Impact of Indices on Stock Price Volatility of BRICS Countries During Crises: Comparative Study

Abstract

This study aims to identify the common indices having an impact on the SPV of BRICS countries during crises. To address this, the monthly data retrieved from the database of the Global Economic Monitor (GEM), World Bank, IMF International Financial Statistics data, and OECD in the period of January 2000 to December 2023 are analyzed in two phases. In the first phase, DM classification techniques are applied to the data to identify the best common classification technique in order to use this technique in the second phase to compare the results with Multiple Linear Regression (MLR) results. In the second phase, to account for the global financial crisis and COVID-19 crisis, the sample period is divided into two sub-periods. For those sub-periods, MLR and the best classification technique that was found in the first phase are utilized to find the common indices that have an impact on the stock price volatility during individual and both crises. The findings indicate that the Random Tree method commonly classified the data among the seven classification techniques. Regarding MLR results, no common indices were identified during the global financial crisis or the COVID-19 crisis. However, based on Random Tree classifications, the CPI price percent, National Currency, and CPI index for all items were common during the global financial crisis, whereas only the CPI price percent was common during the COVID-19 crisis. While some common indices were observed in individual crises for specific countries, no indices were consistently found across both crises. This variation is attributed to the unique nature of each crisis and the diverse economic and socio-political structures of different countries. These findings provide valuable insights for financial institutions and investors to refine financial and policy decisions based on the specific characteristics of each crisis and the indices affecting each country.

1. Introduction

The world economy is monitored by the three major international economic organizations, the World Bank, the International Monetary Fund (IMF), and the World Trade Organization (WTO). In the World Economic Outlook, the world economically is divided into major groups, advanced economies and emerging and developing economies. In the world, to create and coordinate economic and geopolitical issues, some groups have been developed for advanced economies, like the G7, and emerging and developing economies, like BRICS and G20. As a group of fast-growing emerging economies, the BRICS countries, Brazil, Russia, India, China, and South Africa, have an important role in the world economy, accounting for nearly a quarter of the global economy (Castello & Resta, 2022; Fan et al., 2022).

The former Goldman Sachs economist Jim O’Neill coined the term BRIC in the early 2000s to describe the four fast-growing countries, Brazil, Russia, India, and China (O’Neill, 2001). The term was coined as BRICS in 2010 with the inclusion of South Africa. These countries play a significant role in the world economy by having large land areas, populations, and trade volume (Huang et al., 2021; Larionova & Shelepov, 2022; M. Hussain et al., 2024). This group accounted for 26% of the global GDP and 40.8% of the world’s population (Ross, 2024; World Bank Data, 2023). The BRICS countries have diverse economies based on natural resources, industry, and services. Brazil’s economy depends on agriculture and natural resource exports, particularly soybeans, coffee, and iron ore. Russia’s economy depends on its large oil and natural gas reserves. India’s economy is driven by its service sector, IT industry, and manufacturing. China, the second-largest economy in the world, is powered by industrial production, exports, and its growing technology and consumer markets. South Africa’s economy is focused on mining gold and platinum and its financial services. These countries play a major role in global trade, According to Radulescu et al. (2014), in 2009, China emerged as the leading importer of agricultural raw materials (accounting for 17.4% of total global imports) and metals (20.7%), as well as the third-largest importer of oil (6.7% of the total, following the U.S. and Japan). Brazil ranked ninth in the export of agricultural commodities and fifth in the export of food, while Russia held the top position in the export of fossil fuels. In addition to trade, the BRICS countries play a significant role in the global investment landscape, serving as major recipients of foreign direct investment while also becoming key contributors to outward investments (Castello & Resta, 2022).

Economies, stock market performance, societal dynamics, and political systems are greatly affected by unexpected crises and pandemics (Lal, 2023). This impact is particularly seen in emerging economies. During these periods, oil price fluctuations, exchange rates, trade volumes, and total reserves resulted in rising unemployment and inflation, declining production, and increased bankruptcies across countries. Therefore, as emerging economies, the BRICS countries were also impacted by these crises. Claessens and Kose (2013) indicated that the GDP growth of all BRICS countries declined during the global financial crisis in 2008 and again during the COVID-19 pandemic in 2020. The impact of crises on stock markets is significant. Numerous studies have been conducted in the literature on the effects of crises on stock markets and other economic indicators of BRICS countries. Researchers have analyzed the effects of crises on various aspects of the BRICS economies, including economic growth and GDP (Rani & Kumar, 2019; Gaba & Gaba, 2022; Younsi & Bechtini, 2020), stock market returns and volatility (Wang et al., 2023; Ataman & Kahraman, 2022; Mamman et al., 2023; Ruzgar, 2024; Salisu et al., 2021; Panda et al., 2023), the impact of exchange rates on stock market returns (Mroua & Trabelsi, 2020), stock markets in crises (W. Bello, 2015), volatility spillovers and financial connections (Boubaker & Larbi, 2022; Panda et al., 2023), and market efficiency (Sharma et al., 2019; Kulikova et al., 2024; Phiri, 2022) and the relationship between gold and the stock market (Chkili, 2016). They used various methods, including Data Mining (DM) (Ruzive et al., 2021; Ruzgar, 2024; Ataman & Kahraman, 2022), Machine Learning (Castello & Resta, 2022), Multiple Linear Regression (Rababah et al., 2021; Usman et al., 2022), the GMM panel vector autoregressive approach (Gyedu et al., 2021; Balcilar et al., 2021), the panel ARDL method (Mroua & Trabelsi, 2020; Awolusi & Mbonigaba, 2020), panel smooth transition regression (PSTR) (Ruzive et al., 2021), and GARCH, APARCH, ARFIMA, and FIGARCH models (Tripathy, 2022; Mamman et al., 2023).

BRICS countries demographically and economically form a powerful bloc, and as fast-growing emerging countries, their economies have changed the economic and political balance in the global economy (Tripathy, 2022). They are major recipients of international investment flows and have higher economic growth rates than other emerging countries. However, their diverse economies and socio-political structures lead us to ask if common indices affect the SPVs for the individual and both crises’ data. Researchers studied the relationship between the stock market and one or two indices, such as the relationship between the stock market and exchange rate (Mroua & Trabelsi, 2020), the stock market and gold (Chkili, 2016), and the stock market and oil prices (Mudiangombe & Mwamba, 2023). However, there is a lack of studies about the impact of many indices on the SPV of BRICS countries during crises. Although various techniques have been applied to analyze the effects of indices on stock market returns or the stock market, no study has conducted a comparative examination to identify the common indices influencing the SPVs of BRICS countries during crises. This study stands out by addressing a gap in the existing literature. This study aims to identify the common indices impacting the SPV of BRICS countries during the global financial crisis and COVID-19 crisis, working with many indices studied in the literature, alone or in pairs. For this purpose, to obtain more reliable results, all available monthly data were collected from the Global Economic Monitor (GEM) database, World Bank, IMF International Financial Statistics data, and OECD from January 2000 to December 2023. The limitation of this study is that there were no data or data with missing values for one or more countries. The collected data include seventeen indices and stock price volatility. Due to the diverse economic structures of the countries, all data were standardized. The clear data were utilized in two phases. In the first phase, all applicable Data Mining (DM) classification techniques in WEKA were applied to the data of each BRICS country to identify the most effective common classifier; seven of them provided meaningful results. Two reasons were considered when selecting the classification techniques. First, the classification techniques provide structural analysis; identifying the specific categories reduces the noise and inconsistencies and most importantly offers simple output for decision making. Second, classification techniques for stock prices have not been commonly used in the literature. This introduces the first hypothesis, H1: There exists a common best classifier that classifies the data of BRICS countries. To address the issue, seven classification techniques were applied to the data of each BRICS country, and the results revealed that the tree-based classification techniques, Random Forest and Random Tree, presented better results than the others. When comparing the outputs, Random Tree classified the data better than Random Forest did.

In the second phase, the data related to the global financial crisis and the COVID-19 crisis were selected from the clear data, including pre- and post-crisis periods. Then, once all remedial conditions were met, Multiple Linear Regression (MLR) and Random Tree techniques were applied to the crisis data for each country to determine the common indices influencing the SPVs during the two crises that signal how investors, financial institutions, and policymakers should respond during different crises. To identify the common indices for individual and both crises, the MLR and Random Tree results are examined separately and compared to test the following hypotheses: H2: There are common indices in MLR results, influencing the SPV of BRICS countries during the 2007–2010 crisis; H3: There are common indices in MLR results, influencing the SPV of BRICS countries during the 2018–2021 crisis; H4: There are common indices in MLR results, influencing the SPV of BRICS countries during the 2007–2010 and 2018–2021 crises; H5: Indices are similar in MLR and Random Tree during the 2007–2010 crisis; H6: Indices are similar in MLR and Random Tree during the 2018–2021 crisis.

In the second phase, MLR and Random Tree techniques were applied to data from two crises for each BRICS country, yielding varied results. For the global crisis, MLR analysis found no common indices affecting SPVs, while Random Tree identified CPI price percent, CPI for all items, and National Currency as common indices for all BRICS countries. However, these indices impacted SPVs differently in MLR models. For instance, CPI for all items affected the SPV of China, CPI price percent influenced the SPV of Russia, and National Currency showed no effect on any BRICS country in the MLR results. During the COVID-19 crisis, MLR again found no common indices affecting SPVs, but Random Tree identified CPI price percent as a common factor. This index negatively impacted the SPV of India in the MLR results. Although no index consistently affected SPVs across both crises in the MLR results, Random Tree indicated CPI price percent as the only index influencing the SPV of BRICS countries during both crises. These differences arise from the diverse economic and socio-political structures of BRICS countries and the distinct nature of each crisis.

The rest of this study is structured as follows: Section 2 reviews the literature, Section 3 discusses the methodology, Section 4 presents findings and discussion, and Section 5 presents the conclusion.

2. Literature Review

Countries’ economies present their economic wealthiness rank as advanced or developing and emerging countries in the world. Economies depend on some indicators, like gross domestic product (GDP), growth rate, and the stock market. While GDP measures the income earned from the production of goods and services and the growth rate shows how the country’s economy grows in a certain period, the stock market shows the economic activities of the countries. In the literature, numerous studies have been conducted on GDP, growth rate (Younsi & Bechtini, 2020; Gyedu et al., 2021), and stock markets (Mroua & Trabelsi, 2020; Panda & Thiripalraju, 2020).

In the world, many international organizations or groups are formed to monitor the trends in the economies of members, increase and develop the members’ economic activities, and act as catalysts in the worldwide economy. Based on the economic wealth of the member countries, they are broken up into two groups, advanced economies and developing and emerging economies. BRICS is one of the fast-growing and powerful groups of the world’s leading emerging market economies. The acronym BRICS is a significant organization that brings together the most prominent emerging economies worldwide (Lal, 2023). The BRICS countries, Brazil, Russia, India, China, and South Africa, have more than 40% of the world’s population, 28% of the world’s massive land, 24% of the global GDP, and more than 16% of the global commerce (World Economic Outlook, 2024). In 2023, BRICS countries extended by inviting Egypt, Ethiopia, Iran, Saudi Arabia, and the United Arab Emirates (UAE) to become members with effect from 1st January 2024. According to the 2022 World Bank Data and OECD data (OECD Data, 2022; World Bank Data, 2022), with this extension, the new population of BRICS countries became 45.50% of the world population, and their land area represents 32.61% of the world’s land area (World Bank Data, 2022). In the “Situation Report”, it was stated that BRICS countries with the new members represent 28.1% of the global economy and the expanded group holds more than 43% of global oil production (Ross, 2024). In terms of GDP growth, the BRICS countries demonstrate an important increase in the global economy. For example, the BRICS economies are experiencing a more rapid growth rate of 7.41 percent than the global economy’s growth rate of 3.29 percent. China leads the BRICS countries with the largest GDP, followed by India, Russia, Brazil, and South Africa (Singh et al., 2024). Having a good demographic potential and economic structures leads the BRICS countries to attract the attention of investors, regulators, financial agencies, and policymakers in the world (Mensi et al., 2016). BRICS countries have diverse cultures, different political and demographic structures, and also different growth rates (Kalu et al., 2020). In terms of economic structures, Brazil has a liberalized and market-driven economic structure; Russia has a dominant government-controlled economic structure; similar to Russia, India also has a dominant government-controlled economic structure; China has a largely government-controlled economic structure; and South Africa has a market-driven, structured and open economy structure (World Bank Data, 2023; World Economic Outlook, n.d.). Brazil’s abundant natural resources contribute significantly to its trade, with exports ranging from agricultural products like soybeans and coffee to industrial goods such as automobiles and aircraft. Major trade partners include China, the United States, and Argentina, facilitating a robust international exchange that shapes Brazil’s position in the global economy. On the other hand, Russia boasts a diverse mix of industries, including energy, manufacturing, agriculture, and technology. It maintains trade partnerships with countries across Europe, Asia, and other countries in the Commonwealth of Independent States (CIS), exporting energy resources, machinery, agricultural products, and metals while importing machinery, vehicles, and pharmaceuticals. India’s trade is diverse, with exports ranging from textiles and chemicals to machinery and software services, while importing items like crude oil, gold, machinery, and electronics. Key trade partners include the United States, China, United Arab Emirates, and neighboring countries within Asia and the European Union. China’s economy derives its strength from various sources, including manufacturing, agriculture, technology, and services. It is a major player in global trade, exporting a wide range of goods such as electronics, machinery, textiles, and consumer products while importing commodities like oil, natural gas, metals, minerals, and agricultural products. Additionally, South Africa’s economy relies on various sources, including minerals such as gold, platinum, and diamonds, as well as agriculture, tourism, and financial services. It engages in trade with various countries around the world, exporting commodities like precious metals, minerals, and agricultural products, while importing machinery, chemicals, and vehicles. Key trading partners include China, the European Union, and the United States. Ross (2024) stated in “Situation Reports” that BRICS established the New Development Bank in 2015 to mobilize resources for infrastructure and sustainable development projects. According to Castello and Resta (2022), BRICS countries have an important role in the current pattern of global investment because they are major recipients of foreign direct investments. Among BRICS countries, each country has different drivers of growth; for example, Brazil and Russia are mineral-rich countries and possess a high degree of speculative activity in the international market, and India and China have cheap labor and resources (Panda & Thiripalraju, 2020).

In the world, economic and financial crises have occurred in different periods and caused trouble for both emerging and advanced countries, severely impacting countries’ economies and stock markets. The history of crises shows that at least twice, crises occurred in a decay in the world, sometimes global, sometimes local. Some of the factors driving crises have been clarified in the literature, including the countries’ global economic conditions and internal factors. Reinhart and Rogoff (2008) classified crises by definition into two groups, quantitative and qualitative crises. The group using the quantitative definition includes currency and sudden closure crises, like the COVID-19 crisis, while the second one, requiring qualitative and judgmental analysis, contains debt and banking crises, like the 2007–2009 global financial crisis (Claessens & Kose, 2013). The 2007–2009 global financial crisis, known as the subprime mortgage crisis, started in the United States and spread all around the world. It was the most severe economic and financial meltdown since the Great Depression (Ruzgar & Chua-Chow, 2023). According to the OECD data, during the 2007–2009 crisis, all BRICS countries faced significant turbulence in their stock markets and experienced sharp declines in stock prices. They all demonstrated the same pattern even though they have diverse economic structures; the severity of the stock prices varied. Brazil and Russia are the most affected countries among them due to their reliance on commodities and energy exports (OECD Data, 2024). The most recent crisis is COVID-19, which originated in the Chinese city of Wuhan in December 2019 and quickly and widely spread throughout the world (J. Bello et al., 2022). This is the most severe stock market crash in history. After the declaration of the COVID-19 pandemic in March 2020, most of the countries in the world went into lockdown. Oil prices and stock markets dropped, unemployment and inflation rates increased, and approximately three-quarters of small businesses took on debt due to the lockdown (Brewin, 2021). According to the OECD report, during the COVID-19 crisis, BRICS countries exhibited a mixed structure compared to the 2007–2009 crisis. While China and India quickly recovered due to robust economic resilience, Brazil and South Africa had many challenges due to domestic problems. Moreover, Russia is extremely impacted due to oil price fluctuations and the continuing war with Ukraine (Ruzgar, 2024; OECD Data, 2024). Since the BRICS countries have diverse cultures, and different political and demographic structures, changes in the global economic factors affect their GDP, growth rates, and stock markets, such as the 2007–2008 global financial crisis and COVID-19 crisis (Kalu et al., 2020), but the influence severity was heterogeneous across these countries.

Countries’ economic conditions, stock markets, trade, currencies, foreign investments, and the relationships among them during the crises, particularly the global financial crisis and the most current one, the COVID-19 crisis, have attracted the attention of numerous scholars and have been extensively studied using various methods. The stock prices, the relationship between oil prices and the stock market, and the trade of BRICS countries have been studied by numerous scholars in different fields, such as the relationship between macroeconomic variables and the stock market index values (Ataman & Kahraman, 2022; Wang et al., 2023; Lone et al., 2023), volatility spillover index (Panda et al., 2023; Boubaker & Larbi, 2022; Rehman et al., 2024), efficiency of BRICS currency markets during the COVID-19 crisis (Phiri, 2022; Kulikova et al., 2024), BRICS stock markets’ response to global economic policy (Mamman et al., 2023), changes in the structures of BRICS countries’ stock markets pre- and post-COVID-19 crisis (Karadag & Simsek, 2023; Ameer et al., 2023), impact of exchange rates on crude oil prices and the BRICS countries’ stock returns (Mudiangombe & Mwamba, 2023), impact of commodities and foreign exchange rate on the stock prices of BRICs countries (Fasanya et al., 2023; Mroua & Trabelsi, 2020), stock market returns and volatility in BRICS countries (Tripathy, 2022; Zhou et al., 2019), stock market performance and development in BRICS countries (Kalu et al., 2020; Chong et al., 2010), the relationship between gold and stock markets in BRICS countries (Chkili, 2016), and the causality and the dynamic links between exchange rates and stock market indices in BRICS countries (Mroua & Trabelsi, 2020; Chkili & Nguyen, 2014).

In the literature, scholars used various methods in their studies about the stock markets of BRICS countries and the factors impacting them, including panel linear regression (Ataman & Kahraman, 2022; Panda et al., 2023), a Machine Learning technique (Artificial Neural Network) (Ataman & Kahraman, 2022; Castello & Resta, 2022; Ruzgar, 2024), the Monte Carlo Markov Chain (MCMC) technique (Nguyen & Duong, 2021), the MGARCH-BEKK model (Panda et al., 2023), the GARCH model (Mamman et al., 2023; Tripathy, 2022), a Kalman filter approach (Kulikova et al., 2024; M. Hussain et al., 2024), the global vector autoregressive (GVAR) method (Attilio et al., 2024), linear and non-linear SOE SVAR models (Yildirim & Guloglu, 2024), multifractal detrended fluctuation analysis (MF-DFA) (Ameer et al., 2023), the autoregressive distributed lag (ARDL) method (Mroua & Trabelsi, 2020), and the Simple Moving Average (SMA) (Chong et al., 2010).

To investigate the relationship between oil prices and markets, several studies have been conducted by various researchers. From those, Mudiangombe and Mwamba (2023) examined the dependence structure and the time–frequency of the impact of exchange rates on crude oil prices and BRICS countries’ stock returns. Using wavelet analysis for the daily data of exchange rates, crude oil prices, and stock market returns, they found that exchange rates significantly impact the stock markets and crude oil. Similarly, Arfaoui and Rejeb (2017) examined the direct and indirect relationships among oil, gold, the US dollar, and stock prices from 1995 to 2015. The results revealed a negative relationship between oil and stock prices; therefore, the stock markets affect the oil price positively and significantly. Fasanya et al. (2023) studied the predictability of stock prices of the BRICS countries with a large dependence on commodities for foreign exchange earnings using forecast models. They found that both the in-sample and out-of-sample forecast performances of the predicted models support asymmetries in several commodity prices for the stock prices of Brazil, Russia, and South Africa (Fasanya et al., 2023). Moreover, Zhou et al. (2019) examined the quantile dependence and directional predictability from oil volatility to stock returns in BRICS countries by utilizing the cross-quantilogram model. Their empirical results show that oil volatility has a directional predictability for stock returns. There is an increased likelihood of either a large loss or a large gain in the stock market when the oil volatility is in a high quantile, whereas the stock market is less likely to show either a large loss or a large gain when the oil volatility is in a low quantile. Furthermore, some studies examined the effects of macroeconomic factors on the stock prices of BRICS countries during the crises. Wang et al. (2023) studied the response of BRICS stock prices to shocks of internal and external macroeconomic factors in different markets using variational mode decomposition and a quantile model. The results revealed that the influence of each factor varies across the countries and markets. They also found that the relationship between stock prices and macroeconomic variables behaved slightly differently during the financial crisis in 2008 compared to other periods. Similarly, Lone et al. (2023) examined the impact of select macroeconomic variables on stock market performance in the BRICS countries employing the ARDL bounds testing model and PMG/ARDL model to the monthly data over the period 2011–2021. Both models provided confirmatory results regarding short- and long-run relationships for all the BRICS countries except South Africa. They also found that the variables were causally related to each other during the sample period. From a different perspective, Panda and Thiripalraju (2020) researched the financial environment of BRICS countries and the USA with investment opportunities in BRICS countries by assessing the market depth, market microstructure, portfolio weights, and several macroeconomic indicators. The results revealed that BRICS countries are good destinations for investors.

Several studies have been carried out on the persistence of volatility shocks and stock market returns. Tripathy (2022) assessed the persistence of volatility shocks and long memory in stock market returns and volatility of BRICS countries using GARCH, APARCH, ARFIMA, and FIGARCH models from 2000 to 2019. The results of GARCH confirm evidence of persistence in volatility shocks, while APARCH indicates the existence of leverage effects in all BRICS stock markets. The results of the ARFIMA and FIGARCH models offer significant indications of long-range dependence in the mean returns and volatility series. Rout and Das (2024) examined the stock market indices of BRICS countries during the four crisis terms from 1990 to 2021. They found that the stock markets of India, Brazil, and South Africa suffered the worst crisis during COVID-19, whereas China has recovered very quickly. Additionally, the results indicated an increased association between different markets depending on the severity of the crisis. In another study, Ameer et al. (2023) studied the response of the BRICS and MSCI emerging stock market indices during the COVID-19 outbreak, utilizing a multifractal detrended fluctuation analysis (MF-DFA) to investigate the market efficiency dynamics of these indices and then rank them based on their market efficiency. The findings revealed that COVID-19 adversely affected the efficiency of all indices even though improvement in the Chinese market inefficiency was witnessed due to sudden lockdowns. On the other hand, Kulikova et al. (2024) examined the efficiency of BRICS markets by using a moving window test for sample autocorrelations and a Kalman filter approach to the monthly data during the 2008–2009 global financial crisis and COVID-19 crisis. They found that all BRICS stock markets were affected during both crises, but generally weak-form efficient except for China, contradicting the findings of Ameer et al. (2023).

The causality and dynamic relationship between exchange rates and stock market indices in BRICS countries have attracted the interest of scholars. Mroua and Trabelsi (2020) worked on this to identify the short- and long-term effect of the US dollar on major stock market indices by using the panel generalized method of moments model and the panel autoregressive distributed lag (ARDL) method. They found that exchange rate changes have a significant effect on the past and the current volatility of the BRICS stock indices, and exchange rate movements also significantly affect short- and long-term stock market indices of all BRICS countries. In another study, Chkili and Nguyen (2014) used a regime-switching model approach to investigate the dynamic linkages between the exchange rates and stock market returns for the BRICS countries. They found that stock markets have a greater influence on exchange rates during both calm and turbulent periods. Bhutto et al. (2020) found a positive correlation between the exchange rate and the stock market. However, Adeniyi and Kumeka (2020) reported that there was no relationship between the exchange rate and stock prices when they examined the symmetry and asymmetry of the exchange rate–stock price nexus for 54 firms listed on the Nigerian Stock Exchange (NSE) by using an asymmetric autoregressive distributed lag (ARDL) model.

In the literature, it is noted that most of the time, the relationship between the stock price and one or two indices has been considered. To fill the gap in the literature, in this study, seventeen indices are included and assessed to find their influence on the stock price volatility of BRICS countries.

3. Methodology

3.1. Data

The monthly SPV data in US dollars from January 2000 (2000M1) to December 2023 (2023M12) were received from the database of the Global Economic Monitor (GEM), World Bank, IMF International Financial Statistics data, and OECD. Although the data were collected from 2000M01, data used in the analysis started from 2000M03 due to the two-month missing values for India, China, and South Africa. The varying structures of countries and the different scales of their data necessitated data standardization to enable their evaluation on the same basis. This standardization was achieved by taking March 2000 (2000M3) as the baseline value of 100. The value for the subsequent month was divided by the baseline value to calculate the monthly change. This calculated change was then multiplied by the baseline value for that month, ensuring the data were standardized relative to 2000M3.

In the first phase, data from 2000M3 to 2023M12 were utilized to conduct the analysis using classification techniques. In the second phase of this study, first, data from 2000M3 to 2023M12 were analyzed by both MLR and the best classification technique found in the first phase to identify the impact of indices on the SPV of BRICS countries during the global financial crisis and the COVID-19 crisis. Second, the data were analyzed in two crises, the global financial crisis and the COVID-19 pandemic crisis periods. To obtain reliable results, including pre- and post-crisis periods, a wide range of data for two crises was selected, 2007M01–2009M12 for the 2008 global financial crisis and 2018M01–2021M12 for the COVID-19 crisis. The data contain seventeen independent variables (indices) and one dependent variable (stock price volatility (SPV)).

Table 1. Indices and definitions.

Variables	Indices
${\mathrm{X}}_1$	CPI price percent y o y nominal seas adj a
${\mathrm{X}}_2$	Producer Prices Index (aggregated 2000) b
${\mathrm{X}}_3$	National Currency per SDR Period Average b
${\mathrm{X}}_4$	Domestic Currency per USD Period Average rate b
${\mathrm{X}}_5$	Lending Rate Percent per Annum b
${\mathrm{X}}_6$	Official Reserve Assets Gold Volume Fine Troy Ounces (aggregated 2000) b
${\mathrm{X}}_7$	Gold Holdings National Valuation USD (aggregated 2000) b
${\mathrm{X}}_8$	Exports Merchandise Customs current USD (aggregated 2000) seas adj c
${\mathrm{X}}_9$	Imports Merchandise Customs current USD (aggregated 2000) seas adj c
${\mathrm{X}}_{10}$	Nominal Effective Exchange Rate c
${\mathrm{X}}_{11}$	Real Effective Exchange Rate c
${\mathrm{X}}_{12}$	Total Reserves (aggregated 2000) c
${\mathrm{X}}_{13}$	Consumer Price Index All items d
${\mathrm{X}}_{14}$	Energy Index e
${\mathrm{X}}_{15}$	Crude oil average USD bbl e
${\mathrm{X}}_{16}$	Imports Merchandise Customs Price USD seas adj c
${\mathrm{X}}_{17}$	Industrial Production constant USD a
Y	Stock Market Prices USD c

Source: ^a: Global Economic Monitor (GEM) World Bank staff calculations based on Datastream data, accessed on 6 July 2024. ^b: International Financial Statistics (IFS) Metadata by Country (IFS), accessed on 19 July 2024. ^c: Global Economic Monitor (GEM) World Bank staff calculations based on Datastream and IMF International Finance Statistics data, accessed on 6 July 2024. ^d: OECD Data (2024), Inflation (CPI) (indicator). doi: 10.1787/eee82e6e-en (accessed on 1 May 2024) Cross-Country Indexes, Period-over-Period Change, 19 July 2024. ^e: World Bank Commodity Price Data (The Pink Sheet), accessed on 6 July 2024.

presents the list of seventeen indices with their definitions alongside stock price volatility. The dependent variable, SPVs, was transformed into a categorical format by computing the difference between the current year’s and the previous year’s SPVs to apply the classification techniques by WEKA. A positive difference is denoted by ‘P’ (1), whereas a negative difference is denoted by ‘N’ (0). For the multiple regression (MLR), the original data for SPVs were used. The independent variables, indices, were selected as they were not used in the literature together. Some studies have been carried out on the relationship between oil prices and stock markets (Boubaker & Larbi, 2022; Bagchi, 2017; Mudiangombe & Mwamba, 2023), the relationship between macroeconomic factors and stock prices (Wang et al., 2023; Zhou et al., 2019; Lone et al., 2023), volatility spillovers among BRICS countries’ stock markets (Panda et al., 2023), the relationship between the gold prices and the stock market (Trabelsi, 2019), and the relationship among the exchange rate fluctuations, domestic GDP (Jijin et al., 2022), and real interest rate changes (R. Hussain et al., 2023). Although there are many other indices besides the seventeen used, data for other indices, such as unemployment rates, were either unavailable or significantly incomplete for some countries and were therefore excluded from the analysis. This constitutes a limitation of this study. The combined use of these seventeen indices, typically used individually or in pairs in the literature, allows for a broader perspective on their effects on stock price volatility, bringing a new dimension to the literature.

3.2. Classification Techniques

Classification is one of the most important techniques in Data Mining (DM). The data are classified into distinct classes by utilizing DM algorithms. Various pieces of software perform classifications, such as SPSS and WEKA. In this study, WEKA 3.8.6 software was used for classification. There are many classification techniques built into WEKA implementation software, which was developed by the University of New Zealand under the General Public License (WEKA, n.d.). In WEKA, there are seven main classifiers: Bayes, Functions, Lazy, Meta, Misc, Rules, and Trees. These main classifiers contain different numbers of algorithms depending on their features. The use of classification techniques depends on the data type, nominal, ordinal, and interval. For this study, all applicable techniques were employed for the SPV data of BRICS countries, but among them, only seven techniques demonstrated better classification results. These are Naïve Bayes, Simple Logistic, Meta-Bagging, Classification via Regression, Meta-Logit Boost, Random Forest, and Random Tree.

Naïve Bayes is a probabilistic classification technique under the Bayes classifier. It works based on Bayes theory and uses estimator classes. Numeric estimator precision values are chosen based on the analysis of the training data (Elmi et al., 2009). It can be used for the data of binary class, missing class values, and nominal class.

Simple Logistic is a classification technique under the classifier Functions, and it is used for building a linear logistic regression model.

LogitBoost with simple regression functions as base learners is used for fitting the logistic model that predicts the probability of each class (Landwehr et al., 2005). It can be applied to the data of binary class, missing class values, and nominal class. The linear combination of the input features is converted into a probability value between 0 and 1 by the logistic function that is defined as

$$P\left(Y=1|X\right)={\displaystyle \frac{1}{1-e^{-z}}}$$

(1)

where $P\left(Y=1|X\right)$ represents the probability of the dependent variable being 1 given the values of the independent variables X and z is the linear combination of the independent variables and their coefficients.

$$z={\beta }_0+{\displaystyle {\sum }_{i=1}^n}{\beta }_i{X}_i$$

(2)

where ${\beta }_0$ represents the intercept and ${\beta }_i$ (i = 1, 2, …, n) are the coefficients corresponding to the independent variables $X_i$ (i = 1, 2, …, n), respectively (McHugh, 2012).

Meta classification indicates the usage of a combination of multiple classifiers. This combination is obtained in three steps. In the first step, multiple training subsets are constructed from a training set. In the second step, each classifier is individually constructed according to both the algorithm and data training subset. In the third step, the results of base classifiers are integrated, and results are obtained in a higher-level step called Meta classifier (Devi & Sundaram, 2016). Meta-Bagging is one of the algorithms under the Meta Classifier. It can perform classification and regression depending on the base learner (Breiman, 1996). It can be applied to the data of binary class, date class, missing class values, nominal class, and numerical class.

Classification via Regression performs classification using regression methods. Class is binarized, and one regression model is built for each class value (Frank et al., 1998). It can be applied to the data of binary class, missing class values, and nominal class.

The Meta-Logit Boost is another algorithm under the Meta classifier. It performs classification using a regression scheme as the base learner, and it can handle multi-class problems (Friedman et al., 2020). It can be applied to the data of binary class, missing class values, and nominal class.

Random Forest is a classifier under the main classifier Decision Trees. It includes many decision trees and is widely used for classification and regression. Random Forest collects the classifications among the many decision trees and chooses the best prediction as a result (Breiman, 2001). It can be applied to the data of binary class, missing class values, nominal class, and numerical class. Similar to the Random Forest, the Random Tree is also under the main classifier Decision Trees. It is used for constructing a tree that considers K randomly chosen attributes at each node. It performs no pruning, and it has an option to allow the estimation of class probabilities. It can be applied to the data of binary class, missing class values, nominal class, and numeric class.

Measures of Classifier Performance

In classification, classifier performance is measured by accuracy, Kappa statistic, mean absolute error (MAE), root mean square error (RMSE), and various performance metrics such as true positive (TP), false positive (FP), precision, recall, F-statistic, ROC Area, and confusion matrix.

One of the most commonly used performance measures is classification accuracy, which is the ratio of correct predictions to the total number of predictions made. It is calculated as the percentage of correctly predicted instances over the total number of instances. In the literature, 80% is assumed as the threshold point (Mile, 2023). Another measure is the Kappa statistic, which shows the agreement between the model’s prediction and true values in the range from −1 to 1; a value close to 1 represents almost perfect agreement (McHugh, 2012). The mean absolute error (MAE) and the root mean square error (RMSE) are similar measures for evaluating the models. MAE is the sum of the absolute value of the differences between all the expected values and predicted values, whereas RMSE is the quadratic mean of the differences between the observed values and predicted ones. Both have a range from 0 to 1; lower values show small errors. On the other hand, the confusion matrix displays a visualization of the classification performance that summarizes the number of correct and incorrect predictions in a matrix where rows represent the instances in an actual class and columns represent the instances in a predicted class. Among the classification metrics, precision measures the capability of the model that correctly predicts the positive class, whereas recall measures the capability of the model that correctly identifies the number of correct positive predictions made from all positive predictions. Precision is calculated as the sum of true positives (TPs) divided by the sum of true positives and false positives (FPs), while recall is calculated as the sum of TPs divided by the sum of TPs and false negatives (FNs). A large precision value minimizes the number of FPs, whereas a large recall value minimizes the number of FNs (Weiss, 2013). Another performance metric is the F statistic, which is calculated from precision and recall. It is the harmonic mean of precision and recall, dividing two times the product of precision and recall by the sum of them. Similar to precision and recall, its value changes in the range from a poor score of 0 to a perfect score of 1. In addition to other performance metrics, the Receiver Operator Characteristic (ROC Area), measures the overall performance of the classifier based on the area under the curve. It is a probability curve that plots the TP rate against the FP rate at various threshold values. The area under the curve changes from 0 to 1, and 1 indicates perfect classification (Weiss, 2013).

All these performance measures individually cannot indicate the classifier performance very well; therefore, while working on the performance of the classifier, some of the measures should be checked separately. In this work, among the performance metrics, accuracy, Kappa statistic, RMSE, TP rate, FP rate, precision, recall, F-measure, and ROC Area are evaluated for seven classifiers.

3.3. Multiple Linear Regression (MLR)

In the second phase of the work, MLR models were constructed to evaluate the impact of the indices on the SPV of BRICS countries during two crises. Therefore, MLR is applied to the SPV data of each BRICS country. In all models, SPV is the dependent variable, y, and the seventeen indices, $X_i$ (i = 1, 2, …, 17), illustrated in Table 1 are independent variables. The general MLR model is defined in Equation (3):

$$y={\beta }_0+{\displaystyle {\sum }_{i=1}^{17}}{\beta }_i{X}_i+\epsilon$$

(3)

where ${\beta }_0$ is the intercept, ${\beta }_i$ (i = 1, 2, …, 17) are the coefficients of the indices, mainly impact values on the indices, $X_i$ (i = 1, 2, …, 17), and $\epsilon$ is the random error.

The stepwise regression method analyzed the SPV data of BRICS countries in two crisis periods. The stepwise method includes the variable with the highest t-statistic in each step regardless of collinearity and provides different models. In selecting the best model among them, after testing the regression pitfalls, linearity, multicollinearity, normality, and heteroscedasticity and verifying the regression diagnostics for model assessment, the highest adjusted R-squared values, the smallest standard error values, and the change in R-squared values were considered (Ruzgar & Chua-Chow, 2023). The graphs for regression diagnostics are shown in Appendix A.

All MLR models satisfied the remedying violations of the required conditions. The PRESS (Predicted Residual Error Sum of Squares) statistic for all MLR models is very close to zero, indicating that the model accurately predicts the response variable across all data points. This suggests a good fit between the model and the data. Additionally, the Variance Inflation Factor (VIF) values are below 5, confirming that multicollinearity is not a concern. The VIF values of each variable are shown in the MLR output tables beside the coefficient of variables in the model in parentheses. The suitability of the models for prediction was tested using the ANOVA table with the F-test. The MLR model outputs are discussed in the following section. Residue diagnostics were conducted on all MLR models prior to execution, and selected results are presented in Appendix A.

4. Findings and Discussion

4.1. Stock Price Volatility of BRICS Countries

Financial market instability and economic disturbances, like financial crises or pandemics, have a significant impact on the economy, import, export, total reserves, and also the stock market of countries. During these disruptions, unemployment and inflation increase, production decreases, total reserves of countries, import and export rates, and currency change up or down based on the characteristics of the crisis. The SPV of BRICS countries has also been affected by these disruptions. Figure 1 illustrates the monthly SPV percent at constant 2010 prices for BRICS countries from 2000M03 (March 2000) to 2023M12 (December 2023). Since the data for the first two months of 2000 were missing for some countries, overall data started from 2000M03. The SPV of the countries demonstrates fluctuations during the study period.

The SPV of BRICS countries declined during the global financial crisis (2007M07 to 2009M02), the crisis from 2014M04 to 2016M02, and the COVID-19 pandemic (2020M01 to 2021M01) (Figure 1). Among these, the global financial crisis and the COVID-19 pandemic had the most severe impact on the SPV of BRICS countries, and also, they have different characteristics, so this study focuses on these two periods. Data for the global financial crisis were selected from 2007M01 to 2010M12, and for the COVID-19 pandemic crisis, from 2018M01 to 2021M12. To achieve more accurate results, the analysis includes pre- and post-crisis periods. The SPV of Brazil fluctuated until 2000M08 and then declined steadily until 2003M03. It increased with some fluctuations until 2008M05, followed by a sharp drop until 2008M12 due to the global crisis. After an upward trend until 2011M06, it declined again until 2016M06 due to political scandals (Operation Car Wash) and uncertainty. It then increased with fluctuations until 2020M01, sharply dropped in 2020M06 during the COVID-19 pandemic, and gradually increased afterward.

The SPV of Russia showed an overall increase until 2008M09, with fluctuations in 2002M05–2002M09 and 2003M10–2004M01. It sharply declined until 2009M01 and then increased until 2011M08. Fluctuations continued until 2020M01, followed by a decline in 2020M10. The fluctuations in Russia’s SPV are primarily due to events like the war with Georgia, economic sanctions following the annexation of Crimea in 2014, and the ongoing war with Ukraine. As a major commodity exporter, the SPV of Russia has also been negatively impacted by falling oil prices, the global financial crisis, and the COVID-19 pandemic.

The SPV of India shows a mostly declining trend until early 2003 and then slightly increases until 2004M04. After a three-month decline, it increases steadily until 2007M07. A sudden drop occurs in 2007M08 due to the global crisis, followed by a gradual increase until 2007M12. The global financial crisis impacts the SPV of India from 2008M01 to 2009M04. Afterward, it gradually increases with some fluctuations until 2011M07, declines between 2011M07 and 2012M06, and rises again with minor fluctuations until 2020M03, before sharply dropping for two months during the COVID-19 crisis. The SPV of India increased from 2020M05 to 2021M10 and then slowly declined with minor fluctuations until 2023M05. Missing SPV data for China from 2001M03 to 2006M01 and for South Africa due to country policies prevent any analysis during these periods.

The SPV of China gradually increased until 2007M10 and then sharply decreased until 2008M11 due to the global financial crisis which started in Asia first and then spread globally. After recovering, it steadily increased with minor fluctuations until 2015M06. It fluctuated until 2018M01 and then declined until the end of 2018. There was a slight increase until 2020M01, except for 2019M08, but it fell until 2020M04 due to the COVID-19 lockdown. It remained steady with minor fluctuations from 2020M04 to 2021M10, and fluctuations continued until the end of 2023.

The SPV of South Africa steadily increased until 2008M05 and then sharply declined due to the global financial crisis, which lasted until 2009M03. After recovering, it increased until early 2011 but dropped until 2011M11 due to political uncertainty, high inflation, and unemployment. It remained steady with moderate fluctuations until 2020M01 and then gradually declined until 2020M04. From there, it increased with minor fluctuations until the end of 2023.

The global financial crisis and the COVID-19 crisis had significant impacts on the SPV of BRICS countries, but the effects varied due to the diverse economic and political structure of each country. The SPV of all BRICS countries demonstrated sharp declines during these two crises, but the timing of the increases and decreases differed based on their economic resilience and structures.

4.2. Classification of SPV Data for BRICS Countries

The seven classification techniques utilized the SPV of each BRICS country using the classifiers in WEKA. Below, detailed presentations of the outcomes from seven classification techniques, Naïve Bayes, Simple Logistic, Meta-Bagging, Classification via Regression, Random Forest, and Random Tree, are presented.

4.2.1. Naïve Bayes

The Naïve Bayes technique was utilized for the SPV data of each country. The total number of instances of Brazil, Russia, and India is 277, but due to missing data, the total number of instances of China is 207, and that of South Africa is 250. For the classifier model, a full training set was used.

Table 2. The outcomes of Naïve Bayes for the SPV data of BRICS countries from 2000M03 to 2023M12.

	BRAZIL	RUSSIA	INDIA	CHINA	SOUTH AFRICA
Accuracy	59.21%	54.51%	58.85%	55.56%	58.80%
Kappa statistic	0.1776	0.0721	0.1306	0.1491	0.2079
RMSE	0.5307	0.5396	0.5151	0.5597	0.5720
TP Rate *	0.592	0.545	0.588	0.556	0.588
FP Rate *	0.416	0.473	0.462	0.398	0.365
Precision *	0.591	0.547	0.578	0.606	0.634
Recall *	0.592	0.545	0.588	0.556	0.588
F-Measure *	0.589	0.546	0.578	0.535	0.585
ROC Area *	0.640	0.569	0.611	0.534	0.581

* Weighted average is displayed.

displays the outcomes of Naïve Bayes classification for BRICS countries with accuracy, Kappa statistic, root mean squared error (RMSE), and performance metrics.

Naïve Bayes correctly classified the SPV of BRICS countries in order, 164 instances out of 277 for Brazil, 163 instances out of 277 for India, 147 instances out of 250 for South Africa, 115 instances out of 207 for China, and 151 instances out of 277 for Russia. Hence, the accuracies from highest to lowest are 59.21%, 58.85%, 58.80%, 55.56%, and 54.51% for Brazil, India, South Africa, China, and Russia, respectively. These accuracy rates show that the classification is moderate. The Kappa statistic, which measures the agreement between observed and expected classification results, is very low, changing in the range of 0.0721–0.2079. The other performance metric is root mean squared error, which measures the average deviation of predicted values from actual values in classification and is expected to be very low for a good performance of the classifier. All RMSE values are in the range from 0.5151 to 0.5720. This shows the classifier’s performance is not good. The true positive rate (TP rate) and false positive rate (FP rate) provide information about the sensitivity and specificity of the classification model. Table 2 shows the weighted average TP rate and FP rate. TP rates change from 0.545 to 0.592, and FP rates change from 0.365 to 0.473. The metrics precision, recall, F-measure, and ROC Area measure the performance of the classifier in terms of correctness and completeness. High precision indicates fewer false positives, high recall indicates fewer false negatives, F-measure is a balance between them, and high ROC Area indicates good classifier performance.

When comparing these metrics, India shows the best performance, and then South Africa and Russia follow. The performance of the Naïve Bayes classifier is low for China and Brazil. Based on the results, the Naïve Bayes classifier classified the data of India, South Africa, and Russia well and China moderately. Since Brazil has the lowest correctly classified instances and generally lower performance metrics than other countries, Brazil’s data were not classified well. The highest precision is for South Africa with a 0.634 value, and the lowest is 0.547 for Russia. The precision values are close to each other like recall values, F-measures, and ROC Area values. Based on these results, Naïve Bayes moderately classifies the SPV of BRICS countries.

4.2.2. Simple Logistic

Under the classifier “function”, the Simple Logistic technique is the second classifier to classify the SPV of BRICS countries. Full training data were used for evaluation, and the classification performance measures are displayed in

Table 3. The outcomes of the Simple Logistic classifier for the SPV data of BRICS countries from 2000M03 to 2023M12.

	BRAZIL	RUSSIA	INDIA	CHINA	SOUTH AFRICA
Accuracy	65.74%	64.26%	60.65%	64.25%	66.00%
Kappa statistic	0.3114	0.222	0.1307	0.2645	0.2604
RMSE	0.4651	0.4764	0.4811	0.4596	0.4643
TP Rate *	0.657	0.643	0.606	0.643	0.660
FP Rate *	0.346	0.454	0.485	0.383	0.414
Precision *	0.657	0.641	0.597	0.640	0.657
Recall *	0.657	0.643	0.606	0.643	0.660
F-Measure *	0.657	0.617	0.566	0.636	0.641
ROC Area *	0.719	0.656	0.631	0.647	0.656

* Weighted average is displayed.

. The correctly classified instances are 165 out of 250, 182 out of 277, 178 out of 277, 133 out of 207, and 168 out of 277 for South Africa, Brazil, Russia, China, and India, respectively. The accuracies change from 60.65% (India) to 66.00% (South Africa). They are close to each other but better than the accuracies of Naïve Bayes. The highest Kappa statistic has a 0.3114 value for Brazil, and the lowest has a 0.1307 value for India. These values show the agreement between observed and expected classification results is not good. RMSE values are also close to each other, changing from 0.4596 to 0.4811. TP rates, FP rates, and the other measures precision, recall, F-measure, and ROC Area values are close to each other for the individual measures. Although their values are better than the values of Naïve Bayes, the Simple Logistic technique also classified the SPV of BRICS countries moderately.

Simple Logistic generated two sets of equations on the output: one for positive SPV values and another for negative SPV values. The main difference between these equations is the signs of the coefficients of the indices. If a coefficient is positive for positive SPV values, it is negative for the negative SPV values and vice versa. The following logistic equations were achieved for positive values of SPV:

$${\mathrm{Z}}_{\mathrm{B}\mathrm{r}\mathrm{a}\mathrm{z}\mathrm{i}\mathrm{l}}=4.22+0.03{\mathrm{X}}_1-0.04{\mathrm{X}}_2+0.03{\mathrm{X}}_3-0.01{\mathrm{X}}_5-0.01{\mathrm{X}}_9-0.02{\mathrm{X}}_{10}+0.04{\mathrm{X}}_{11}+0.15{\mathrm{X}}_{13}-0.01{\mathrm{X}}_{16}$$

(4)

$${\mathrm{Z}}_{\mathrm{R}\mathrm{u}\mathrm{s}\mathrm{s}\mathrm{i}\mathrm{a}}=0.92-0.03{\mathrm{X}}_1-0.03{\mathrm{X}}_5+0.01{\mathrm{X}}_{11}+0.01{\mathrm{X}}_{15}$$

(5)

$${\mathrm{Z}}_{\mathrm{I}\mathrm{n}\mathrm{d}\mathrm{i}\mathrm{a}}=1.34-0.05{\mathrm{X}}_1-0.01{\mathrm{X}}_4-0.1{\mathrm{X}}_5+0.01{\mathrm{X}}_{11}-0.06{\mathrm{X}}_{13}$$

(6)

$${\mathrm{Z}}_{\mathrm{C}\mathrm{h}\mathrm{i}\mathrm{n}\mathrm{a}}=-4.06-0.13{\mathrm{X}}_1-0.01{\mathrm{X}}_2+0.28{\mathrm{X}}_3+0.46{\mathrm{X}}_4+0.23{\mathrm{X}}_5-0.02{\mathrm{X}}_{11}-0.03{\mathrm{X}}_{13}-0.01{\mathrm{X}}_{14}-0.01{\mathrm{X}}_{16}$$

(7)

$${\mathrm{Z}}_{\mathrm{S}\mathrm{o}\mathrm{u}\mathrm{t}\mathrm{h} \mathrm{A}\mathrm{f}\mathrm{r}\mathrm{i}\mathrm{c}\mathrm{a}}=2.33+0.02{\mathrm{X}}_1-0.03{\mathrm{X}}_4-0.01{\mathrm{X}}_6-0.04{\mathrm{X}}_5+0.02{\mathrm{X}}_{11}-0.13{\mathrm{X}}_{13}-0.01{\mathrm{X}}_{14}-0.01{\mathrm{X}}_{16}-0.01{\mathrm{X}}_{17}$$

(8)

In terms of the results of Simple Logistic, $X_1$ (CPI price percent y o y nominal seas adj), $X_5$ (Lending Rate Percent per Annum), and $X_{11}$ (Real Effective Exchange Rate) are common indices. $X_1$ (CPI price percent y o y nominal seas adj) has a positive impact on the SPV of Brazil and South Africa, and it has a negative effect on the SPV of Russia, India, and China. $X_5$ (Lending Rate Percent per Annum) has different effects on the SPV of BRICS countries. It has a negative effect on the SPV of Brazil, Russia, India, and South Africa, but a positive effect on the SPV of China. Moreover, $X_{11}$ (Real Effective Exchange Rate) has a positive influence on the SPV of Brazil, Russia, India, and South Africa, whereas it has a negative influence on the SPV of China. Other than these common indices, $X_{13}$ (Consumer Price Index All items) has an impact on four countries, a positive influence on the SPV of Brazil and a negative influence on the SPV of India, China, and South Africa.

4.2.3. Meta-Bagging

Meta-Bagging classified the SPV of BRICS countries, and the results are presented in

Table 4. The outcomes of Meta-Bagging for the SPV data of BRICS countries from 2000M03 to 2023M12.

	BRAZIL	RUSSIA	INDIA	CHINA	SOUTH AFRICA
Accuracy	83.39%	87.73%	81.59%	85.51%	84.00%
Kappa statistic	0.6671	0.7437	0.6134	0.7048	0.6651
RMSE	0.3699	0.3697	0.3742	0.3622	0.3759
TP Rate *	0.834	0.877	0.816	0.855	0.840
FP Rate *	0.167	0.147	0.217	0.156	0.186
Precision *	0.834	0.880	0.819	0.856	0.841
Recall *	0.834	0.877	0.816	0.855	0.840
F-Measure *	0.834	0.876	0.812	0.854	0.838
ROC Area *	0.915	0.947	0.917	0.775	0.850

* Weighted average is displayed.

. Full training data, bagging with 10 iterations, and base learner were utilized for the evaluation process.

The accuracies of the classifications with Meta-Bagging are adequate-level, changing from 81.59% to 87.73%, and better than the accuracies of the Naïve Bayes and Simple Logistic classifiers. In terms of correctly classified instances, Russia demonstrates a high accuracy of 87.73% (243 instances out of 277), and China closely follows with 85.51% (177 instances out of 207) accuracy. For South Africa, the classifier achieved a good accuracy of 84% (210 instances out of 250). For Brazil and India, the Meta-Bagging classifier classified the data again with adequate accuracies of 83.39% and 81.51%, respectively. The Kappa statistic for Russia is adequate, but for China, Brazil, South Africa, and India, it is moderate. The RMSE value is the highest for the SPV of South Africa at 0.3759 and the lowest for the SPV of China at 0.3622. These values are not close to zero. The TP and FP rates for all BRICS countries are close to each other. The TP rates are in the range of 0.816–0.877, and FP rates are in the range of 0.147–0.217. In terms of the performance metrics precision and F-measure, the SPV of Russia demonstrates the highest performance with 0.880, followed by the precision and F-measure values for the SPV of China, South Africa, Brazil, and India. Moreover, in terms of the ROC Area, the Meta-Bagging classifier demonstrates performance from strong to weak for Russia, India, Brazil, South Africa, and China, in order. Based on the results in the table, Russia stands out as the best-performing country.

4.2.4. Meta-Classification via Regression

The Meta-Classification via Regression technique was utilized to classify the SPV of BRICS countries, and the results are presented in

Table 5. The outcomes of Meta-Classification via Regression for the SPV data of BRICS countries from 2000M03 to 2023M12.

	BRAZIL	RUSSIA	INDIA	CHINA	SOUTH AFRICA
Accuracy	63.90%	64.62%	75.45%	66.67%	63.60%
Kappa statistic	0.2739	0.2473	0.4839	0.3190	0.2081
RMSE	0.4707	0.4630	0.4167	0.4558	0.4649
TP Rate *	0.639	0.646	0.755	0.667	0.636
FP Rate *	0.366	0.408	0.283	0.351	0.439
Precision *	0.638	0.640	0.755	0.665	0.628
Recall *	0.639	0.646	0.755	0.667	0.636
F-Measure *	0.638	0.634	0.750	0.667	0.615
ROC Area *	0.699	0.697	0.819	0.692	0.642

* Weighted average is displayed.

. Full training data were used for the evaluation process.

Meta-Classification via Regression classified the SPV data as moderately similar to Simple Logistic and better than Naïve Bayes. For India, 209 instances out of 277 were correctly classified, with an accuracy of 75.45%. It is followed by China with an accuracy of 66.67% (138 instances out of 207) and Russia with an accuracy of 64.62% (179 instances out of 277). The accuracies for Brazil and South Africa are very close to each other, and they are 63.90% (177 instances out of 277) for Brazil and 63.60% (159 instances out of 250) for South Africa. The Kappa statistics are lower than 0.5. They range from 0.2081 to 0.4839. The RMSEs also do not satisfactorily say that this classifier classified the data well; they are in the range of 0.4167–0.4707. The other metrics, TP rate and FP rate, are not at a satisfactory level. India has the highest TP rate (0.755) and the lowest FP rate (0.283). The TP rates change in the range of 0.636 and 0.755, while the FP rates change in the range of 0.283 and 0.439. Precision, recall, and F-measures demonstrate moderate performance with the highest value of 0.755 for the SPV of India. China, Russia Brazil, and South Africa follow India. ROC Area values are similar to each other, except for India whose ROC Area value is 0.819, while the others have values from 0.642 to 0.699. When comparing the Meta-Classification via Regression with the previous classifiers, it classifies the data better than Naive Bayes, similar to Simple Logistic, and worse than Meta-Bagging classifiers. Overall, the Meta-Classification via Regression technique classified the SPV of BRICS countries moderately.

The Meta-Classification via Regression technique provides the regression equations in the output. The following equations have been obtained for the BRICS countries:

$$Y_{Brazil}=-0.1076-{0.0272X}_1-{0.2898X}_3+0.5082X_4+0.0082X_5-0.0036X_8+0.0046 X_9$$

(9)

$$Y_{Russia}=1.5671+0.0001X_2-0.0021X_6+0.0016X_5+0.0016X_9-0.012X_{10}-0.001X_{11}+0.0162X_{14}-0.0275X_{15}$$

(10)

$$Y_{India}=1.423-0.0045X_2+0.0036X_3-0.0025X_4-0.0002X_7-0.0087X_5-0.0002X_9-0.0019X_{10}+0.0128X_{11}-0.0002X_{12}-0.0113X_{13}-0.0077 X_{14}+0.0018X_{15}$$

(11)

$$Y_{China}=-0.1226+0.0822X_1-0.0225X_{13}-0.2979X_5+0.0006X_8-0.0006X_9+0.0335X_{11}-0.0008X_{12}+0.0043X_{14}+0.013X_{16}$$

(12)

$$Y_{South Africa}=-0.0021+0.0056X_2-0.0177X_{11}-0.0018X_{12}+0.0117X_{14}-0.0145X_{15}+0.0128X_{16}$$

(13)

According to Equations (9)–(13), there is no common index that has an impact on the SPV of the BRICS countries. Although there is no common index for all countries, some indices impact the SPV of four of them. For example, $X_5$ (Lending Rate Percent per Annum) and $X_9$ (Imports Merchandise Customs current USD (aggregated 2000) seas adj) are common indices for Brazil, Russia, India, and China, while $X_{11}$ (Real Effective Exchange Rate) and $X_{14}$ (Energy Index) are the common indices for Russia, India, China, and South Africa. The other indices vary. All these results show that indices having an impact on the SPV of countries depend on the countries’ economic, financial, and political structures and the events occurring around them.

4.2.5. Meta-Logit Boost

Meta-Logit Boost is another classifier that was utilized for the SPV of BRICS countries. A full training set was used for the classifier model. Ten iterations were applied.

Table 6. The outcomes of Meta-Logit Boost for the SPV data of BRICS countries from 2000M03 to 2023M12.

	BRAZIL	RUSSIA	INDIA	CHINA	SOUTH AFRICA
Accuracy	73.65%	71.84%	74.37%	78.26%	73.20%
Kappa statistic	0.4755	0.3907	0.4474	0.555	0.4118
RMSE	0.4213	0.4317	0.4243	0.3939	0.4338
TP Rate *	0.736	0.718	0.744	0.783	0.732
FP Rate *	0.258	0.348	0.318	0.235	0.346
Precision *	0.744	0.731	0.758	0.784	0.751
Recall *	0.736	0.718	0.744	0.783	0.732
F-Measure *	0.736	0.720	0.730	0.780	0.713
ROC Area *	0.817	0.780	0.804	0.737	0.708

* Weighted average is displayed.

illustrates the results of Meta-Logit Boost from WEKA across BRICS countries.

According to the results presented in Table 6, the correctly classified instances are 204, 199, and 206 out of 277 instances, 162 out of 207 instances, and 183 out of 250 instances. Based on these, China shows the highest accuracy (78.26%). India, Brazil, South Africa, and Russia follow China with accuracies of 74.37%, 73.65%, 73.20%, and 71.84%, respectively. The Kappa statistic shows that China has the highest agreement between observed and expected accuracy, (0.555), followed by Brazil (0.4755), India (0.4474), South Africa (0.4118), and Russia (0.3907). Kappa statistic values are low, indicating low agreement. The RMSE values are in the range of 0.3939 and 0.4338. These are higher than the expected value. When considering the TP rate (FP rate), China displays the highest (lowest) rate; the other countries India, Brazil, South Africa, and Russia follow in order. In terms of the performance metrics precision, recall, and F-measure, again, China has the highest values, and the other countries follow it closely. According to another performance metric, ROC Area, Brazil demonstrates the highest performance (0.817), and then India (0.804), Russia (0.780), and China (0.737) follow. South Africa has the lowest ROC Area value, 0.708. The output provides the performance metrics for positive, negative, and weighted average values, but for simplicity, only weighted averages are presented in the tables. The different performances for positive and negative values affect the change in the order of the highest performance of the countries. Brazil shows the highest ROC Area performance, whereas China displays the highest performance for the other metrics.

4.2.6. Random Forest

The sixth classification technique utilized for the SPV of BRICS countries is Random Forest. Full training data were utilized for evaluation, which employed bagging with 100 iterations, and the results are illustrated in

Table 7. The outcomes of Random Forest for the SPV data of BRICS countries from 2000M03 to 2023M12.

	BRAZIL	RUSSIA	INDIA	CHINA	SOUTH AFRICA
Accuracy	100%	100%	100%	100%	100%
Kappa statistic	1.000	1.000	1.000	1.000	1.000
RMSE	0.1793	0.1888	0.1833	0.1868	0.1821
TP Rate *	1.000	1.000	1.000	1.000	1.000
FP Rate *	0.000	0.000	0.000	0.000	0.000
Precision *	1.000	1.000	1.000	1.000	1.000
Recall *	1.000	1.000	1.000	1.000	1.000
F-Measure *	1.000	1.000	1.000	1.000	1.000
ROC Area *	1.000	1.000	1.000	0.978	0.989

* Weighted average is displayed.

. Based on the results in Table 7, Random Forest classified the SPV of all BRICS countries perfectly.

All instances are correctly classified with 100% accuracy. The Kappa statistic for all countries is perfect, 1.000. All TP rates, precisions, recalls, and F-measures show impressive perfect performances. The RMSE values are very low. When compared to the other five classifiers, Random Forest showed the best performance.

4.2.7. Random Tree

Random Tree is similar to the Random Forest, classifying the SPV of BRICS countries perfectly. The results are shown in

Table 8. The outcomes of Random Tree for the SPV data of BRICS countries from 2000M03 to 2023M12.

	BRAZIL	RUSSIA	INDIA	CHINA	SOUTH AFRICA
Accuracy	100%	99.64%	100%	99.52%	100%
Kappa statistic	1.000	0.9926	1.000	0.9902	1.000
RMSE	0.000	0.044	0.0222	0.0491	0.000
TP Rate *	1.000	0.996	1.000	0.995	1.000
FP Rate *	0.000	0.005	0.000	0.006	0.000
Precision *	1.000	0.996	1.000	0.995	1.000
Recall *	1.000	0.996	1.000	0.995	1.000
F-Measure *	1.000	0.996	1.000	0.995	1.000
ROC Area *	1.000	1.000	1.000	0.900	0.944

* Weighted average is displayed.

. Full training data were utilized for evaluation.

In terms of correctly classified instances, all data from Brazil, India, and South Africa were classified with 100% accuracy. Russia and China have one incorrectly classified instance with almost 100% accuracy. The Kappa statistics show perfect agreement between observed and expected accuracy for all BRICS countries. The RMSE values are very small when compared with Random Forest, except for Russia and China. The performance metrics precision, recall, F-measure, and ROC Area are also almost perfect.

4.2.8. Comparison of the Classifiers

All available classification techniques in WEKA were applied to the SPV data of BRICS countries; however, some of them classified the data with very low accuracy, Kappa statistic and performance statistics, J48, Decision Tree, and Decision Stump. The above seven classification techniques classified the data better than the others, so they were included in this study.

In comparing the seven classification techniques, the initial consideration is given to the accuracy, and then the Kappa statistic and RMSE are considered. In terms of accuracy, it is followed the accuracy criteria. If the accuracy exceeds 80%, the classification technique classifies the data strongly, and if it achieves 100% or close, the classification technique classifies the data perfectly. Based on these criteria, Random Forest and Random Tree demonstrated perfect classification, and Meta-Bagging follows them with strong classification. The other four classification techniques classified the data moderately. Similarly, using the criteria “the high values Kappa statistic indicates strong agreement between observed and expected classification”, Random Forest and Random Tree demonstrated overwhelming agreement between observed and expected classification results. From the rest, only Meta-Bagging showed moderate agreement. The Kappa statistic of the others is very low. In classification, the RMSE measures the average deviation of predicted values from the actual values; hence, for the optimal performance of the classification technique, a low value of RMSE is expected. When comparing the RMSE values, Random Tree showed the best performance. The RMSE values of Brazil and South Africa are zero, and the RMSE values of India, Russia, and China are almost zero. Random Forest follows Random Tree with very low RMSE values, changing in the range of 0.1793 and 0.1888. The RMSE values of the other classification techniques are in the range of 0.3622 and 0.5597. While high performance measures were given consideration to compare the seven different classification techniques, overfitting and bias in techniques were also considered, giving Random Forest a concern of more overfitting compared to Random Tree and other methods given almost all performance measures were at the highest levels. When the seven classification techniques are compared in terms of the performance metrics, Random Tree and Random Forest demonstrated the best classification performance among the seven classification techniques. This shows that these two tree-based classification techniques commonly classify the SPV data of BRICS countries; hence, the hypothesis “H1: There exists a common best classifier classifying the data of BRICS countries” is rejected. In conclusion, the two tree-based techniques, Random Tree and Random Forest, can be utilized to find the indices that have an impact on the SPV of BRICS countries, and the results provide good information for investors.

4.3. Crises

Crises have a big impact on not only a country’s economy but also on the stock market. During the study period, 2000M3–2023M12, the world faced three crises, the 2007–2009 global financial crisis, the 2014–2016 crisis, and the 2020–2021 COVID-19 pandemic crisis. Of these crises, only two of them, the global financial crisis and the COVID-19 pandemic crisis, are considered to identify the indices that impact the SPV of BRICS countries. To search for a significant effect on the SPVs and to determine the common indices influencing the SPVs during the two crisis periods, the MLR and Random Tree classification techniques were utilized for the seventeen indices given in Table 1. In Section 4.2.8, it was found that the Random Tree and Random Forest classification techniques classified the SPVs perfectly; however, Random Tree demonstrated better results than Random Forest, so in this section, from the classification techniques, only Random Tree along with MLR is used to analyze the SPV data.

4.3.1. The 2007–2010 Global Financial Crisis

This crisis was the most severe worldwide economic crisis that originated in the United States as a result of the collapse of the US housing market. It is also called subprime mortgage crisis (Duignan, 2024). It started in mid-2007 and ended in mid-2009, but the recovery was very slow. It is the worst economic downturn since the Great Depression which continued for ten years from 1929 to 1939. It dramatically affected the international financial system, banks, insurance companies, and mortgage lenders. During the crisis, numerous large financial firms faced financial distress, and financial markets experienced significant turbulence. The crisis threatened to collapse the international financial system, leading to the failure or near-failure of several major investment and commercial banks, including the 168-year-old Lehman Brothers. It also impacted mortgage lenders, insurance companies, and savings and loan associations, ultimately triggering the Great Recession. Stock markets experienced their most significant declines in over 75 years. Financial markets became unfunctional as everyone tried to sell simultaneously and many institutions wanted new financing (Federal Reserve History, 2013).

MLR Results for 2007–2010

The MLR used the data for each BRICS country for the 2007–2010 and 2018–2021 crisis periods. In this analysis, the stock market prices in USD were used instead of categorical data. The MLR results for the 2007–2010 crisis are shown in

Table 9. Multiple Linear Regression outputs for 2007–2010 crisis.

	BRAZIL	RUSSIA	INDIA	CHINA	SOUTH AFRICA
R-Squared	0.956	0.919	0.839	0.801	0.810
Std. Error of the Estimate	0.0009990963	0.001968757	0.001467655	0.0016610777	0.001388063
ANOVA Sig.	<0.001	<0.001	<0.001	<0.001	<0.001
Constant	0.128574 *	0.020494 *	0.018491 *	−0.023049 *	−0.008262 ***
$X_1$		0.001537 * (1.473)
$X_2$	−0.000710 * (1.541)		0.000410 * (2.340)
$X_3$
$X_4$
$X_5$					0.001402 * (2.395)
$X_6$		0.000108 * (1.399)
$X_7$
$X_8$	0.0000237 * (2.745)				−0.000024 * (3.562)
$X_9$
$X_{10}$
$X_{11}$	−0.000540 * (3.606)		−0.000506 * (1.430)	0.000421 * (1.597)
$X_{12}$	0.0000042 *** (3.073)				0.000033 * (2.407)
$X_{13}$				−0.000898 *** (1.088)
$X_{14}$			0.000132 * (1.987)
$X_{15}$	−0.0000545 * (3.044)	0.000224 * (1.886)			0.000108 * (3.674)
$X_{16}$
$X_{17}$		0.000155 * (1.772)		−0.000021 ** (1.503)

Dependent variable: Stock Markets USD, * p < 0.001, ** p < 0.01,*** p < 0.05. VIF values are given beside the coefficients in parentheses.

. The VIF values of the variables are presented in parentheses beside the variable, and the selected residue diagnostic graphs are given in Appendix A.

Based on the MLR results presented in Table 9, the R-squared values for each country are very high, ranging from 0.801 to 0.956. This indicates that the indices in the models explain between 80.1% and 95.6% of the variance in SPVs. Additionally, the standard errors of the estimates are highly low, which highlight the reliability of the models. Among the BRICS countries, Brazil has the strongest model performance with the highest R-squared value and the lowest standard error of the estimate. Russia follows Brazil with the second-highest R-squared, but the highest standard error of estimate. These results indicate the models fit the data well. India demonstrates a moderate R-squared, rising commodity prices, and a low standard error of the estimate. China and South Africa show weaker R-squared values when compared to the other countries, but the models remain statistically significant. Moreover, ANOVA results show that all models are statistically significant at the 0.001 level of significance. This presents strong evidence that the models are used for prediction. The indices in the models are all significant at the level of 0.001, 0.01, and 0.05 (Table 9).

From Table 9, MLR results for Brazil indicate five indices that significantly influence the SPV. Among these, $X_8$ (Exports Merchandise Customs current USD (aggregated 2000) seas adj) and $X_{12}$ (Total Reserves (aggregated 2000)) have a positive impact on the SPV. Conversely, $X_2$ (Producer Prices Index (aggregated 2000)), $X_{11}$ (Real Effective Exchange Rate), and $X_{15}$ (Crude oil average dollars bbl) have a negative effect on the SPV. A big portion of Brazil’s economy depends on the export of commodities, particularly iron ore, petroleum, and soybean. During the crisis period, rising commodity prices combined with political instability affected Brazil’s economic performance and, therefore, the stock market. With increasing international commodities and domestic expansion of social programs, Brazil experienced a severe economic crisis (Akrur, 2016). The findings contribute to the condition of the country.

The MLR results for Russia indicate that four indices influence the SPV, all having a positive impact. They are $X_1$ (CPI price percent y o y nominal seas adj), $X_6$ (Domestic Currency per USD Period Average rate), $X_{15}$ (Crude oil average dollars bbl), and $X_{17}$ (Industrial Production constant USD (aggregated 2000)). Global crisis dreadfully affected Russian financial markets due to the war with Georgia and dropped prices of commodities. Russia is a major exporter of commodities such as metal, gas, and oil, and the Russian economy depends on crude oil and gas exports. Russia has participated militarily in several conflicts across former Soviet states and other nations, including its conflict with Georgia in 2008. In the model, the strong positive effect of $X_{15}$ (Crude oil average dollars per bbl) on SPV is consistent with Russia’s current situation. The collapse of the prices of oil commodity exports compounded the effects of the financial crisis. Therefore, any oil price fluctuation negatively (positively) affects stock market performance. Since a higher (lower) oil price represents higher (lower) input costs, oil price changes are likely to directly affect the earnings of an organization, which contributes to the findings of Jebran et al. (2017). This also contributes to the economic conditions of Russia.

The MLR results for India reveal three indices that influence the SPV. Among these, $X_2$ (Producer Prices Index (aggregated 2000)) and $X_{14}$ (Energy Index) have a strong positive effect on the SPV, while $X_{11}$ (Real Effective Exchange Rate) has a negative impact. India has cheap labor and specializes in exporting commodities such as textiles, chemicals, machinery, and software services while importing oil (Mroua & Trabelsi, 2020). Trade plays a crucial role in the economies of BRICS countries. Brazil and Russia are net oil exporters, whereas China, South Africa, and India are net oil importers. Changes in oil prices have a significant impact on economic stability and currency values; therefore, they affect stock market indices.

The MLR results for China indicate that the SPV is positively affected by $X_{11}$ (Real Effective Exchange Rate) and negatively affected by $X_{13}$ (Consumer Price Index All items) and $X_{17}$ (Industrial Production constant USD (aggregated 2000)). China, which has one of the largest economies in the world by GDP, was also affected by the global economic crisis. The growth rate has been declining since 2007, but in late 2008, GDP increased by 9%, and China did not have a recession. China benefits from a large labor pool and is a leading exporter of electronics, machinery, textiles, and other goods (Mroua & Trabelsi, 2020). The indices in the model contribute the studies of Radulescu et al. (2014), Mroua and Trabelsi (2020), and Salisu et al. (2021).

Finally, the MLR results for South Africa shows that $X_{12}$ (Total Reserves (aggregated 2000)), $X_{15}$ (Crude oil average dollars bbl), and $X_5$ (Lending Rate Percent per Annum), have positive influence on the SPV; however, $X_8$ (Exports Merchandise Customs current USD (aggregated 2000) seas adj.) has negative impact. South Africa, classified as a middle-income country, depends on financial services and exports of manufactured goods and primary commodities such as gold, platinum, and chrome to drive its economy. Steytler and Powell (2010) stated that the main reasons for the recession in South Africa were mostly related to reducing trade and fluctuation in financial flows, increasing public expenditure, and a sharp reduction in consumer demand. These led to a fragile economy and growing job losses, and these circumstances prevented foreign investors from investing in South Africa.

Based on the MLR results in Table 9, there are no common indices that have an influence on the SPVs. This rejects the hypothesis “H2: There are common indices in MLR results, influencing the SPV of BRICS countries during the 2007–2010 crisis”. While Brazil and South Africa have three common indices, $X_8$ (Exports Merchandise Customs current USD (aggregated 2000) seas adj.), $X_{12}$ (Total Reserves (aggregated 2000)), and $X_{15}$ (Crude oil average dollars bbl), Brazil, India and China have one common index, $X_{11}$ (Real Effective Exchange Rate). In addition, Russia and China have one common index, $X_{17}$ (Industrial Production constant USD (aggregated 2000)), which positively affects the SPV of Russia and negatively affects the SPV of China. In conclusion, each country’s model demonstrates a unique pattern of significance and contributions, highlighting different influential factors.

MLR Results for 2018–2021

The 2018–2021 COVID-19 pandemic structure is different from the global financial crisis. It started in China and spread all around the world. After the World Health Organization (WHO) declared the COVID-19 pandemic on 11 March 2020, the COVID-19 pandemic has affected economies globally, with a severe impact on stock market indexes, the banking sector, and many indicators of financial performance (Assous et al., 2020; Ruzgar & Chua-Chow, 2023). The shutdowns seriously affected the economies due to a decrease in commodity prices, production, demand, and investments and an increase in unemployment and inflation (Demers et al., 2021; Ruzgar & Chua-Chow, 2023). The reduction in the demand for travel and the lack of factory activity due to the COVID-19 pandemic significantly impacted oil demand, causing its price to fall. These variations demonstrate that the impact of crises on a country’s economy depends not only on its economic and socio-political structures and resources but also on the nature of the crisis itself (Ruzgar & Chua-Chow, 2023).

MLR analysis was utilized for the SPV data for each BRICS country for the 2018–2021 crisis, and the results are displayed in

Table 10. The 2018–2021 Multiple Linear Regression output.

	BRAZIL	RUSSIA	INDIA	CHINA	SOUTH AFRICA
R Square	0.716	0.922	0.980	0.792	0.931
Std. Error of the Estimate	0.002179877	0.001167656	0.000277608	0.000743215	0.000560249
ANOVA Sig.	<0.001	<0.001	<0.001	<0.001	<0.001
Constant	0.042096 *	0.027453 *	0.009410 *	0.029232 *	−0.001857 *
$X_1$			−0.000142 * (1.348)
$X_2$			−0.000124 * (1.173)
$X_3$			0.000183 * (1.034)
$X_4$		0.000739 * (2.821)			0.000909 * (3.157)
$X_5$
$X_6$
$X_7$				0.000001 * (1.004)
$X_8$	−0.000020 * (1.083)
$X_9$
$X_{10}$			−0.000004 * (1.141)
$X_{11}$	0.000250 * (1.083)			0.000165 * (1.004)
$X_{12}$		0.000012 * (2.599)
$X_{13}$					0.000019 * (2.896)
$X_{14}$
$X_{15}$		0.000156 * (1.157)
$X_{16}$
$X_{17}$					−0.000014 ** (2.943)

Dependent variable: Stock Market (USD). * p < 0.001, ** p < 0.01. VIF values are given beside the coefficients in parentheses.

.

The regression analysis highlights varying strengths and dynamics in the models for BRICS countries (Table 10). India demonstrates the strongest model fit with the highest R-squared value (0.980) and the lowest standard error of the estimate (0.000278). South Africa and Russia follow with high R-squared values of 0.931 and 0.922, respectively. Their standard error of estimates is moderately low, as for the other countries. China and Brazil demonstrate a weaker model fit with an R-squared of 0.792 and 0.716 and a standard error of 0.000743 and 0.00218, respectively, but retain significance. These results show the models fit the data well. In terms of the use of models for prediction and the reliability of the models, ANOVA results demonstrate that all models are statistically significant at the 0.001 level of significance.

The MLR model for Brazil was statistically significant with the lowest R-squared and a higher error compared the other countries; it has two indices that influence the SPV, $X_8$ (Exports Merchandise Customs current USD (aggregated 2000) seas adj) and $X_{11}$ (Real Effective Exchange Rate). While $X_{11}$ (Real Effective Exchange Rate) positively affects the SPV, $X_8$ (Exports Merchandise Customs current USD (aggregated 2000) seas adj) negatively affects it. The lockdown during the COVID-19 pandemic negatively affected the economy, concluding with high interest rates and inflation and reduced consumption and investment. Increasing international commodities and domestic expansion of social programs, among others, Brazil experienced a severe economic crisis. Operation Car Wash was another reason for the economic crisis in Brazil (Lal, 2023). Brazil saw substantial growth in the early 2010s until political and economic difficulties led to a recession, from which recovery has been difficult.

The MLR model for Russia includes three indices that influence the SPV; all have a positive influence on the SPV. These indices are $X_4$ (Domestic Currency per USD Period Average rate), $X_{12}$ (Total Reserves (aggregated 2000)), and $X_{15}$ (Crude oil average dollars bbl). Since the Russian economy depends on mainly crude oil and gas exports, the reduction in the demand for travel and the lack of factory activity due to the COVID-19 pandemic significantly impacted oil demand, causing its price to fall. Additionally, with the continuing annexation of Crimea from Ukraine since 2014, Russia further annexed four other regions in 2022 amidst an ongoing invasion (Sonnenfeld, 2022). This led Russia to be the most sanctioned country in the world, so the economy, mainly GDP, GDP growth, and stock market, has been negatively affected. According to BBC News, the US and UK banned Russian oil and natural gas (https://www.bbc.com/news/world-europe-60125659 (accessed on 23 February 2024)).

The MLR model for India indicates four indices that influence the SPV. These are completely different from the indices in the other models. Among them, $X_3$ (National Currency per SDR Period Average) has a positive impact on the SPV while $X_1$ (CPI price percent y o y nominal seas adj), $X_2$ (Producer Prices Index (aggregated 2000)), and $X_{10}$ (Nominal Effective Exchange Rate) have a negative impact on the SPV.

The MLR model for China includes only two indices, $X_7$ (Gold Holdings National Valuation USD (aggregated 2000)) and $X_{11}$ (Real Effective Exchange Rate). Both of the indices positively affect the SPV. On 20 February 2020, stock markets collapsed all around the world due to COVID-19 pandemic uncertainty, and the stock market in China declined by 8%. In 2021, China had a property sector crisis caused by the debt limits of the Evergrande Group and other Chinese property developers.

Finally, the MLR model for South Africa indicates three indices. Two of them, $X_4$ (Domestic Currency per USD Period Average rate) and $X_{13}$ (Consumer Price Index All items), have a positive impact on the SPV while $X_{17}$ (Industrial Production constant USD (aggregated 2000)) has a negative impact on the SPV. South Africa faced significant economic challenges during the pandemic. The lockdown increased the job-lost rate and inflation while decreasing trade, GDP, and stock markets. These circumstances prevented foreign investors from investing in South Africa. The impact of foreign investment was reflected in the stock markets, with a widespread decline observed in the market indices.

When comparing the MLR models to identify common indices impacting the SPV of BRICS countries, no common indices were found to influence the SPV during the 2018–2021 period. This result leads to the rejection of the hypothesis “H3: There are common indices in MLR results influencing the SPV of BRICS countries during the 2018–2021 crisis.” The absence of a common index can be attributed to the diverse economic and socio-political structures of the countries and the varying nature of the crises.

Comparing MLR Results for 2007–2010 and 2018–2021 Crises

For the 2007–2010 crisis, MLR results in Table 9 indicate that Brazil exhibits the strongest model fit among the BRICS countries with the highest R-squared value and the lowest standard error. Then, Russia with the second-highest R-squared, India with a moderate R-squared, China with a weaker R-squared, and South Africa with the smallest R-squared follow Brazil. All models are statistically significant. Similarly, for the 2018–2021 COVID-19 crisis, MLR results show that India demonstrated the best performance with a high R-squared and the lowest standard error among the BRICS countries. South Africa and Russia follow with high R-squared values and low standard errors. China showed a moderate model fit with a moderate R-squared. Among the BRICS countries, the MLR model for Brazil is weaker than the others. Similar to the 2007–2010 global crisis, all models are statistically significant.

In the MLR models for the 2007–2010 global financial crisis, the indices $X_3$ (National Currency per SDR Period Average), $X_4$ (Domestic Currency per USD Period Average rate), $X_7$ (Gold Holdings National Valuation USD (aggregated 2000)), $X_9$ (Imports Merchandise Customs Price USD seas adj), $X_{10}$ (Nominal Effective Exchange Rate), and $X_{16}$ (Imports Merchandise Customs Price USD seas adj) were not included in any of the models, which indicates no measurable impact on the stock markets of BRICS countries during this period. Although they do not have a significant influence on the SPVs of BRICS countries during the 2007–2010 crisis, they have either a positive or negative impact on the SPVs during the 2018–2021 COVID-19 crisis. The indices $X_3$ (National Currency per SDR Period Average) and $X_{10}$ (Nominal Effective Exchange Rate) have a positive impact on the SPV of India, and the index $X_4$ (Domestic Currency per USD Period Average rate) has a positive impact on the SPV of Russia and South Africa, while the index $X_7$ (Gold Holdings National Valuation USD (aggregated 2000)) influences the SPV of China positively.

For the 2018–2021 COVID-19 crisis, indices such as $X_5$ (Lending Rate Percent per Annum), $X_6$ (Domestic Currency per USD Period Average rate), $X_9$ (Imports Merchandise Customs Price USD seas adj), $X_{14}$ (Energy Index), and $X_{16}$ (Imports Merchandise Customs Price USD seas adj) similarly showed no impact on the SPVs of the BRICS countries. Although they have no overall impact on the SPVs, these indices individually influence the SPVs of certain countries during the 2007–2010 global financial crisis. The index $X_5$ (Lending Rate Percent per Annum) positively affects the SPV of South Africa, and the index $X_6$ (Domestic Currency per USD Period Average rate) has a positive impact on the SPV of Russia, while the index $X_{14}$ (Energy Index) influences the SPV of India. This shows a change in the importance of economic variables and factors affecting market performance during the two crises, meaning the indices in the models depend on the nature of the crises. It is interesting that $X_9$ (Imports Merchandise Customs Price USD seas adj) and $X_{16}$ (Imports Merchandise Customs Price USD seas adj) are the common indices that have no impact on the SPVs in both crises.

The indices $X_8$ (Exports Merchandise Customs current USD (aggregated 2000) seas adj) and $X_{11}$ (Real Effective Exchange Rate) both impact Brazil’s SPV during both crises, but their effects are opposite. $X_8$ (Exports Merchandise Customs current USD (aggregated 2000) seas adj) has a positive effect on Brazil’s SPV during the 2007–2010 crisis, whereas it negatively impacts the SPV during the 2018–2021 crisis. On the other hand, the $X_{11}$ (Real Effective Exchange Rate) index has a negative impact on Brazil’s SPV during the 2007–2010 crisis, but a positive effect during the 2018–2021 COVID-19 crisis. For Russia, $X_{15}$ (Crude oil average dollars bbl), and for China, the $X_{11}$ (Real Effective Exchange Rate) index (Real Effective Exchange Rate) positively influences the SPV during both crises. However, for India, the $X_2$ (Producer Prices Index (aggregated 2000)) has a positive impact during the 2007–2010 crisis and a negative impact during the 2018–2021 COVID-19 crisis. Although some indices are common during both crises for Brazil, Russia, China, and India, the are no common indices for India. Although some indices are common during both crises for Brazil, Russia, and China separately, there are no common indices for India.

During the 2007–2010 crisis, certain indices impacted the SPV of individual countries. These include $X_1$ (CPI price percent y o y nominal seas adj) for Russia, $X_5$ (Lending Rate Percent per Annum) for South Africa, $X_6$ (Official Reserve Assets Gold Volume Fine Troy Ounces (aggregated 2000)) for Russia, $X_{13}$ (Consumer Price Index All items) for China, and $X_{14}$ (Energy Index) for India. Additionally, $X_{11}$ (Real Effective Exchange Rate) had a positive effect on China’s SPV but negatively affected the SPVs of Brazil and India. Similarly, the $X_{15}$ (Crude oil average dollars bbl) positively influenced the SPVs of Russia and South Africa while negatively impacting Brazil’s SPV.

During the 2018–2021 COVID-19 crisis, as in the 2007–2010 crisis, the indices impacting the SPV of individual countries varied. These include $X_1$ (CPI price percent y o y nominal seas adj), $X_2$ (Producer Prices Index (aggregated 2000)), $X_3$ (National Currency per SDR Period Average), and $X_{10}$ (Nominal Effective Exchange Rate) for India; $X_8$ (Exports Merchandise Customs current USD (aggregated 2000) seas adj) for Brazil; $X_{15}$ (Crude oil average dollars bbl) and $X_{15}$ (Crude oil average dollars bbl) for Russia; $X_7$ (Gold Holdings National Valuation USD (aggregated 2000)) for China; and $X_{13}$ (Consumer Price Index All items) and $X_{17}$ (Industrial Production constant USD (aggregated 2000)) for South Africa. In addition, there are two indices that have an impact on the SPV of two countries. These are $X_4$ (Domestic Currency per USD Period Average rate) for Russia and South Africa and $X_{11}$ (Real Effective Exchange Rate) for Brazil and China.

The MLR results for the two crises indicate no common indices across all BRICS countries, as none were identified for the individual crises. Hence, the hypothesis “H4: There are common indices in MLR results, having an influence on SPV of BRICS countries during the 2007–2010 and 2018–2021 crises” is rejected. These findings contribute to the studies by Arfaoui and Rejeb (2017), Zhou et al. (2019), and Mudiangombe and Mwamba (2023) in the literature.

Random Tree Results for 2007–2010

Random Tree has been utilized for datasets of each BRICS country for the 2007–2010 term. The results are depicted in

Table 11. The 2007–2010 Random Tree outputs.

	BRAZIL	RUSSIA	INDIA	CHINA	SOUTH AFRICA
Accuracy	48 100%	48 100%	48 100%	48 100%	48 100%
Confusion Matrix	a b 31 0 | a = P 0 17 | b = N	a b 21 0 | a = N 0 27 | b = P	a b 28 0 | a = P 0 20 | b = N	a b 26 0 | a = P 0 22 | b = N	a b 29 0 | a = P 0 19 | b = N
$X_1$	$\surd$	$\surd$	$\surd$	$\surd$	$\surd$
$X_2$	$\surd$
$X_3$	$\surd$	$\surd$	$\surd$	$\surd$	$\surd$
$X_4$			$\surd$		$\surd$
$X_5$	$\surd$	$\surd$
$X_6$	$\surd$	$\surd$
$X_7$	$\surd$	$\surd$	$\surd$
$X_8$	$\surd$	$\surd$	$\surd$	$\surd$
$X_9$
$X_{10}$					$\surd$
$X_{11}$		$\surd$
$X_{12}$		$\surd$			$\surd$
$X_{13}$	$\surd$	$\surd$	$\surd$	$\surd$	$\surd$
$X_{14}$			$\surd$
$X_{15}$		$\surd$		$\surd$
$X_{16}$			$\surd$
$X_{17}$		$\surd$		$\surd$	$\surd$

. Random Tree classified the SPV data of each BRICS country with 100% accuracy. Classification graphs are illustrated in Appendix A. According to the confusion matrix, 31 positive and 17 negative data from Brazil, 21 positive and 27 negative data from Russia, 28 positive and 20 negative data from India, 26 positive and 22 negative data from China, and finally 29 positive and 19 negative data from South Africa were classified perfectly. According to the classification results, $X_1$ (CPI Price percent y o y nominal seas adj), $X_3$ (National Currency per SDR Period Average), and $X_{13}$ (Consumer Price Index All items) are the common indices that affected the SPV of BRICS countries during the 2007–2010 crisis. Other than the common indices, $X_8$ (Exports Merchandise Customs current USD (aggregated 2000) seas adj) has an influence on the SPV of all BRICS countries, except South Africa. On the other hand, $X_2$ (Producer Prices Index (aggregated 2000)) has an influence only on the SPV of Brazil. Similarly, $X_{10}$ (Nominal Effective Exchange Rate) has an influence on the SPV of South Africa, $X_{11}$ (Real Effective Exchange Rate) has an influence on the SPV of Russia and $X_{16}$ (Imports Merchandise Customs Price USD seas adj) has an influence on the SPV of India. Out of 17 indices, only $X_9$ does not have any influence on the SPV of BRICS countries. These diversities of indices depend on their different economic and socio-political structures.

Random Tree Results for 2018–2021

Random Tree was utilized to classify the SPV of each BRICS country. The results are presented in

Table 12. 2018–2021 Random Tree outputs.

	BRAZIL	RUSSIA	INDIA	CHINA	SOUTH AFRICA
Accuracy	48 100%	48 100%	48 100%	48 100%	48 100%
Confusion Matrix	a b 21 0 | a = P 0 27 | b = N	a b 29 0 | a = P 0 19 | b = N	a b 31 0 | a = P 0 17 | b = N	a b 25 0 | a = P 0 23 | b = N	a b 26 0 | a = P 0 22 | b = N
$X_1$	$\surd$	$\surd$	$\surd$	$\surd$	$\surd$
$X_2$	$\surd$	$\surd$		$\surd$
$X_3$			$\surd$
$X_4$	$\surd$	$\surd$	$\surd$	$\surd$
$X_5$
$X_6$				$\surd$
$X_7$	$\surd$		$\surd$	$\surd$
$X_8$		$\surd$	$\surd$	$\surd$	$\surd$
$X_9$		$\surd$	$\surd$	$\surd$	$\surd$
$X_{10}$	$\surd$				$\surd$
$X_{11}$	$\surd$	$\surd$	$\surd$	$\surd$
$X_{12}$			$\surd$		$\surd$
$X_{13}$	$\surd$			$\surd$
$X_{14}$		$\surd$
$X_{15}$			$\surd$		$\surd$
$X_{16}$
$X_{17}$				$\surd$	$\surd$

. Random Tree classified the SPV data for all countries with 100% accuracy. According to the confusion matrix for Brazil, 21 positive and 27 negative data are classified correctly. Similarly, 29 positive and 19 negative data for Russia, 31 positive and 17 negative data for India, 25 positive and 23 negative data for China, and finally 26 positive and 22 negative data for South Africa are classified perfectly.

Based on the Random Tree classification results, only $X_1$ (CPI price percent y o y nominal seas adj) is the common index that influences the SPV of BRICS countries. It contributes to the reality that during the crisis period, the inflation rate increases. Moreover, $X_4$ (Domestic Currency per USD Period Average rate) and $X_{11}$ (Real Effective Exchange Rate) have the same effects on the SPV of Brazil, Russia, India, and China, whereas $X_3$ (Exports Merchandise Customs current USD (aggregated 2000) seas adj) and $X_9$ (Imports Merchandise Customs current USD (aggregated 2000) seas adj) have the same influences on the SPV of Russia, India, China, and South Africa. These results contribute to the studies by Mroua and Trabelsi (2020), Chkili and Nguyen (2014), and Bhutto et al. (2020). $X_5$ (Lending Rate Percent per Annum) and $X_{16}$ (Imports Merchandise Customs Price USD seas adj) do not have any influence on the SPV of BRICS countries.

Comparing MLR and Random Tree Outputs for 2007–2010

During the global financial crisis, Random Tree analysis identified $X_1$ (CPI price percent y o y nominal seas adj), $X_3$ (National Currency per SDR Period Average), and $X_{13}$ (Consumer Price Index All items) as common indices influencing the SPV of BRICS countries. In contrast, MLR analysis found no common index affecting the SPV of all BRICS countries. According to the MLR results, $X_1$ (CPI price percent y o y nominal seas adj) influences only the SPV of Russia, whereas Random Tree analysis suggests it impacts the SPV of all BRICS countries. Additionally, MLR results indicate that $X_2$ (Producer Prices Index (aggregated 2000)) negatively affects the SPV of Brazil and positively impacts the SPV of India, while Random Tree results show its influence only on the SPV of Brazil. In the MLR results, the indices $X_3$ (National Currency per SDR Period Average), $X_4$ (Domestic Currency per USD Period Average rate), $X_7$ (Gold Holdings National Valuation USD (aggregated 2000)), $X_9$ (Imports Merchandise Customs current USD (aggregated 2000) seas adj), $X_{10}$ (Nominal Effective Exchange Rate), and $X_{16}$ (Imports Merchandise Customs Price USD seas adj) have no impact on the SPV of any BRICS country. However, in the Random Tree results, $X_3$ (National Currency per SDR Period Average) influences the SPV of all BRICS countries, $X_4$ (Domestic Currency per USD Period Average rate) affects the SPV of India and South Africa, $X_7$ (Gold Holdings National Valuation USD (aggregated 2000)) impacts the SPV of Brazil, Russia, and India, $X_{10}$ (Nominal Effective Exchange Rate) influences only the SPV of South Africa, and $X_{16}$ (Imports Merchandise Customs Price USD seas adj) affects only the SPV of India. Additionally, $X_6$ (Official Reserve Assets Gold Volume Fine Troy Ounces (aggregated 2000)) influences the SPV of Russia and South Africa in the MLR results, and Brazil and Russia in the Random Tree results. In the MLR results, $X_8$ (Exports Merchandise Customs current USD (aggregated 2000) seas adj) positively impacts the SPV of Brazil but negatively affects South Africa, while in Random Tree results, it influences all BRICS countries except South Africa. $X_{11}$ (Real Effective Exchange Rate) negatively impacts the SPV of Brazil and India but positively affects the SPV of China in MLR results, and influences only the SPV of China in Random Tree results. $X_{12}$ (Total Reserves (aggregated 2000)) positively affects the SPV of Brazil and South Africa in MLR results and influences the SPV of Russia in Random Tree results. $X_{13}$ (Consumer Price Index All items) negatively impacts the SPV of China in MLR results but influences the SPV of all BRICS countries in Random Tree results. $X_{14}$ (Energy Index) affects only the SPV of India in both methods. $X_{15}$ (Crude oil average USD bbl) negatively affects Brazil but positively impacts the SPV of Russia and South Africa in MLR results, influencing the SPV of Russia and China in Random Tree results. Lastly, $X_{17}$ (Industrial Production constant USD) positively impacts the SPV of Russia and negatively affects the SPV of China in MLR results, while influencing the SPV of Russia, China, and South Africa in Random Tree results. Based on the results, MLR and Random Tree do not present the same common indices; hence, the hypothesis “H5: Indices are similar in MLR and Random Tree during the 2007–2010 crisis.” is rejected.

While no common indices were identified as influencing the SPV of the overall BRICS countries based on the results of the two techniques, the findings indicate that certain indices have a significant impact when the countries are assessed individually. For instance, in Brazil, the indices $X_2$ (Producer Prices Index (aggregated 2000)) and $X_8$ (Exports Merchandise Customs current USD (aggregated 2000) seas adj) play a key role. For Russia, the relevant indices include $X_1$ (CPI price percent y o y nominal seas adj), $X_6$ (Official Reserve Assets Gold Volume Fine Troy Ounces (aggregated 2000)), $X_{15}$ (Crude oil average USD bbl), and $X_{17}$ (Industrial Production constant USD). India is influenced by $X_{14}$ (Energy Index) while the SPV of China is affected by $X_{13}$ (Consumer Price Index All items). For South Africa, $X_{12}$ (Total Reserves (aggregated 2000)) is a significant factor. These findings show the necessity of assessing the SPV of each BRICS country individually, as no common indices were found to influence all five countries together.

Comparison of MLR and Random Tree for 2018–2021

During the COVID-19 crisis, Random Tree analysis identified $X_1$ (CPI price percent y o y nominal seas adj) as the only common index affecting the SPV of BRICS countries, while MLR results show that no common indices affect the SPV of BRICS countries. Based on the MLR results, $X_1$ (CPI price percent y o y nominal seas adj) influences only the SPV of India, whereas Random Tree results show that it impacts the SPV of all BRICS countries. According to the MLR results, $X_2$ (Producer Prices Index (aggregated 2000)) and $X_3$ (National Currency per SDR Period Average) only affect the SPV of India, while $X_2$ (Producer Prices Index (aggregated 2000)) impacts the SPV of Brazil, Russia, and China, and $X_3$ (National Currency per SDR Period Average) affects the SPV of India only in the Random Tree results. Additionally, MLR results show that the indices $X_5$ (Lending Rate Percent per Annum), $X_6$ (Official Reserve Assets Gold Volume Fine Troy Ounces (aggregated 2000)), $X_9$ (Imports Merchandise Customs current USD (aggregated 2000) seas adj), $X_{14}$ (Energy Index), and $X_{16}$ (Imports Merchandise Customs Price USD seas adj) have no impact on the SPV of any BRICS country. However, in the Random Tree results, $X_5$ (Lending Rate Percent per Annum) and $X_{16}$ (Imports Merchandise Customs Price USD seas adj) have no impact on the SPV of any BRICS country. MLR results show that $X_4$ (Domestic Currency per USD Period Average rate) affects the SPV of Russia and South Africa. In contrast, Random Tree results indicate it influences the SPV of Brazil, Russia, India, and China. Similarly, $X_7$ (Gold Holdings National Valuation USD (aggregated 2000)) affects only the SPV of China in MLR results but impacts the SPV of Brazil, India, and China in Random Tree results. $X_8$ (Exports Merchandise Customs current USD (aggregated 2000) seas adj) influences the SPV of Brazil in MLR results, while in Random Tree results, it affects the SPV of Russia, India, China, and South Africa. $X_{10}$ (Nominal Effective Exchange Rate) negatively affects the SPV of India in MLR results, while in Random Tree results, it influences the SPV of Brazil and South Africa. $X_{11}$ (Real Effective Exchange Rate) positively affects the SPV of Brazil and China in MLR results, while in Random Tree results, it impacts the SPV of Brazil, Russia, India, and China. $X_{12}$ (Total Reserves (aggregated 2000)) positively affects the SPV of Russia in MLR results, while in Random Tree results, it influences the SPV of India and South Africa. Similarly, $X_{13}$ (Consumer Price Index All items) positively impacts the SPV of South Africa in MLR results but influences the SPV of Brazil and China in Random Tree results. $X_{15}$ (Crude oil average USD bbl) positively affects South Africa in MLR results and influences the SPV of India and South Africa in Random Tree results. Lastly, $X_{17}$ (Industrial Production constant USD) negatively affects the SPV of South Africa in MLR results, but influences the SPV of China and South Africa in Random Tree results. These findings demonstrate that MLR and Random Tree do not identify the same common indices for all BRICS countries, leading to the rejection of the hypothesis “H6: Indices are similar in MLR and Random Tree during the 2018–2021 crisis.”

The results indicate that while no common indices influence the SPV of all BRICS countries, certain indices significantly impact individual countries. $X_{11}$ (Real Effective Exchange Rate) is the key influencing factor for Brazil. The SPV of Russia is impacted by $X_4$ (Domestic Currency per USD Period Average rate). India is affected by $X_1$ (CPI price percent y o y nominal seas adj) and $X_3$ (National Currency per SDR Period Average). The SPV of China is influenced by $X_7$ (Gold Holdings National Valuation USD (aggregated 2000)) and $X_{11}$ (Real Effective Exchange Rate). In South Africa, $X_{17}$ (Industrial Production constant USD) plays a significant role. These findings show the need to assess the SPV of each BRICS country individually, as no common indices were identified that influence all five countries together.

5. Conclusions

This study aimed to identify the indices influencing the SPVs of BRICS countries during the global financial crisis and the COVID-19 pandemic. Monthly data from January 2000 to December 2023 were obtained from the Global Economic Monitor (GEM) database, World Bank, IMF International Financial Statistics, and OECD and then standardized for analysis. Although numerous other indices exist beyond the seventeen utilized in this study, data for many of them, such as unemployment rates, were either unavailable or incomplete for certain countries. Consequently, these indices were excluded from the analysis, which represents a limitation of this study. To test six hypotheses, this study was conducted in two phases. In the first phase, Data Mining classification techniques were applied to the data of each BRICS country to determine the best classification technique. In the second phase, this technique was used alongside MLR analysis to identify common indices affecting SPVs during both crises. The first phase identified Random Tree as the best classification technique among the six classification techniques. Random Tree and MLR were then applied to each BRICS country’s SPV data during the two crises to identify common indices affecting SPVs. While high performance measures were given consideration to compare the seven different classification techniques, overfitting and bias in techniques were also considered, giving Random Forest a concern of more overfitting compared to Random Tree and other methods given almost all performance measures were at the highest levels.

When MLR and Random Tree were applied to the global financial crisis data for each BRICS country, the Random Tree analysis identified CPI price percent y o y nominal, National Currency per SDR Period Average, and Consumer Price Index (All items) as common indices influencing all BRICS countries, whereas MLR found no common indices. The results highlight varied responses due to the diverse economic and socio-political structures of BRICS nations, consistent with Wang et al. (2023), who observed that the impact of factors varies across countries and markets, particularly during crises. However, these findings differ from studies by Mudiangombe and Mwamba (2023), Arfaoui and Rejeb (2017), Zhou et al. (2019), and Mroua and Trabelsi (2020), which emphasized the significant impacts of exchange rates and oil prices on stock markets. On the other hand, Adeniyi and Kumeka (2020) found no relationship between exchange rates and stock prices. Unlike prior studies focusing on one or two indices, this research analyzed seventeen indices to identify those commonly influencing the SPV of BRICS countries.

For the COVID-19 crisis, the Random Tree analysis identified CPI price percent y o y nominal as the only common index for all BRICS countries, while MLR found no common indices. These findings reflect varied economic and socio-political structures in the countries, the unique characteristics of the crisis, and the specific indicators analyzed. The results contradict studies such as those of Bhutto et al. (2020), which reported a positive correlation between exchange rates and stock markets, and R. Hussain et al. (2023), which found a strong relationship between exchange rates and stock return volatilities during the COVID-19 pandemic.

As Wang et al. (2023) mentioned, the influence of various factors differs across countries and markets, especially during crises. This, combined with the diverse economic and socio-political structures of the BRICS countries, raises the question of whether common indices exist for individual countries during crises. During the global financial crisis, both MLR and Random Tree analyses identified two common indices, the Producer Prices Index and Exports Merchandise Customs current (USD), affecting the SPV of Brazil. For Russia, the indices CPI price percent y o y nominal, Official Reserve Assets Gold Volume Fine Troy Ounces, Crude Oil Average (USD bbl), and Industrial Production constant (USD) were common in both techniques. Similarly, both methods highlighted the Energy Index as influencing the SPV of India, while the Consumer Price Index (All Items) and Industrial Production constant (USD) impacted the SPV of China. For South Africa, the Total Reserves index was identified as significant.

During the COVID-19 crisis, the common indices affecting the SPV of each country, as identified by both MLR and Random Tree results, are Real Effective Exchange Rate for Brazil, Domestic Currency per USD Period Average rate for Russia, CPI price percent y o y (seasonally adjusted) and National Currency per SDR Period Average for India, Gold Holdings National Valuation (USD) and Real Effective Exchange Rate for China, and Industrial Production constant (USD) for South Africa. These findings align with Fasanya et al. (2023), who predicted stock prices for Brazil, Russia, and South Africa using commodity prices. Although no common indices were identified through the MLR analysis, the results revealed common indices influencing the SPV of each BRICS country during both crises. For Brazil, Exports Merchandise Customs current USD had a positive impact during the global crisis but a negative one during the COVID-19 crisis, while the Real Effective Exchange Rate showed the opposite effect. The SPV of Russia was positively influenced by Crude Oil Average (USD bbl) in both crises. Similarly, the SPV of China was positively impacted by the Real Effective Exchange Rate during both periods. No common index was found to affect the SPV of South Africa, while India’s SPV was positively influenced by the Producer Prices Index during the global crisis but negatively affected during the COVID-19 crisis.

According to the Random Tree results, CPI price percent y o y nominal seas adj is the only common index influencing the SPV of all countries during both crises. Other than this index, the common indices vary by country. For Brazil, CPI price percent y o y nominal seas adj, Producer Prices Index, Gold Holdings National Valuation (USD), and Consumer Price Index All items are common. For Russia, the common indices include CPI price percent y o y nominal seas adj, Exports Merchandise Customs current (USD), and Real Effective Exchange Rate. For India, the common indices are CPI price percent y o y nominal seas adj, National Currency per SDR Period Average, Domestic Currency per USD Period Average rate, Gold Holdings National Valuation USD, and Exports Merchandise Customs current (USD). For China, the common indices are CPI price percent y o y nominal seas adj, Exports Merchandise Customs current (USD), Consumer Price Index All items, and Industrial Production constant USD. Finally, for South Africa, the common indices are CPI price percent y o y nominal seas adj, Nominal Effective Exchange Rate, Total Reserves, and Industrial Production constant (USD).

Although there are many other indices besides the seventeen used, data for other indices, such as unemployment rates, were either unavailable or significantly incomplete for some countries and were therefore excluded from the analysis. This constitutes a limitation of this study.

In conclusion, each BRICS country faced economic crises at different times. The severity of crises depends on the global and internal conditions. For example, Brazil and South Africa struggled with political and healthcare issues, while Russia dealt with the dropped oil prices, sanctions from the EU, and ongoing war with Ukraine. The impacts of both crises on the BRICS countries varied due to these internal and external factors. As a result, the indices in this study had different effects on the SPV of each country during the crises. Although some common indices were identified for individual crises in the MLR and Random Tree results, there were no common indices across both crises in both methods, except for CPI price percent, which was identified as common in both crises by Random Tree. As Wang et al. (2023) and Rout and Das (2024) stated, the impact of each index varies across the countries and the severity of the crisis due to the nature of the crises, and the diverse economic and socio-political structures of the countries. The results provide insights for investors and financial institutions paying attention to the conditions of each country during similar crisis periods.

During periods of crisis, identifying multiple indices affecting the stock prices of BRICS countries using two different methods, MLR and classification techniques, has contributed a new perspective to the literature. In the future, the effects on stock prices can be further studied using these methods with different indices. In the BRICS summit that took place in Johannesburg on 22–24 August 2023, the official summit declaration announced that BRICS countries would be extended with the admission of five new members, Egypt, Ethiopia, Iran, Saudi Arabia, and the United Arab Emirates (UAE) in January 2024 (Ross, 2024). With this expansion, the group will control over 43% of global oil production and around 72% of the world’s rare earth mineral reserves. The new group will also represent 45% of the global population (Ross, 2024). This expansion shifts the global economic balance. Future research will likely focus on various aspects of this change, including its impact on the global economy, how oil prices affect the GDP of the new members during crises, and how these indices influence their stock markets.