the US stock index, the S&P 500.

2.2. Empirical Literature

Using the generalized vector autoregressive (VAR) GARCH approach, Arouri et al. (2011) examined the transmission of yield and volatility between world oil prices and stock markets in the Gulf Cooperation Council (GCC) member countries during the 2005–2010 period. Their results indicate significant volatility spillovers between oil and stock markets in three GCC countries (Bahrain, Oman, and Qatar). The effect of oil was positive on the stock markets of Qatar and Oman but negative on the Bahrain stock market. As for the transmission of volatility, it is more apparent from oil to stock markets. The modelling of DCC-GARCH on a set of 25 commodities from different sectors over a period spanning from 3 January 2001 to 28 November 2011 enabled Creti et al. (2013) to demonstrate that the correlations between stock markets and commodity markets are highly volatile.

Using an event research methodology and the GARCH model, the study by Endri et al. (2021) investigated how stock prices on the Indonesia Stock Exchange (IDX) responded to COVID-19. The Composite Stock Price Index (JCI) closing price and companies that were part of LQ-45 throughout the 40 days before the COVID-19 incident, one day during the COVID-19 incident (2 March 2020), and the 10 days following, from 6 January 2020 to 16 March 2020, comprised the research sample. The GARCH (1,2) model may be used to evaluate volatility and forecast abnormal stock returns in IDX in market conditions affected by COVID-19. Empirical data demonstrate that abnormal returns reacted negatively to COVID-19 and that JCI volatility swung substantially throughout the COVID-19 event. This study’s conclusions have real-world implications for investors since stock market volatility brought on by the COVID-19 pandemic influenced anomalous returns. As a result, maintaining a stock portfolio requires multiple lines of risk management in order to deal with future conditions of uncertainty and greater volatility. Furthermore, it creates chances for speculators to make money in an inefficient market. The empirical literature that is presently being generated to examine the phenomena of stock price volatility behavior during COVID-19 on the IDX serves as the foundation for this investigation. The GARCH model demonstrates that stock market volatility rose and abnormal returns fell during the COVID-19 epidemic. The empirical results also support the idea of financial behavior associated with uncertainty and the efficient market hypothesis theory related to event analysis.

Mensi et al. (2013) used a VAR-GARCH model applied to daily data from 3 January 2000 to 31 January 2011 on certain commodity markets and stock markets. They demonstrated the significant correlation and transmission of volatility between commodity and equity markets. Ghorbel and Boujelbene (2013) applied the multivariate GARCH models (BEKK and DCC) to monthly data between May 2005 and December 2011 for the oil prices and stock indices of the US, GCC countries, and Brazil, Russia, India, and China (BRIC). Their results showed a persistent level of volatility in the relevant crude oil and stock markets.

Using a trivariate GARCH model with BEKK parameterization, Lajili (2013) showed that the US financial market has an impact on the oil market and other financial markets in oil-producing countries (Russia, Kuwait, Indonesia, and Venezuela). He also found a transmission of oil market volatility to all financial markets in producer countries. His study also showed the existence of a strict relationship between physical markets and financial markets. The results of this study could be an interesting basis for building a pricing model of financial assets in producer countries, allowing for the prediction of oil price and volatility. In the same context, by applying a VAR-GARCH model to the data of the Kingdom of Saudi Arabia and Egypt from 1 January 2007 to 31 December 2011, Suliman and Idris (2013) were able to show that changes in the price of oil led to an increase in the volatility of stock market returns.

Cheng and Xiong (2014) argued that the massive abundance of investment capital in commodity futures markets over the past decade sparked a debate about whether financialization is distorting commodity prices. They critically examined academic studies from the perspective of how financial investors affect risk sharing and discovery of information on commodity markets and concluded that through these mechanisms, financialization has significantly changed commodity markets. Bunnag (2015) used three multivariate models, in this case, the vector error correction higher order (VECH; Bollerslev et al., 1988), BEKK, and constant conditional correlations (CCC; Bollerslev, 1990) models applied to daily data during the 2009–2014 period, to conclude that the volatility of oil futures affects the volatility of carbon emissions futures. It also showed that the BEKK model is more reliable for examining the volatility of oil futures and the volatility of carbon futures yields. Basak and Pavlova (2016) analyzed how financialization affects commodity futures prices, volatility, and correlation. They demonstrated that financial markets pass on shocks not only to forward prices but also to spot commodity prices and stocks. Spot prices rise with financialization and shocks on any commodity index thus affecting all stock market commodity prices.

In order to evaluate the impact of various investor groups (fund managers and index investors) as well as the fundamental and macroeconomic factors on the prices of coffee, cotton, wheat, and oil, Ederer et al. (2016) developed a VAR model. They discovered that in contrast to index investors, fund managers’ net long holdings have a big impact on commodity prices, which can cause the markets for commodity derivatives to stop playing their essential role in growth. Tsuji (2018) examined the best ways to hedge oil futures and oil stocks in oil-producing nations, as well as the transmission of returns and volatility spillovers. He discovered a unidirectional transmission of returns between oil futures and oil stocks when he applied the DCC matrix exponential (MEGARCH) model on the daily prices of oil and gas indices for the US, Russia, Australia, and Canada between January 2000 and 15 August 2017. Additionally, its findings show one-way spillovers for the US and Canada and two-sided asymmetric volatility spillovers for Australia and Russia between oil futures and oil stocks.

Youcef (2019) used the threshold quantile auto-regressive (TQAR) model, which has shown the existence of strengthening links between equity markets and agricultural products market since 2004, which corresponds to the increase in institutional investment flows on the commodity markets. These results suggest that agents have a profound effect on commodity prices when the value of the commodity index is high. Additionally, when the commodities index’s return is in the higher regime, there is always a considerable correlation between agricultural and stock market returns. This implies that the dynamics of agricultural commodity prices are significantly influenced by stock markets. From the standpoint of market integration, Baochen et al. (2020) investigated the financialization of the Chinese market. Using multivariate GARCH models, they examined the integration of commodity markets with financial capital markets, including stock, bond, and foreign exchange markets. As a result, there is a financialization phenomenon in the Chinese commodities futures market, particularly in the energy futures market.

Applying a tri varied BEKK GARCH to daily data from 2 July 2012 to 2017, Ahmed and Huo (2021) found a significant one-way effect of oil yield to Chinese stock market yield, suggesting a strong reliance on the Chinese stock market in the oil market. Hung and Vo (2021) examined the directional effects and time frequency relationship between oil and gold markets and equity markets over the period before and during the COVID-19 pandemic. They concluded that before the COVID-19 period, the S&P 500 and oil series were the net risk receivers, while gold was a net shock emitter. In contrast, during the pandemic, crude oil and S&P 500 markets are the transmitters of yield fallout up to a maximum level of about 32%, so the gold market is a destination of the fallout. Although research on the aforementioned links is well established, it has not demonstrated how the pandemic influenced the financial and commodity markets of African nations to become more interconnected with the global financial market. Furthermore, it is still unknown how the global pandemic influences the dependency and connectivity between the global commodity markets and the African financial market (Urom et al., 2023). The COVID-19 pandemic, which began in December 2019, is still regarded as one of the most significant natural disasters to hit the world in recent memory. In addition to the direct impact of the pandemic on these markets, the existing degree of global financial linkages provides evidence that the COVID-19 pandemic may be increasing the degree of interdependence and connectivity between these markets.

Takyi and Bentum-Ennin (2021) evaluated and quantified the short-term impacts of the coronavirus disease of 2019 (COVID-19) on stock market performance in thirteen (13) African countries. Using daily time series stock market data from 1 October 2019 to 30 June 2020 and a novel Bayesian structural time series approach (a state-space model), estimates show that stock market performances for ten countries in Africa declined significantly in relative terms during and after the COVID-19 pandemic. Aboluwodi et al. (2022) looked into the long-term connections between the South African stock (JSE) and real estate markets and the global asset markets, including those for gold, platinum, oil, and cryptocurrencies. They show that before the COVID-19 pandemic, there were significant cointegration links between the JSE and Bitcoin, the JSE and oil, and the JSE and real estate; but, during the pandemic, these ties weakened or disappeared. On the other hand, there were cointegration linkages in the oil platinum and gold real estate markets. This suggests that, in contrast to the South African markets for gold, platinum, and oil, the JSE became more volatile throughout the COVID-19 period.

Urom et al. (2023) investigated the connectivity between 12 African equity markets and the global commodity, developed equity markets. Although there is a modest connection between African equities markets and these markets, they discovered that during the pandemic, there was a notable improvement in the degree of connectivity between these markets. Furthermore, the energy market controls how shocks are transmitted in the commodity market system. With respect to the equity market system, the French and South African equity markets exhibit the highest levels of spillover during the entire sample and during the peak of the epidemic, respectively.

In their study, Aawaar et al. (2023) looked at the variables affecting the time-varying return volatility of the African stock markets. Through the use of monthly indices of the top eight African stock markets, the authors find that the dynamic process of volatility in African stock markets is influenced by a number of factors, including history, domestic exchange rates, treasury bill rates, money supply, inflation rates, changes in the price of crude oil globally, volatility in the US and UK stock markets, and COVID-19 shocks. Furthermore, it seems that the only African markets that are not affected by advanced market volatility spillovers are those in North Africa. For portfolio managers, these markets may therefore offer chances for global diversification.

3. Econometric Methods

We describe the econometric methods applied to the asymmetric BEKK-GARCH process, the empirical problem addressed in the paper. Market volatility forecasting frequently uses GARCH models for conditional volatility. This is because they can display time series characteristics like volatility clustering and represent the time-varying conditional variances. Similarly, it has been demonstrated that multivariate GARCH models can forecast the dynamics of stock market volatility across various financial institutions. Multivariate MGARCH models have been widely utilized to examine how the correlation and covariance between various series evolve over time by defining the conditional variance and covariance equations.

Multivariate models like BEKK, CCC, or DCC specifications are more relevant than univariate models when analyzing volatility interdependence and transmission mechanisms among different financial time series (Arouri et al., 2011). The studies of El Ghini and Saidi (2017), Anyikwa and Le Roux (2020), Ahmed and Huo (2021), Chang et al. (2011), Agnolucci (2009), Hammoudeh et al. (2009), Hassan and Malik (2007), and several more empirical investigations attest to the superiority of these models. However, only the bivariate relationship is examined in the current studies that use MGARCH to examine volatility transmissions.

The nature of the aforementioned market is examined in our paper. A GARCH model with BEKK specification has been successfully used to evaluate and capture the spillovers between equities and commodity markets (Jouini & Harrathi, 2014; Salisu & Oloko, 2015; Ahmed & Huo, 2021). Here, we examine the return and volatility transmission in a few African countries using the multivariate BEKK-GARCH technique within simultaneous equation systems (Engle & Kroner, 1995). The conditional mean equation, which may be summarized as follows, allows us to define our model:

$$r_t=\mu +{\epsilon }_t\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}{\epsilon }_t={\displaystyle \frac{D_t{\phi }_t}{I_{t-1}}}\to N(0,H_t)$$

(1)

where $r_t$ is a $(6\times 1)$ vector of stock and commodity returns; $\mu$ is a $(6\times 1)$ vector of constant terms; ${\epsilon }_t$ is a $(6\times 1)$ vector of error terms, whose $(6\times 6)$ conditional variance-covariance matrix is $H_t$, $D_t=diag(h_{11,t}^{1/2},....,h_{66,t}^{1/2})$ with $h_{ii,t}$ as the conditional variance of the market i; ${\varphi }_t$ is a sequence of independently and identically distributed random variables; and $I_{t-1}$ is the market information available at time t − 1.

The matrix $H_t$ that depends on the squares and cross products of the error terms ${\epsilon }_t$ and volatility is guaranteed to be positively semi-definite by the multivariate BEKK-GARH parameterization put forward by Engle and Kroner (1995). After that, it gives the conditional variance equation’s volatility and cross-market shock effects. By taking into account the following matrix structure, Kroner and Ng (1998) offer a BEKK specification to examine the asymmetric responses of conditional volatility to negative shocks.

$$H_t=C^{\prime }C+A^{\prime }{\epsilon }_{t-1}^{\prime }{\epsilon }_{t-1}A+B^{\prime }{H}_{t-1}B+D^{\prime }{\xi }_{t-1}^{\prime }{\xi }_{t-1}D$$

(2)

$C$ is a lower triangular $(6\times 6)$ matrix of constants, where ${\xi }_t$ is defined as ${\epsilon }_t$ if ${\epsilon }_t$ is negative and 0 otherwise. The diagonal parameters of the $(6\times 6)$ matrices $A$ and $B$ measure the impact of the return series’ previous volatility and shocks on its current conditional volatility, respectively. These matrices’ off-diagonal components quantify the volatility and shock spillovers between the return series. While the off-diagonal parameters $d_{ij}$ reflect how market i responds to a negative shock of market j1, the diagonal coefficients of the matrix D of order $(6\times 6)$ measure how the negative shocks of return series affect its present conditional volatility. There is asymmetric volatility transmission between markets I and J, as indicated by the coefficient’s importance.

Based on the AIC and SIC criteria, we determined that the model provided by Equations (1) and (2) is the most suitable specification. It has been demonstrated in the literature that this type of model enables the accurate capture of market shock and volatility spillovers. The maximum likelihood approach, which is based on the Broyden Fletcher–Goldfarb Shanno (BFGS) optimization algorithm, was used to estimate the considered model.

4. Data and Preliminary Analysis

We investigate the transmissions of volatility among global commodities (oil, cocoa, and gold) and equity markets (nse, brvm, and gse) in African selected countries. To avoid the aggregation bias of global commodity prices, we use individual commodity futures including oil, cocoa, and gold.

The data used are from 2 January 2018 to 31 December 2021, which covers COVID-19 episodes of wide instabilities for both stock and commodity markets. To identify a more effective hedging tool for the COVID-19 period, we divide the study into the following two distinct periods: Period 1, which was not under the influence of COVID-19, and Period 2, under the influence of COVID-19. All daily series are converted to log returns by taking the log-difference of index values rX_t = ln(X_t/X_t−1), where X_t is the futures price at time t. Figure 1 shows the daily returns for the markets under review.

We observe that there are significant occurrences of elevated return volatility in each case during the COVID-19 pandemic period. This is why we are motivated to look at the interconnectedness of these markets within this particular time frame in order to determine whether there is a chance of an increase or decrease in shock transmission given the unstable state of the global financial and commodity markets as a result of the epidemic. Descriptive statistics for market return are shown in Table 1.

Table 1. Descriptive statistics and stochastic properties of return series2.

	roil	rcocoa	rgold	rnse	rbrvm	rgse
Mean	0.000352	0.000382	0.000308	0.000089	−0.00011	−0.00021
Median	0.001507	0.001150	0.000504	−0.00027	−0.00037	0.0000
Maximum	0.287098	0.114913	0.057754	0.060478	0.034804	0.046232
Minimum	−0.27851	−0.08902	−0.05055	−0.05033	−0.04405	−0.05127
Std. Dev	0.034435	0.018902	0.009497	0.00962	0.006909	0.008042
Skewness	−0.03103	−0.03579	−0.21704	0.417345	0.152220	−0.20895
Kurtosis	25.65900	5.041799	9.277966	9.193079	7.221705	11.93962
Jarque–Bera	22013.5	169.2235	1711.105	1553.902	712.1402	2956.706
ARCH test
F-Statistics	276.215	4.907	35.768	68.709	14.311	110.831
N*R2	217.736	4.892	34.636	64.055	14.120	98.051
Unit root tests
ADFL	−22.173	−31.275	−32.515	−17.496	−16.063	−32.826
PPL	−61.297	−31.295	−33.299	−24.043	−27.168	−33.447
KPSSL	0.2072	0.0258	0.1414	0.3392	0.2859	0.2298

Note: rnse, rbrvm3, and rgse stands, respectively, for Nigerian, Côte d’Ivoirian, and Ghanaian stock markets. ARCH values are all significant at the 1% level. When conducting Augmented Dickey–Fuller (ADF) and Phillips Perron (PP) tests, we include an intercept in the test equation. ADF^L, PP^L, and KPSS^L are for level data, which are return series. ADF^L and PP^L are significant at the 1% level. Since its null hypothesis is that the time series is stationary, all KPSS^L are not significant.

Table 1. Descriptive statistics and stochastic properties of return series2.

	roil	rcocoa	rgold	rnse	rbrvm	rgse
Mean	0.000352	0.000382	0.000308	0.000089	−0.00011	−0.00021
Median	0.001507	0.001150	0.000504	−0.00027	−0.00037	0.0000
Maximum	0.287098	0.114913	0.057754	0.060478	0.034804	0.046232
Minimum	−0.27851	−0.08902	−0.05055	−0.05033	−0.04405	−0.05127
Std. Dev	0.034435	0.018902	0.009497	0.00962	0.006909	0.008042
Skewness	−0.03103	−0.03579	−0.21704	0.417345	0.152220	−0.20895
Kurtosis	25.65900	5.041799	9.277966	9.193079	7.221705	11.93962
Jarque–Bera	22013.5	169.2235	1711.105	1553.902	712.1402	2956.706
ARCH test
F-Statistics	276.215	4.907	35.768	68.709	14.311	110.831
N*R2	217.736	4.892	34.636	64.055	14.120	98.051
Unit root tests
ADFL	−22.173	−31.275	−32.515	−17.496	−16.063	−32.826
PPL	−61.297	−31.295	−33.299	−24.043	−27.168	−33.447
KPSSL	0.2072	0.0258	0.1414	0.3392	0.2859	0.2298

Note: rnse, rbrvm3, and rgse stands, respectively, for Nigerian, Côte d’Ivoirian, and Ghanaian stock markets. ARCH values are all significant at the 1% level. When conducting Augmented Dickey–Fuller (ADF) and Phillips Perron (PP) tests, we include an intercept in the test equation. ADF^L, PP^L, and KPSS^L are for level data, which are return series. ADF^L and PP^L are significant at the 1% level. Since its null hypothesis is that the time series is stationary, all KPSS^L are not significant.

According to the data in Table 1, the mean return for the sample period is positive for all of the selected commodity indices, with uranium showing the highest mean return. Nigeria’s mean returns on the African equities markets are positive, whereas those of the other markets are negative.

Additionally, the global commodity market for cocoa has the greatest mean returns. Furthermore, all return series seem to be negatively skewed, with the exception of the Côte d’Ivoire and Nigerian equity markets, which show positive skewness. In contrast to a normal distribution, the return is strongly leptokurtic with fat tails, as indicated by the large value of kurtosis, which ranges from the lowest, at 5.04, for the cocoa return to the greatest, at 25.66, for the oil return. Significant asymmetry and excess kurtosis are seen in these early descriptive statistics. The Jarque–Bera test statistics, which reject the null hypothesis of normality for all of the market returns under investigation at a 1% significance level, further support the non-normality.

The findings of the ARCH test demonstrate the existence of the ARCH effect at a 5% significance level inside all returns, in accordance with the F and N*R² statistics, which reject the null hypothesis that a set of residuals shows no conditional heteroscedasticity. Therefore, it is appropriate and justified for us to measure return volatility using GARCH family models. To investigate trend stationarity, we combine the PP and ADF tests with KPSS tests. All test results show that price level data demonstrate a stationary feature, as shown in Table 1.

The unconditional correlation matrix between market returns is shown in

Table 2. Correlation matrices.

	roil	rcocoa	rgold	rnse	rbrvm	rgse
roil	1.000
rcocoa	0.122	1.000
rgold	0.042	0.082	1.000
rnse	−0.078	0.024	−0.009	1.000
rbrvm	−0.061	−0.028	0.018	−0.006	1.000
rgse	−0.002	0.027	−0.040	0.046	−0.016	1.000

. The potential advantages of portfolio diversification and assistance opportunities are suggested by the low correlation between the indicators. But when compared to other commodity and equity combinations, the connections between the Johannesburg stock exchange and oil and cocoa are stronger. This result is expected given the distinct factors influencing commodities and stock values.

5. Results and Discussion

To better understand the links between African equity and global commodity markets in terms of shocks and volatility, we estimated4 the BEKK-GARCH (1,1) process given by Equations (1) and (2).

Table 3. Estimation results (total period).

	roil (i = 1)	rcocoa (i = 2)	rgold (i = 3)	rnse (i = 4)	rbrvm (i = 5)	rgse (i = 6)
$\mu$	0.00041 *	0.00025	−0.00007	−0.00017	−0.00009	0.00007
ai1	−0.072 *	0.137 *	−0.283 ***	−0.172 **	−0.144 *	−0.124 **
ai2	−0.028 ***	0.147 ***	−0.137 ***	0.068 **	0.007	0.008
ai3	−0.025	0.080	−0.097 ***	0.122 **	−0.061 **	−0.082 ***
ai4	−0.042 ***	−0.106 ***	0.069 ***	0.325 ***	0.029	−0.029 *
ai5	0.028	0.031	−0.079 ***	0.238 ***	0.221 ***	0.060 ***
ai6	−0.033 *	−0.125 ***	0.103 ***	0.082 *	−0.00005	−0.075 **
bi1	0.504 ***	−0.1333 **	0.124 ***	0.304 ***	0.348 ***	0.123 ***
bi2	−0.052 ***	1.081 ***	−0.243 ***	−0.012	0.077 ***	0.097 ***
bi3	−0.026	0.818 ***	0.693 ***	−0.225 ***	0.122 **	−0.005
bi4	0.047 **	−0.029	−0.021 **	0.586 ***	0.260 ***	0.041 ***
bi5	−0.197 ***	−0.130 ***	0.037 **	−0.556 ***	0.518 ***	0.048 **
bi6	0.081 ***	0.078 ***	0.008	−0.282 ***	−0.055	0.906 ***
di1	−0.110 **	0.169	−0.062	0.210	−0.033	0.329 ***
di2	0.022	−0.096 ***	−0.012	−0.010	−0.075 **	0.115 ***
di3	0.053	−0.153 **	−0.053	0.115	0.032	0.072 *
di4	0.023	0.194 ***	−0.019	−0.169 **	−0.346 ***	−0.015
di5	−0.392 ***	−0.209 ***	0.139 ***	0.148 *	0.313 ***	−0.027
di6	−0.075 **	−0.049	0.014	0.054	−0.032	0.264 ***
JB	46,212.40 ***	194.485 ***	869.456 ***	791.616 ***	991.136 ***	22,210.47 ***
LB	86.042 ***	38.825	27.848	102.44 ***	89.477 ***	73.819 ***
LB2	46.848	39.257	22.951	19.702	40465	84.623 ***
ARCH	1.179	0.129	0.436	0.048	0.013	0.163

JB is the Jarque–Bera normality test of the standardized residuals; LB is the Ljung–Box test for the autocorrelation of order 36 of the standardized residuals; LB² is the Ljung–Box test for the autocorrelation of order 36 of the squared standardized residuals; and ARCH refers to the test for the conditional heteroscedasticity of the standardized residuals. *, **, and *** indicate significance level of 10%, 5%, and 1%, respectively.

,

Table 4. Estimation results (COVID-19 period).

	roil (i = 1)	rcocoa (i = 2)	rgold (i = 3)	rnse (i = 4)	rbrvm (i = 5)	rgse (i = 6)
$\mu$	0.00028	0.00045	0.00024	0.00076 ***	0.00037	0.00074
ai1	−0.077 **	−0.073	−0.107 ***	−0.288 ***	−0.082	−0.014
ai2	0.006	−0.113 ***	−0.053 ***	−0.028	−0.093 **	−0.120 ***
ai3	−0.054	−0.459 ***	−0.47	−0.259 *	−0.137	0.024
ai4	0.009	−0.034	0.012	0.122 ***	0.059	−0.005
ai5	−0.449 ***	−0.082 *	−0.038 *	0.713 ***	−0.234 ***	−0.156 ***
ai6	0.023	−0.066	0.088 ***	−0.034	0.017	0.0003
bi1	0.906 ***	−0.296 ***	0.158 ***	−0.316 ***	−0.119 *	−0.023
bi2	−0.044 ***	0.787 ***	0.039 ***	−0.294 ***	−0.023	0.031 *
bi3	0.010	0.274 ***	0.648 ***	0.303 ***	−0.099	0.112 ***
bi4	0.052 ***	−0.158 ***	−0.078 ***	0.696 ***	0.151 ***	0.027 **
bi5	−0.095 ***	−0.236 ***	0.134 ***	−0.341 ***	0.190 ***	−0.002
bi6	0.017	0.085 **	−0.065 ***	−0.032	0.151 ***	0.938 ***
di1	−0.035	0.227 **	0.026	0.131	−0.394 ***	0.121
di2	0.128 ***	−0.144*	0.136 ***	0.421 ***	−0.432 ***	0.005
di3	0.144 *	0.376 **	−0.169 ***	0.910 ***	0.513 ***	0.172 ***
di4	0.097 ***	−0.013 **	0.053*	0.121	−0.468 ***	−0.038
di5	−0.053	−0.111	0.064	0.125	0.006	−0.065
di6	−0.038	0.979	−0.137 ***	0.171 *	0.112	0.478 ***
JB	2993.99 ***	306.84 ***	142.94 ***	693.46 ***	941.46	14,541.96 ***
LB	31.005	29.550	40.369	71.371 ***	36.883	37.941
LB2	17.931	24.396	19.910	41.859	28.073	56.675 **
ARCH	0.286	0.000000001	0.075	2.594	0.188	0.081

JB is the Jarque–Bera normality test of the standardized residuals; LB is the Ljung–Box test for the autocorrelation of order 36 of the standardized residuals; LB² is the Ljung–Box test for the autocorrelation of order 36 of the squared standardized residuals; and ARCH refers to the test for the conditional heteroscedasticity of the standardized residuals. *, **, and *** indicate significance level of 10%, 5%, and 1%, respectively.

and

Table 5. Estimation results (Before the COVID-19 period).

	roil (i = 1)	rcocoa (i = 2)	rgold (i = 3)	rnse (i = 4)	rbrvm (i = 5)	rgse (i = 6)
$\mu$	0.00127 *	0.00026	0.000006	−0.00095 ***	−0.00041	0.00009
ai1	−0.066	−0.251 **	0.0309	0.025	0.152 *	0.160 *
ai2	−0.044 ***	0.176 ***	−0.168 ***	0.253 ***	−0.028	0.116 ***
ai3	−0.019	−0.282 ***	0.151 ***	0.200 ***	−0.084	0.238 ***
ai4	−0.025	−0.194 ***	0.121 ***	0.263 ***	0.070 **	0.032
ai5	0.103 ***	−0.110 **	0.012	0.045	−0.306 ***	−0.006
ai6	−0.028	−0.273 ***	0.006	0.079	−0.044	−0.046
bi1	0.929 ***	0.299 ***	−0.153 **	−0.007	0.706 ***	−0.063
bi2	0.014	0.662 ***	−0.428 ***	−0.007	−0.098 ***	0.155 ***
bi3	−0.033	0.743 ***	0.071	−0.079	0.432 ***	0.156 ***
bi4	−0.007	0.206 ***	0.052 **	0.846 ***	0.0049	−0.077 ***
bi5	0.011	−0.441 ***	−0.107 ***	0.103 **	0.292 ***	−0.335 ***
bi6	−0.102 ***	0.176 ***	−0.297 ***	0.016	1.024 ***	0.605 ***
di1	0.035	−0.514 ***	0.094	−0.170	0.241 **	−0.061
di2	0.005	0.041	−0.175 ***	0.169 **	−0.065	0.386 ***
di3	−0.033	−0.066	0.032	−0.079	−0.068	0.315 ***
di4	0.077 ***	0.116 *	0.028	−0.283 ***	−0.136 ***	−0.116 ***
di5	−0.003	−0.141	0.139 **	−0.093	0.044	−0.042
di6	−0.022	−0.186	0.348 ***	−0.251**	−0.133 *	−0.062
JB	34,126.78 ***	1.66	466.51 ***	328.91 ***	114.53 ***	2015.64 ***
LB	63.247 ***	34.651	39.211	58.192 **	69.102 ***	72.339 ***
LB2	30.598	55.897 **	18.766	22.500	22.282	13.394
ARCH	0.415	1.153	1.261	0.023	0.817	0.988

JB is the Jarque–Bera normality test of the standardized residuals; LB is the Ljung–BoxLjung-Box test for the autocorrelation of order 36 of the standardized residuals; LB² is the Ljung–BoxLjung-Box test for the autocorrelation of order 36 of the squared standardized residuals; and ARCH refers to the test for the conditional heteroscedasticity of the standardized residuals. *, **, and *** indicate significance level of 10%, 5%, and 1%, respectively.

below report the results of estimates, respectively, for the total period, COVID-19 period and before COVID-19 period with diagnostic tests.

While Table 3 shows the effects and shocks and volatility spillover effects between markets, Table 4 and Table 5 provide an assessment of the role of COVID-19 on changing these effects.

5.1. Past Effects

The estimated results for the total period reported in Table 3 indicate that for all markets, the current values of conditional volatility are sensitive (positively for world cocoa price and Nigerian and brvm stock markets, and negatively for world oil price, world gold price and Ghanaian stock market) to past shocks since the corresponding diagonal coefficients a_ii are statistically significant. Table 4 and Table 5 show the same results for oil and the Nigerian stock market during COVID and before the COVID COVID-19 periods, suggesting no impact of COVID COVID-19 for these two markets. For the other markets, COVID-19 has mixed effects, transforming the positive sensitivity of past shocks to negative for gold and vice versa for the brvm stock market. For cocoa and the Ghanaian stock market, the sensitivity is the same over the total period compared as before the COVID-19 period but is different to that after the COVID-19 period. For the past volatility effect in the case of the total period, the results reveal that for all markets, the current conditional volatility is positively influenced by its past value since the corresponding diagonal coefficients b_ii are positive and statistically significant. As noted in Table 3, the estimated coefficients for the ARCH and GARCH models in our conditional variance equations for all the groups are statistically significant. This shows that the African stock markets (Nigerian, brvm, and Ghanaian) and global commodity markets (oil, cocoa, and gold) have strong ARCH and GARCH effects. Our results are in line with those of Beirne et al. (2009), who emphasize the suitability of the GARCH family models in these analyses and offer compelling evidence of ARCH and GARCH effects in emerging markets.

One noteworthy characteristic is that, for all markets, past volatility is higher than past own shocks. This suggests that, for all markets, previous volatility is more significant in forecasting current conditional volatility than past shocks. With the exception of gold, which has higher past shocks than past volatility prior to the COVID-19 period, these findings hold true for all markets during the COVID-19 period and before it.

5.2. Shocks and Volatility Spillovers Between Stock and Global Commodity Markets

Four bidirectional shock and volatility transmissions are identified by the empirical results in Table 5. Unexpected news has a negative impact, but historical volatility between the price of oil and the stock markets in Nigeria, Ghana, and Brazil has a favorable impact. The spillovers from the most recent bidirectional transmissions between the Nigerian stock market and gold are negative for the previous volatility and favorable for the unexpected news. Additionally, we find evidence of bilateral shock transmission between the Nigerian stock market and the cocoa market (negative in the opposite direction and positive from the cocoa to the stock index) and between the Ghanaian stock market and the gold market, as well as negative shock spillover effects between the world oil price and the BRM stock market.

While the price of cocoa and the brvm stock index are correlated in terms of volatility, with the cocoa price having a positive impact on the stock index and the stock index having a negative influence on the cocoa, the Ghanaian stock and cocoa markets have bidirectional positive volatility linkages. There is only one negative unidirectional shock transmission from cocoa to the Ghanaian stock index, in contrast to these bidirectional transmissions. The historical volatility of the Nigerian and Ghanaian stock markets has a positive (negative) impact on the current conditional volatility of the price of oil (gold), and vice versa for brvm.

The Ghanaian stock market has a favorable impact on the cocoa price, while the BRM stock markets have a negative impact on the current value of conditional volatility. Conversely, the historical volatility of the oil price has a favorable impact on the conditional volatility of the Nigerian stock market, while the historical volatility of the gold price has a negative impact. The Ghanaian stock market, or brvm, has a favorable impact on all commodity markets, including those for cocoa and oil.

Overall, the shock and volatility spillover effect run at the same time from global commodity price to stock markets, such as from stock markets to commodity price. According to multivariate GARCH type models, Jouini and Harrathi (2014) found that volatility spillovers flow more from GCC stock markets to global oil prices than from oil to stock markets. This finding runs counter to their findings. These findings highlight how crucial it is to choose a precise methodology and use a sufficiently advanced econometric technique in order to empirically examine the correlations between the volatility of the African stock and commodity markets. The data also show that there are mixed (positive and negative) shock connections and volatility spillovers.

The results presented in Table 4 and Table 5 show that both shocks and volatility transmissions between markets are affected by COVID-19. New transmissions emerge while others disappear. For shocks from stock markets to commodity markets, transmissions appear between brvm and Ghanaian markets to gold, while those from Nigerian markets to cocoa and gold disappear. In the opposite direction, shocks are transmitted from oil price to both Nigerian and Ghanaian markets and from cocoa to brvm, with some transmissions disappearing (from oil price to brvm, from cocoa to Nigerian markets, and from gold to Ghanaian markets). Regarding volatility transmissions from stock to commodity markets, new transmissions are observed from Nigerian and brvm markets to oil, while transmissions from the Ghanaian market to oil disappear. In the reverse direction, volatility transmissions emerge from oil, cocoa, and gold to Nigerian markets and from cocoa and gold to brvm market.

5.3. Shocks and Volatility Spillovers Among Commodity Markets

Table 5 shows bi-directional mixed transmissions of shock spillovers for oil/cocoa (which disappear in COVID-19 period) and unidirectional negative from oil and cocoa to gold. There is strong evidence of volatility spillovers, which is bidirectional negative for oil/cocoa and mixed for cocoa/gold. Similarly, our results reveal no shock and volatility spillover effects from gold to oil. No COVID-19 impact on volatility transmission is detected.

5.4. Shocks and Volatility Spillovers Among Stock Markets

From the perspective of shock and volatility transmissions among selected African stock markets, the results in Table 3 reveal interesting insights. For the Nigeria/Ghana country pair, the shock linkage from the first country to the second one is negative, and positive for the other direction. For the other country pairs, there are unidirectional positive shock spillovers from brvm to Ghanaian to Nigeria and no evidence of shock interdependence from Nigerian and Ghanaian stock markets to brvm. For volatility spillover effects, the results display mixed bidirectional links (Nigeria/Ghana/brvm) and positive unidirectional relationships from brvm to Ghanaian markets. During the COVID-19 period, new shock transmissions mixed are observed, positive from brvm to the Nigerian stock market and negative from Ghanaian to Nigerian markets. Shock transmissions from the Nigerian market to brvm disappear and emerge as volatility transmissions.

Consistent with Ahmed and Huo’s (2021) research, we discover that the conditional volatility of stock and commodity markets typically vary more quickly over time due to internal innovation impulsions and volatility than cross-market values. These findings imply that personal values are more capable than cross-market values of forecasting future conditional volatility. The fact that, aside from the coefficients, the differences between the cross-market ARCH and GARCH coefficients are generally not very significant indicates that the sensitivity of the current conditional volatility to cross-market historical news and volatility is nearly equal.

These observations assume that conditional volatilities are extremely unstable and fluctuate significantly over external shocks. These characteristics align with those inferred from the market return dynamics presented in Figure 1, where the returns’ behavior vary significantly throughout the COVID-19 pandemic.

5.5. Asymmetric Effects

The results presented in Table 3 show evidence of asymmetrical responses to negative shocks, except in the gold market. The impacts are negative for oil, cocoa, and Nigeria but positive for brvm and Ghana. Regarding the magnitude of the estimates, the observed impact on the stock markets is more important (double to triple) compared to commodity markets. For the cross-market asymmetric responses between commodity and stock prices, we find bidirectional asymmetric effects between oil/Ghana and cocoa/brvm with different signs. Among stock markets, there is evidence of bidirectional asymmetric responses between the Nigerian and brvm stock markets. The results also display positive (Nigeria/cocoa, cocoa/gold/Ghana) and negative (brvm/gold/oil) unidirectional asymmetric responses from market one to market two, and no asymmetric spillovers for the oil/cocoa/gold commodity pairs, Nigeria/brvm/Ghana country pairs and oil/gold/Nigeria commodity stock pairs. Compared to before COVID-19 period (Table 5), results for COVID-19 period (Table 4) indicate that the pandemic supports asymmetric responses to negative shocks for cocoa, gold, and Ghanaian markets. Among commodity prices, COVID-19 allows asymmetric responses from cocoa and gold to oil. Other new asymmetric responses due to COVID-19 are detected from gold to cocoa, Nigeria, and brvm; from Nigeria to gold; and from cocoa to brvm. In contrast, COVID-19 resulted in non-asymmetric responses from cocoa and Nigeria to Ghana; from brvm to gold; and from Ghana to brvm.

6. Conclusions and Policy Implications

Using the asymmetric BEKK-GARCH process created by Kroner and Ng (1998), this study investigates the empirical problem of shock and volatility transmissions between African stock and international commodity markets. To the best of our knowledge, no multivariate models have been used to analyze the volatility transmissions of African countries in prior publications, which lends credence to this analysis. The findings are generally acceptable and show that, for patterns of volatility, the effects of shock spillovers on stock markets and commodity prices are comparable.

Additionally, the findings demonstrate both unidirectional and bidirectional volatility interdependencies inside and across a few chosen markets. Except for the cocoa/gold/Nigeria/oil, gold/Nigeria, and Nigeria/brvm/Ghana pairs, where non-asymmetric responses are noted, the results are noteworthy from the standpoint of asymmetry in the conditional variances since there are asymmetric spillovers to negative shocks among and across selected markets. Return volatility in certain markets has been found to have increased as a result of the COVID-19 outbreak and the ensuing economic uncertainty.

These results might indicate that investors are confident in the actions taken by different African governments to address this issue. These findings indicate that shock and volatility transmissions between and across markets with varying signs and levels were both impacted by the pandemic. Asymmetric market reactions to adverse shocks are also impacted by pandemics, which encourage the formation of new asymmetric reactions while eradicating others. Policymakers need to understand how certain African country stocks and commodity markets relate to one another in terms of volatility transmissions. Based on wise choices, stock market and commodity price regulation can be implemented. The information contained in each market that allows for the forecast of future variations in the other markets is revealed by volatility transmissions between markets on a global scale.

7. Limitations and Future Directions

This study has a number of limitations even if it offers insightful information. First of all, by concentrating on a small number of indices, the study may have missed a number of other important international markets that might provide further information about volatility spillovers. Second, by dividing the data into pre-COVID-19 and during COVID-19 eras instead of taking into account a post-COVID-19 phase, the dynamic effects of the pandemic on international markets may be oversimplified. Opportunities for additional research into intermarket volatility during and after the pandemic are also created by this insight. A more thorough grasp of global market interdependencies and volatility transmission mechanisms during crises like pandemics, wars, etc., could be obtained by utilizing high-frequency data and broadening the dataset to include more diverse markets.