Abstract
The spread of the coronavirus has reduced the value of stock indexes, depressed energy and metals commodities prices including oil, and caused instability in financial markets around the world. Due to this situation, investors should consider investing in more secure assets, such as real estate property, cash, gold, and crypto assets. In recent years, among secure assets, cryptoassets are gaining more attention than traditional investments. This study compares the Bitcoin market, the gold market, and American stock indexes (S&P500, Nasdaq, and Dow Jones) before and during the COVID-19 pandemic. For this purpose, the dynamic conditional correlation exponential generalized autoregressive conditional heteroskedasticity model was used to estimate the DCC coefficient and compare this model with the artificial neural network approach to predict volatility of these markets. Our empirical findings showed a substantial dynamic conditional correlation between Bitcoin, gold, and stock markets. In particular, we observed that Bitcoin offered better diversification opportunities to reduce risks in key stock markets during the COVID-19 period. This paper provides practical impacts on risk management and portfolio diversification.
Similar content being viewed by others
Explore related subjects
Find the latest articles, discoveries, and news in related topics.Introduction
Today, financial markets play such an important role in the development of a country that market booms directly affect country development. Those considering entering financial markets are concerned with losing capital and reducing asset values. Thus, reducing financial risks and risks that may threaten capital has always been an area of concern for traders and investors (Toque and Terraza 2011, 2014; Peng et al. 2011; Kou et al. 2014, 2019; Li et al. 2022a). Alternatively, banks and business sectors have been exposed to funding risk as a major source of vulnerability throughout the financial crises. Some studies have used financial ratios to examine bankruptcy predictions for the banks and business sectors based on financial crises and busts of the other financial markets (Kwak et al. 2012; Lardic and Terraza 2019; Kou et al. 2021a, b).
In recent years, the worldwide spread of the coronavirus disease 2019 (COVID-19) has created a big shock in the economies of the world. This shock was accompanied by a fall in the value of stock market indexes and oil prices, as well as other financial assets. In response to this pandemic crisis, governments have decided on extensive shutdowns and heavy restrictions, which have enhanced instability in the financial markets and sustained the crisis phenomenon. During financial crises, investors search for more secure investments. In particular, they tend to prefer investing more in cash and low risk assets. In recent years, the development of cryptocurrencies has recently gained the attention of investors as a means of enhancing portfolio returns (Makarov and Schoar 2020; García-Medina and Luu Duc Huynh 2021; Moreno and Garcia Medina 2023) and improving the risk and return profile of a well-diversified portfolio (Briere et al. 2015).
The stock market is one of the most important financial markets. An index’s change reflects the performance of the market and the boom or bust of a country’s economy. There are different ways in which stock market activity can affect a country’s economy. It is a constituent part of the financial markets and one of the main arteries of finance in an economy. A strong stock market plays such an important role in a country’s economy that some economists believe that the difference between developed and underdeveloped countries lies not in the presence of advanced technology but rather in the presence of an integrated and active stock market (Kyrtsou and Terraza 2000; Göçken et al. 2016, 2019; Rounaghi and Nasirzadeh 2016; Abbaszadeh et al. 2020; Arashi and Rounaghi 2022).
In addition to the stock market, investors are also interested in the gold market as a way to maximize profit and minimize risk. Gold has maintained its value for many years, making it popular among investors. Gold is often viewed as a long-term investment that preserves investors' purchasing power during periods of high inflation. As with other asset classes, investing in gold depends on several factors. The right decision requires an analysis of past trends and a thorough examination of the current state of the global market. It also involves the determination of how to invest based on the data and the current situation. Investing in this type of asset has the advantages of high long-term profit and quick liquidity.
The situation is different when it comes to the Bitcoin market. Bitcoin is a relatively new investment market, having entered the market only in the last few years. There are active Bitcoin markets 24 h a day, 7 days a week. Understanding Bitcoin’s capabilities is crucial for financial market participants (Ciaian et al. 2016; Stensas et al. 2019; Nasir et al. 2019; Kim et al. 2019; Hakim das Neves 2020; Ante 2020; Mizerka et al. 2020; Kristoufek 2020; Lahiani et al. 2021; Malladi and Dheeriya 2021; Kwon 2021; Li et al. 2022b; Lorenzo and Arroyo 2022). Among the digital currencies that have emerged in the last decade are Bitcoin, LiteCoin, PeerCoin, AuroraCoin, DogeCoin, and Ripple. Among them, Bitcoin stands out due to its price volatility and outstanding growth. Several studies have shown that Bitcoin is a highly innovative and attractive digital currency (Brandvold et al. 2015; Shaikh 2020; Giudici et al. 2020; Kayal and Rohilla 2021; Ma and Tanizaki 2022).
Despite being created as a digital currency, Bitcoin is also used as an asset (Baur et al. 2018a, b). As such, several authors have examined Bitcoin with other conventional financial instruments, including its role as an asset or hedging tool (Bouri et al. 2017, 2018; Shahzad et al. 2019). Some existing studies suggest that Bitcoin should be considered an asset due to its efficient market hypothesis (Jakub 2015; Wei 2018; Tiwari et al. 2018; Le Tran and Leirvik 2020; Noda 2020; Ghazani and Jafari 2021). Meanwhile, other studies have found that Bitcoin is highly volatile and has substantial returns (Baek and Elbeck 2015; Symitsi and Chalvatzis 2019; Agosto and Cafferata 2020). Consequently, speculators and investors consider Bitcoin an alternative asset class to conventional currencies.
Investments in gold and Bitcoin generated big profits during the COVID-19 pandemic (Jin et al. 2019; Bouri et al. 2020a, b), and there is still debate about whether Bitcoin can replace gold in times of financial crisis. The dynamic nexus between Bitcoin, gold, and American stock markets during the COVID-19 pandemic was investigated because investors are interested in determining the degree of uncertainty of the financial markets during times of financial crises.
This paper’s main finding is showing how different asset classes contribute to improving risk-adjusted returns and how Bitcoin investment could improve portfolio diversification benefits for investors during financial crises.
To achieve this objective, this study analyzes the joint dynamics of conditional volatility and correlation under an asymmetric relationship between volatility and shocks in returns using a VAR-DCC-EGARCH specification. This model is compared with an attractive and efficient alternative forecasting tool that uses Artificial Neural Networks (ANNs). Several distinguishing properties of ANNs have made them extremely popular in forecasting. One of their most notable characteristics is that they are nonlinear, nonparametric, data-driven, and self-adaptive.
In this study, we try to find a safe haven for Bitcoin, gold, and stock markets by applying a hybrid VAR-DCC-EGARCH-ANN method that considers a time-varying investment horizon. In the literature, various hybrid ANN models such as the EGARCH in-mean model-ANN (Episcopos and Davis 1996), EGARCH-ANN (Hajizadeh et al. 2012; Kristjanpoller and Minutolo 2015; Lahmiri and Boukadoum 2015; Lu et al. 2016), ANN-ARMA-GARCH (Mademlis and Dritsakis 2021) are developed. The innovation in this paper is related to the use of new econometrics and econophysics techniques including hybrid VAR-DCC-EGARCH and ANN for forecasting in finance and economic areas, especially for forecasting in Bitcoin, gold, and stock markets.
The paper is organized as follows: section "Literature review and theoretical background" discusses the stock markets, gold markets, and Bitcoin markets, as well as different aspects of their financial behavior. The trends of these markets before and during the COVID-19 pandemic are compared in section "Financial behaviors of the Bitcoin, gold, and stock markets before and during the COVID-19 pandemic". Sections "Data and empirical methodology" to "Discussions and conclusion" explain our methodology and discuss the results. A multivariate GARCH model was used to take the time-varying effect of covariation between markets into account, and we compared the results of this methodology with those obtained by a hybrid ANN method. The conclusion states the limits of our study and makes some suggestions for future research.
Literature review and theoretical background
In this paper, the behaviors of the Bitcoin, gold, and stock markets were analyzed. Because investors are familiar with the traditional gold and stock markets, only Bitcoin’s characteristics will be covered, since it is a newly emerging market. Studies about Bitcoin, gold, and the stock market will be covered here.
The inventor of Bitcoin is Satoshi Nakamoto. Bitcoin do not have banknotes or coins like other currencies, such as the dollar or the euro. Bitcoin is a virtual currency that can be bought, sold, ordered online, and traded like a stock. However, it is based on computer code, so it follows its own rules. The production and distribution of Bitcoin are not controlled by any government, group, or organization.
The price of Bitcoin is generally determined by supply and demand. However, several factors can affect it. For example, legislation banning Bitcoin mining or trading of Bitcoin in one of the major economies could affect its price. Development situations, developers’ decisions, important and expected events, the effect of financial and economic variables and other factors can influence the price of Bitcoin. Some of the factors mentioned above can have a positive effect on the price of Bitcoin. For example, offering more financial products such as futures contracts and Exchange Traded Funds (ETFs) can attract the attention of many investors. Positive legislation in this area could also benefit Bitcoin (Xu et al. 2019; Fang et al. 2022).
Recently, considerable research has been conducted on Bitcoin’s price behavior. Kapar and Olmo (2019) analyzed the price discovery between Bitcoin futures and spot markets. They discovered that a common component drives both prices, provided by a weighted combination of futures and spot markets. They also demonstrated that deviations from the equilibrium condition equating the futures and spot log price can predict the return on the Bitcoin spot price but not the futures price. Philippas et al. (2019) proposed a dual-process diffusion model to investigate whether Bitcoin prices respond to informative signals with jumps. These signals were derived from the volume of corresponding hashtags on Twitter and Google Trends. The empirical findings suggest that Bitcoin prices are influenced in part by social media attention, implying a new evidence on the sentiment-price relation for Bitcoin.
In another study, Sebastião and Godinho (2021) examined the predictability of three major cryptocurrencies—Bitcoin, Ethereum, and LiteCoin—and the profitability of trading strategies devised through machine learning techniques. According to their findings, machine learning provides robust techniques for exploring the predictability of cryptocurrencies and for devising profitable trading strategies in these markets, even under adverse market conditions.
Additionally, many researchers have compared different aspects of Bitcoin, gold, and stock markets before and during the COVID-19 pandemic that influenced the decisions of investors and business and government policymakers. These studies are listed in Table 1. Among them, Al-Yahyaee et al. (2018) compared the three markets and concluded that Bitcoin has the strongest long-memory and multifractality features; it is also the least efficient.
Some studies concern the interesting results of the diversification benefits of cryptocurrencies. The benefits of incorporating Bitcoin in a traditional benchmark portfolio of stocks and bonds were investigated by Platanakis and Urquhart (2019). According to their findings, investors should incorporate Bitcoin in their portfolios because it provides significantly higher risk-adjusted returns. In a complementary study, Shahzad et al. (2020) compared the hedging characteristics of gold, Bitcoin, and G7 stock markets. Their findings indicate that gold offers comparatively higher and more stable conditional diversification benefits than Bitcoin for stock investments in G7 markets. According to some studies, Bitcoin has lower dependence on other asset classes. In particular, Bouri et al. (2020b) examined the time frequency dependency between Bitcoin, gold, commodities and the stock markets. Specifically, they showed that the benefits of diversification vary in the time–frequency space, with Bitcoin exhibiting a superiority over both gold and commodities.
Baur et al. (2018a) analyzed the relationship between Bitcoin, gold, and the U.S. dollar, and their results show that Bitcoin returns, volatility, and correlation characteristics are distinctively different compared with gold and the U.S. dollar. Kwon (2020) expanded this investigation to a value-at-risk analysis examining Bitcoin's tail behavior with the dollar, gold, and stock market index. Based on the contemporaneous correlation, Bitcoin and the dollar, and the stock market index exhibit similar tail behavior.
Several empirical studies have been used to investigate risk spillovers and estimate the correlations between asset market returns. There are two perspectives on risk analysis: the relationship of COVID-19 metrics with stock market performance and economic uncertainty and the transmission volatility during the COVID-19 crisis. Kakinuma (2021) investigated the nexus between Southeast Asian stock markets, Bitcoin, and gold before and during the COVID-19 pandemic. According to the results, Southeast Asian stocks markets, Bitcoin, and gold appear to be more interdependent during pandemics. Matkovskyy and Jalan (2019) found significant contagion effects between the financial and Bitcoin markets. They suggest that risk-averse investors avoid risky Bitcoin markets during crisis periods in favor of less volatile and more established markets, especially NASDAQ and NIKKEI.
Jiang et al. (2022) investigated the volatility spillover mechanism between Bitcoin, crude oil, gold, stocks, foreign exchange and natural gas market. They observed that shifts in external market attention across various markets are more likely to cause overall volatility spillovers. Moreover, they showed that Bitcoin acts as a hedge in the financial system rather than a safe haven.
Earlier literature has discussed hedges and safe havens investments as they have a strategic role for investors. According to Baur and Lucey (2010) a hedge is an asset that is uncorrelated or negatively correlated with another asset on average while a safe haven asset, on the other hand, has a low correlation or a negative correlation with another asset only during a market crash. Safe haven assets are designed to help investors mitigate downside market risk during stressful times. Another distinction is between a strong (weak) safe asset which has a negative correlation (uncorrelation) with another asset.
Evidence from these studies suggests that the diversification benefits of cryptocurrencies are not robust geographically or across markets. To the best of our knowledge, this study is the first attempt to test whether adding Bitcoin to a portfolio of traditional assets can enhance the risk/reward relationship during a crisis period and then contribute to the literature on the diversification benefits of cryptocurrencies during the COVID-19 period. Furthermore, other factors—including investor attitudes and economic conditions—can affect the accuracy of prediction. For this reason, precise prediction is still a challenging process in the Bitcoin, gold, and stock markets. Therefore, this paper’s motivation is to use fewer input data and a more straightforward model structure to get better prediction results for Bitcoin, gold, and stock markets.
Financial behaviors of the Bitcoin, gold, and stock markets before and during the COVID-19 pandemic
Coronavirus was first identified in late 2019 and broke out globally in early 2020. COVID-19 has swept into many countries and was announced as a global pandemic by the World Health Organization (WHO) on March 11, 2020. Like any other industry, the Bitcoin, gold, and stock markets were affected by the COVID-19 pandemic (Chen et al. 2020; Yousaf and Ali 2020; Sikiru and Salisu 2021; Arif et al. 2021; Shahzad et al. 2021; Youssef et al. 2021; Wang and Liu 2022; Hui and Chan 2022).
However, the virus provided more opportunities for some financial assets, especially cryptoassets. Since Bitcoin was created, there has always been an expectation that this digital currency is a safe investment. In other words, with the stock market crashing, investors can take refuge in Bitcoin and virtual currencies. It is the same relationship that exists between the stock market and precious metals.
Many studies have examined whether cryptocurrencies (especially Bitcoin) can act as hedges and safe havens. Jareno et al. (2020) found the existence of positive and statistically significant connectedness between Bitcoin and gold. A study by Bahloul et al. (2021) examined whether the Morgan Stanley Capital International (MSCI) all-country world index, the Islamic index, gold, and Bitcoin could be used as hedges or safe haven assets against world conventional stock markets from April 30, 2015, to March 27, 2020. In the sub-period of COVID-19, empirical findings suggest that gold is only a weak safe asset, while Bitcoin is more of a weak hedge asset. Będowska-Sójka and Kliber (2021) also determined that cryptocurrencies can play the role of weak safe havens in the stock market. During the four months following the WHO’s official designation of COVID-19 as a global pandemic, Diniz-Maganini et al. (2021) looked at the price efficiency and net cross-correlations of Bitcoin, gold, a U.S. dollar index, and the Morgan Stanley Capital International (MSCI) world index. They used intraday price data at 5-min intervals for Bitcoin, gold, the MSCI world index, and the US dollar index for March 11, 2020, through July 10, 2020. Based on their results, when short time scales for returns series of data were considered, the net cross-correlations between these assets were relatively weak, but when longer time scales for returns series of data were considered, net cross-correlations were negative and significantly higher. Futhermore, they found that when the time is greater than two months, gold can be considered a safe haven for investors holding the MSCI world and U.S. dollar indexes, and when the time scale exceeds three months, Bitcoin can be considered a safe haven for the MSCI world index.
Despite the similarities found in the above-mentioned studies, Chemkha et al. (2021) demonstrated that gold is a weak safe haven for the assets considered during COVID-19, and Bitcoin cannot provide shelter due to its increased volatility. Omane-Adjepong and Paul Alagidede (2021) examined the COVID-19 effects on the Bitcoin market, gold market, and Africa’s stock markets. According to their findings, neither traditional safe havens nor Bitcoin can provide a safe haven for Africa’s emerging stock markets. Palladium and gold, however, provided a more stable environment for small-sized stock markets than the other candidates. Shehzad et al. (2021) compared gold and Bitcoin as safe-havens during the COVID-19 pandemic using a wavelet approach.Their findings highlighted that gold had more robust safe -haven properties than Bitcoin during COVID-19.
It appears that there is no consensus regarding the safe haven properties of Bitcoin during COVID-19. Therefore, the current study contributes to the literature by examining Bitcoin volatility before and during COVID-19. Several aspects of Bitcoin’s volatility can be analyzed to better understand its dynamics and capabilities as a financial asset. Examining an assets’ trends is the first step to understanding how volatility changes over time. The evolution of Bitcoin’s price between 2015 and 2020 is represented in Fig. 1, while Fig. 2 shows Bitcoin’s price performance during the COVID-19 pandemic. We observed a sustained upward trend from 2015 to 2018, with a peak at over $19,000 in December 2017. However, there was a reverse in the trend in 2018 due to some viewpoints in the financial and investment sectors and other economic and financial factors. While this decreasing trend continued in 2019, Bitcoin's price increased sharply during the COVID-19 crisis from $ 7,149.44 at the end of 2019 to $ 65,930.54 at the end of 2021, as illustrated in Figs. 1 and 2.
![figure 1](http://media.springernature.com/lw685/springer-static/image/art%3A10.1186%2Fs40854-023-00520-3/MediaObjects/40854_2023_520_Fig1_HTML.png)
Source: https://www.koyfin.com
Bitcoin trend (2015–2020).
![figure 2](http://media.springernature.com/lw685/springer-static/image/art%3A10.1186%2Fs40854-023-00520-3/MediaObjects/40854_2023_520_Fig2_HTML.png)
Source: https://www.koyfin.com
Bitcoin and COVID-19 pandemic.
To better understand these trends, it could be helpful to observe the evolution of Bitcoin mining's geographical distribution. In Fig. 3, we compared the Cambridge Bitcoin Electricity Consumption Index (CBECI)) at the end of 2019 with the index at the end of 2021. With 73.46% of the average monthly hashrate share, China dominated this technology until the end of 2019. However, this share fell to 19.14% in 2021, and China’s major player is gradually ceasing its Bitcoin mining activities for political, energy, and economic reasons. In contrast, the United States share has risen from 3.87% to 37.45%, which placed it in first place in 2021. The pandemic crisis, coupled with a weak dollar, caused big financial companies to shift to cryptocurrency, and Bitcoin has seen a significant rise in its price.
![figure 3](http://media.springernature.com/lw685/springer-static/image/art%3A10.1186%2Fs40854-023-00520-3/MediaObjects/40854_2023_520_Fig3_HTML.png)
Source: https://ccaf.io/cbeci/index
Comparison of the cambridge Bitcoin electricity consumption index for the periods 2019 and 2021.
The pandemic crisis resulted in the economy becoming more digital. This explains the why cost of energy is driving Bitcoin’s geographical redeployment. Bitcoin’s insatiable appetite for electricity has ignited a global debate about reducing carbon emissions based on cryptocurrencies. As the energy transition becomes a crucial issue for economies, the question of finding alternative energy sources arises. In their paper, Kou et al. (2022) analyzed innovative ways for solving carbon emission problem by generating more electricity using solar energy investment projects.
In Figs. 4 and 5, the Bitcoin market trend is compared with the gold and the stock markets before and during the COVID-19 pandemic. Before the pandemic, Bitcoin was in general disconnected from traditional financial markets. However, when COVID-19 emerged, the price of Bitcoin has risen significantly, and the question was raised about the correlation structure and its evolution between all markets.
![figure 4](http://media.springernature.com/lw685/springer-static/image/art%3A10.1186%2Fs40854-023-00520-3/MediaObjects/40854_2023_520_Fig4_HTML.png)
Source: https://www.koyfin.com
Fluctuates of the Bitcoin market in comparison with the gold market and stock markets before the COVID-19 pandemic (2018–2019).
![figure 5](http://media.springernature.com/lw685/springer-static/image/art%3A10.1186%2Fs40854-023-00520-3/MediaObjects/40854_2023_520_Fig5_HTML.png)
Source: https://www.koyfin.com
Fluctuates of the Bitcoin market in comparison with the gold market and stock markets during the COVID-19 pandemic (2020–2021).
The dynamic relationship between the Bitcoin, gold, and stock markets was investigated before the COVID-19 pandemic outbreak. Consequently, we asked the question: Were Bitcoin, gold, and American stock markets independent before the COVID-19 pandemic? Additionally, our study examines the dynamic nexus between the Bitcoin, gold, and American stock markets during the outbreak of the COVID-19 pandemic and verified the following hypothesis: Have the Bitcoin, gold, and American stock markets become interdependent during the COVID-19 pandemic.
Data and empirical methodology
Data
To investigate the effect of the COVID-19 pandemic on the Bitcoin, gold, and American stock markets, we collected two data samples from each asset class: before the COVID-19 pandemic (2018–2019) and during the COVID-19 pandemic (2020–2021). The daily closing prices were collected from Yahoo Finance. Because the closing price series are non-stationary, the series are transformed into return series. The choice of returns is motivated by the strong rejection of the Phillips-Perron test for unit roots for all the data series included in our analysis.Footnote 1
Descriptive statistics of the returns
Tables 2 and 3 demonstrate the descriptive statistics of the returns of the Bitcoin, gold, and stock markets over a period from 2018 to 2019 (before the COVID-19 pandemic), and from 2020 to 2021 (during the COVID-19 pandemic).
When comparing the average return over both periods for all investments, the return was higher over the second period. In particular, Bitcoin returns were higher compared to other investments, even if its return reaches more negative values over the second period. Except for Bitcoin, the return volatility is substantially the same for all investments with a lower variability for gold.
The difference between the maximum and minimum returns for Bitcoin was the highest, suggesting that Bitcoin fluctuations were significant relative to other markets. Indeed, Bitcoin exhibited the greatest variability for the two periods. During the COVID-19 pandemic, Bitcoin appeared to be the riskiest asset with more negative extremes.
Non-linearity of the data and autocorrelation of the data
Before modeling, it is necessary to determine the presence of nonlinear components in our data sets. The results of the Brock et al. (1987) test are given for all the return series (see the tables in Appendix A, Tables 8, 9, 10, 11, 12, 13, 14, 15, 16, 17), and autocorrelation in the returns are tested using the Ljung Box test (the tables are given in Appendix B, Tables 18, 19).
For American stock markets, the non-linearity hypothesis is accepted regardless of the period. The results are different according to the periods for gold. Before the COVID-19 pandemic, the hypothesis of non-linearity was rejected. During the COVID-19 pandemic, the test accepted the hypothesis of non-linearity in the returns. Concerning Bitcoin, the non-linearity was rejected for the two periods.
There is autocorrelation in the square of the residuals of the processes (see the results of the Lagrange Multiplier test in Appendix C, Tables 20, 21, 22, 23, 24, 25, 26, 27, 28, 29). Then, a model of conditional volatility is required for all assets.
Another stage of the econometric analysis is to test for the interdependence of the markets. In particular, to determine the impact of the COVID-19 pandemic on the dynamics of market correlations.
Empirical methodology
To demonstrate the effect of the COVID-19 pandemic on the Bitcoin, gold, and stock markets, two approaches were considered. First, the dynamic connectedness between the markets was investigated by employing the class of the VAR-DCC-GARCH models, and the ANN model was explained. A second time, these models will be used for the comparison of predicted values.
VAR-DCC-GARCH–type models
Originally, GARCH models propose to measure conditional variance for individual assets or indexes. This takes the sensitivity and persistence of volatility shock into account. In this study, we are interested in a specific model that analyzes the various relationships between the assets. Indeed, volatility moves together more or less closely over time across assets and markets. GARCH multivariate models (MGARCH) allow for analyzing volatility transmission between different assets, and the introduction of DCC-GARCH models enables the analyzes of interdependence among markets by estimating time-varying conditional correlations (Engle 2002).
To measure both the transmission of returns and volatility spillovers among different markets, first, we compare different orders of vector autoregressive processes (VAR models). A VAR model explains the joint evolution of assets through their lags. Using the Schwarz criterion, we consider the vector autoregressive processes of order 1. The conditional mean of a VAR(1) can be written as follows:
where ηt is a vector of independent and identically distributed random vectors.
According to the study, from Eq. (1), \(r_{t}\) is a 5 × 1 vector of returns, μ is a 5 × 1 vector of constants, \(\Phi\) is a 5 × 5 matrix of autoregressive coefficients, and \(\varepsilon_{t}\) is a 5 × 1 vector of innovations:
The conditional variance is defined as
where Dt = diag (√ℎ11,t, √ℎ22,t, … ….√ℎ55,) is a diagonal matrix of standard deviations for each of the return series obtained from estimating a univariate GARCH (1,1) process formulated by the following equation:
With ℎii,, the conditional variance depends on the unknown parameters ωi (the constant), αi, (the coefficient of the ARCH part of the process), and βi (the coefficient of the GARCH part of the process).
\(R_{t} = (\left( {Q_{t} } \right))^{ - 1/2} Q_{t} (diag\left( {Q_{t} } \right))^{ - 1/2}\) represents the time-varying conditional correlation matrix.
Qt is (n × n) variance–covariance matrix of standardized residuals, defined by:
with
\(\overline{Q}\) represents the unconditional covariance of the standardized residuals obtained by the univariate GARCH model α, and β are the parameters to be estimated. The sum of these coefficients must be less than one to respect the positivity of the matrix Qt.
To ensure that the matrix \(H_{{\text{t}}}\) is defined as positive, it is necessary to verify the conditions on the joint correlation coefficients:
In the DCC-GARCH model, volatility is assumed to follow a symmetric response to volatility shocks. Usually, in the analysis of the financial data, negative market shock causes volatility to rise more than similar positive market shock. In this paper, we can improve the GARCH specification and forecasts by calculating volatility asymmetry if it is identified in the data. One of the asymmetric GARCH processes is the (EGARCH) model proposed by Nelson (1991). A feature of the DCC-EGARCH model is that the Dt matrix elements are generated not by using univariate symmetric GARCH processes, but by using an asymmetric EGARCH model, where the volatility is defined by:
In Eq. (7), the parameter γ reflects the effect of asymmetry. The DCC-EGARCH models estimate univariate EGARCH-type processes (which could differ for each asset). Then the EGARCH models are used to standardize the individual residuals. A second time, the correlation dynamics of these standardized residuals can be specified. We note that to adapt the EGARCH model to the multivariate case using a DCC specification, the changes relative to the symmetric DCC-GARCH model concern only the implementation of the first step of the procedure. These models offer the flexibility of the univariate GARCH family models without the complexity of multivariate GARCH, and the main benefit of the EGARCH model is the ability to calculate for potential asymmetries in the response to volatility shocks via the gamma term.
VAR-DCC-EGARCH-ANN model
Artificial intelligence modeling has recently attracted attention as a new technology in finance and economic forecasting areas. In this paper, we used an alternative approach that relies on an ANN to capture the nonlinear relationships between market volatility. In the prediction, ANN is a strong competitor to regression and time series. It is well suited to modeling problems with unknown variables. It is also appropriate when static circumstances or other conditions make traditional techniques ineffective and when applying a time series is difficult. In situations when it is necessary to learn linear or nonlinear mapping, the attributes that make up an ANN provide good solutions. As a result of these attributes, ANNs would be able to tackle complicated problems precisely and flexibly (Azadeh et al. 2007).
The ANN includes three layers: the input layer, the output layer, and the hidden layer. The neuron takes the values of the input parameters, adds a bias, and then adds them up using the weights assigned. The transfer function would be used to calculate the output’ value. The number of input parameters matched the number of neurons in the input layer. In mathematical terms, neuron \(P\) performance can be given as follows:
where \({\text{x}}_{1} , \ldots ,{\text{x}}_{{\text{n}}}\) are denoted as input parameters. \({\text{w}}_{{{\text{P}}1}} , \ldots ,{\text{w}}_{{{\text{Pn}}}}\) are defined as the connection weights of neuron \({\text{P}}\).\({\text{ u}}_{{\text{P}}}\) is given as the input combiner while \({\text{b}}_{{\text{P}}}\) is denoted as the bias. \(\varphi\) is the activation function. Finally, \({\text{y}}_{{\text{P}}}\) is denoted as the neuron output. Details about the ANN can be found in Moghaddam et al. (2016).
In this paper, a multilayer feed-forward back propagation neural network is used. The proposed hybrid ANN model uses a Levenberg–Marquardt algorithm as a training algorithm. This algorithm is used to solve a nonlinear least squares problem (Selvamuthu et al. 2019).
VAR-DCC-EGARCH was first created, as explained in the previous section. Second, ANN used lagged returns and predicted conditional volatility from the VAR-DCC-EGARCH models. Thus, the proposed method is created by inputting the outcome of the preferred VAR-DCC-EGARCH model into the ANN, called a VAR-DCC-EGARCH-ANN model.
Results of the VAR-DCC-EGARCH model and VAR-DCC-EGARCH-ANN model
For each time series, the relationships between assets’ returns that influence each other were analyzed. The conditional mean equation is estimated using a VAR(1) model (Tables 30, 31 in Appendix D). Before the COVID-19 period, the results show that there was no significant return spillover between the series. However, during the COVID-19 period, the coefficients of own mean spillovers for Bitcoin and gold were significant. Then, the lag of the returns had a direct effect on the current returns of these assets.
This effect is positive for gold, while it is negative for Bitcoin. The cross-market spillover reveals a unidirectional negative return spillover from the stock markets to Bitcoin and a positive return spillover from gold to Bitcoin and from gold to Nasdaq. Accordingly, when Bitcoin returns increase, investors tend to decrease their investment in stock markets and increase their investment in gold.
In the next step, the residuals from the VAR(1) models are used to estimate the time-varying DCC series. Tables 4 and 5 present the estimation results of the conditional variance models. The Ljung Box test on the standardized residuals of the VAR-DCC-EGARCH models can be found in Tables 32 and 33 in Appendix D. The results of the test suggest no autocorrelation in the standardized residuals of our models.
It can be seen from Tables 4 and 5 that the majority of the coefficients are significant. For some data series, the α coefficients from the variance equation are not significant, especially concerning the first and the second periods for Bitcoin and the second period for gold. However, the results show that the β coefficients from Eq. (3) are always significantly positive. This indicated that the lag volatility had a positive impact on the conditional volatility for all series. The leverage effect is significant for all data series, except Bitcoin and gold in the second period.
We noticed that the joint coefficients αDCC and βDCC, which represent the parameters of the conditional correlations, are significant. The persistence of the conditional correlation is calculated from the sum of αDCC and βDCC. For the two periods, we found a persistently high level of values superior at 0.9. The estimated VAR-DCC-EGARCH model parameters allow for determining the values of the conditional correlation for the pairs of series. The correlation values for a particular pair of series indicate the strength of the relationship between the two series. It also shows changes in the upward index and downward trends of these interrelationships over time.
Table 6 reports the means of conditional correlations. The tail behavior of Bitcoin and gold, as well as the stock market indexes, is very similar in terms of contemporaneous correlation. The results show that the conditional correlations are the lowest for gold and Bitcoin whatever the period considered, indicating the role of Bitcoin and gold in hedging against stock indexes.
Conversely, the conditional correlation of stock market indexes is strongly positive with a value above 0.7 for both periods. Finally, the data comparison between both periods highlights the conditional correlation between Bitcoin and the stock market indexes over the second period.
Figures 6, 7, and 8 analyze the dynamics of the relationship between the Bitcoin, gold, and stock market indexes before and during the COVID-19 pandemic.
With the exception of pairwise comparison, conditional correlations are very volatile throughout the periods and markets, but they remain relatively low with values below 0.5.
The study found that there was a more positive dependency between Bitcoin and the S&P500 during the first part of each period, with the highest positive correlation in late 2020 (0.53). The decoupling between the Bitcoin and gold markets is more pronounced just before the beginning of the COVID-19 pandemic, and from 2021, with the highest negative peak obtained in late 2019 (−0.2).
In addition, Bitcoin has a higher relationship with the S&P500 with the most positive conditional correlation values, during the COVID-19 pandemic. In particular, the strongest correlation value is observed in March 2020, with a value above 0.5. This indicates that the behavior of Bitcoin is quite similar to traditional investments.
During the pandemic crisis period, correlations rose, reducing the effect of potential diversification of assets. Further, conditional correlations between gold-Nasdaq reached the highest positive values in the first period and the highest negative during the COVID-19 pandemic which brings into question its behavior as an asset class. This result confirms the general observation that gold returns are inversely related to the situation in the stock markets. Furthermore, the conditional correlations between gold and other assets are the lowest regardless of the period.
The forecasting performance of the VAR-DCC-EGARCH (1,1) model was, first, the predicted covariances and correlations are compared (Figs. 9, 10, and 11). They are both visually observed. Forecasting values calculated in a sample from the last 10 days, are represented in red. Correlations figures give focus on the last 20 days’ estimations.
It was observed that the predicted interdependences of Bitcoin with gold are relatively low whatever the period (around 0.04).
The negatively correlated interrelations between Bitcoin and the S&P500 during the first period are expected to increase at the end of 2019, and during the second period, the forecasting values show a long-run tendency to behave as any asset investment with a positive correlation of around 0.2.
The same trend is observed between the gold and the Nasdaq for the first period, showing that at the end of 2019, the forecasted correlation values are positive but to a lesser extent (around 0.1). However, the forecasted conditional correlations are expected to decline during the COVID-19 period.
More generally, it should be observed that an increasingly noticeable value of the conditional correlations at the end of 2019 corresponds to the beginning of the pandemic period.
We carry out the analysis by forecasting conditional volatility (Figs. 12, 13). Forecasting results were calculated for horizons from 1 to 10 days. To compare the conditional volatility, we simply use the absolute values of daily returns as a proxy measure for the realized volatility.
From the above graphs, we can observe that the volatility has a time-varying nature. While the volatility trend is similar to the stock market indexes with a sharp increase at the end of 2019, Bitcoin has two phases with relatively low volatility until the end of November 2018 and a strong upward recovery thereafter. As for gold, it seems to have stochastic volatility. While the forecasted conditional volatility for stock market indexes and Bitcoin follows a similar upward trend, the gold volatility prediction is stable.
In the second period, all markets show close movements of volatility to higher levels than before gold which acts differently from the others.
The gold market does not seem to be integrated with the other markets over the whole period. One of the major reasons for this smooth volatility in the gold market is the herding behavior of investors toward the markets where their returns were relatively much higher in particular in Bitcoin. Therefore, the forecasts of volatility are then expected to rise.
To test and compare the forecasting ability of our model, we use different measures of forecast error accuracies. The average squared difference between outputs and targets is known as MSE. It is better if the value is as low as possible. There is no error if the value of MSE, RMSE, and MAE is zero. Three performance measures, including MSE, RMSE, and MAE, are used to compare the results of the proposed methods. Table 7 shows the performance measures of the methods before and during the COVID-19 pandemic.
The MSE, RMSE, and MAE measures reveal that the VAR-DCC-EGARCH model performed better for Bitcoin during the COVID-19 pandemic. To obtain better forecasting values, the VAR-DCC-EGARCH-ANN model is applied to predict Bitcoin, gold, and stock markets’ values. The results of the performance measures, including MSE, RMSE, and MAE, demonstrate that the proposed VAR-DCC-EGARCH-ANN has remarkable prediction performance for Bitcoin, gold, and stock markets. For example, MSE’s maximum value is 0.000028617. To model and predict nonlinear time series, VAR-DCC-EGARCH-ANN can be used as a powerful computational method for Bitcoin, gold, and stock markets.
Discussions and conclusion
Since late 2019, COVID-19 has spread around the world, affecting more than human health. There has been an unprecedented worldwide economic recession, caused primarily by political restrictions, such as stay-at-home mandates and business closures. The value of the dollar, the euro, the pound, and other global currencies fell sharply, as well as industrial and economic indicators such as the S&P 500, Nasdaq, and Dow Jones in the United States, which have reached a point on the chart that may be unprecedented in the last two decades. At the same time, bondholders have seen their savings value decline.
This paper investigates the dynamic nexus of Bitcoin, gold, and American stock markets during the COVID-19 pandemic. We tested the model conditional volatility, and we used VAR-DCC-EGARCH and VAR-DCC-EGARCH-ANN models to observe spillovers across markets and the nature of such spillovers through different periods.
We explored the relationship between Bitcoin and other financial assets’ volatility using data from Bitcoin, American stock indexes (S&P500, Nasdaq, and Dow Jones), and gold prices. Because the Bitcoin market exhibits low dynamic conditional correlations with financial assets during the stability phase, our findings support the notion that they are a new investment asset class. However, we notice that the link between Bitcoin, American stock indexes, and gold has strengthened since the beginning of 2020, confirming the coronavirus’s contagious effect.
We tested whether Bitcoin can be used as a stock market hedge in our study. We have looked into the advantages of hedging through diversification between Bitcoin and stock markets. We may compare its hedging ability to that of gold using this method of study. If the COVID-19–confirmed case shocks are integrated into variance specifications, our empirical findings demonstrate a substantial dynamic conditional correlation between the Bitcoin, gold, and stock markets. The existence of the financialization of Bitcoin, gold, and stock markets is demonstrated by these empirical findings.
Based on our results, the estimate of the VAR-DCC-EGARCH model parameters allows for determining the values of the conditional correlation for the pairs of series. By using the VAR-DCC-EGARCH model, we observed that the tail behavior of Bitcoin and gold, as well as the stock market indexes, is very similar in terms of contemporaneous correlation. Also, MSE, RMSE, and MAE measures reveal that the VAR-DCC-EGARCH estimations achieve better forecasting performance during the COVID-19 pandemic for the stock market indexes, while for the other assets, the model better explains the volatility before the COVID-19 pandemic period, especially for gold.
The results of performance measures—including MSE, RMSE, and MAE—demonstrated that the proposed VAR-DCC-EGARCH-ANN has remarkable performance for the Bitcoin, gold, and stock markets.
The forecasting performance comparisons between the econometric model and the ANN model show that the proposed ANN model forecasts Bitcoin with higher accuracy. This confirms that Bitcoin price excess volatility is better captured by the VAR-DCC-EGARCH-ANN model.
These results can be confirmed in future research by including a greater number of hybrid ANN types and architectures. Particularly, to determine if hybrid models have been shown to outperform in different forecasting experiments and to understand to which specific situations each model may be better suited. This would expand the evidence obtained in this study and provide greater guidance on which models to use for different volatility profiles for the best forecasting results.
Our findings contribute to the study of the pandemic’s financial and economic effects by demonstrating that “COVID-19 surprises” have bidirectional spillover impacts on the Bitcoin, gold, and stock markets. These results demonstrate that while all markets have shown signs of “COVID-19 surprises,” there was a difference in the extent to which the pandemic influenced the financial markets.
Managerial and theoretical implications
This paper provides evidence on which analyzed assets provide the best safe haven for investors in times of crisis. In addition, there are important implications for investors who seek protection from downward movements in financial markets. Furthermore, our findings could be of interest to regulators and governments when engaging in further discussions on the role of Bitcoin in financial markets.
The results of our study also give theoretical proof that COVID-19 affected the Bitcoin, gold, and stock markets.
From a policymaking perspective, getting accurate practical justifications for the volatility of the Bitcoin, gold, and stock markets during the COVID-19 pandemic is an essential stage in establishing advantageous monetary policy strategies and correct tactics.
From the perspective of portfolio risk managers, the diversification benefits of Bitcoin are generally consistent and increase dramatically during periods of market volatility. As a result, using Bitcoin in a stock market portfolio lowers the portfolio’s risk.
These findings have important implications for investors and portfolio managers. Also, our findings have substantial implications for regulators’ oversight of financial markets during a global crisis, as well as investors’ cross-market hedging of systemic shock spillover risks.
Limitations of the study and scope of further research
The key limitation of the study is the small study duration that is covered by the pandemic period. The extension in time gives more choices to select other proxies as a market return to evaluate financial markets. In addition, it is still unclear whether the economic or political conditions of each country under study may affect the empirical results.
These limitations open the door for future research to investigate the nexus between the volatility of the Bitcoin, gold, and stock markets over a longer period and for the development of different models to help policymakers, investors, and portfolio risk managers invest in these markets. Additionally, an expanded analyzes of the observation of structural breaks in the level of correlation with the separation of high- and low volatility periods of the Bitcoin, gold, and stock markets concerning the reported volatility interaction, it would be interesting.
Availability of data and materials
The datasets used and analyzed during the current study are available from the corresponding author upon reasonable request.
Notes
Details on the test and tables showing the results are omitted for the sake of brevity. This can be requested from the authors.
Abbreviations
- DCC-EGARCH:
-
Dynamic conditional correlation-exponential generalized autoregressive conditional heteroskedasticity
- ANN:
-
Artificial neural network
- VAR-DCC-EGARCH:
-
Vector autoregressive-dynamic conditional correlation-exponential generalized autoregressive conditional heteroskedasticity
- VAR-DCC-EGARCH-ANN:
-
Vector autoregressive-dynamic conditional correlation-exponential generalized autoregressive conditional heteroskedasticity-artificial neural network
- EGARCH:
-
Exponential generalized autoregressive conditional heteroskedasticity
- EGARCH-ANN:
-
Exponential generalized autoregressive conditional heteroskedasticity-artificial neural network
- ANN-ARMA-GARCH:
-
Artificial neural network-autoregressive moving average-generalized autoregressive conditional heteroskedasticity
- GARCH:
-
Generalized autoregressive conditional heteroskedasticity
- ETFs:
-
Exchange traded funds
- MSCI:
-
Morgan stanley capital international
- CBECI:
-
Cambridge bitcoin electricity consumption index
- VAR-DCC-GARCH:
-
Vector autoregressive-dynamic conditional correlation-generalized autoregressive conditional heteroskedasticity
- MGARCH:
-
Multivariate generalized autoregressive conditional heteroskedasticity
- DCC-GARCH:
-
Dynamic conditional correlation- generalized autoregressive conditional heteroskedasticity
- ARCH:
-
Autoregressive conditional heteroskedasticity
- MSE:
-
Mean squared error
- RMSE:
-
Root mean square error
- MAE:
-
Mean absolute error
References
Abbaszadeh MR, Jabbari Nooghabi M, Rounaghi MM (2020) Using Lyapunov’s method for analysing of chaotic behaviour on financial time series data: a case study on Tehran stock exchange. Natl Account Rev 2(3):297–308
Agosto A, Cafferata A (2020) Financial bubbles: a study of co-explosivity in the cryptocurrency market. Risk 8:1–14
Al-Yahyaee KH, Mensi W, Min Yoon S (2018) Efficiency, multifractality, and the long-memory property of the Bitcoin market: a comparative analysis with stock, currency, and gold markets. Financ Res Lett 27:228–234
Ante L (2020) Bitcoin transactions, information asymmetry and trading volume. Quant Finance Econ 4(3):365–381
Arashi M, Rounaghi MM (2022) Analysis of market efficiency and fractal feature of NASDAQ stock exchange: time series modeling and forecasting of stock index using ARMA-GARCH model. Future Bus J 8(14):1–12
Arif M, Abubakr Naeem M, Hasan M, Alawi SM, Taghizadeh-Hesary F (2021) Pandemic crisis versus global financial crisis: Are Islamic stocks a safe-haven for G7 markets? Econ Res-Ekonomska Istraživanja 35(1):1707–1733
Azadeh A, Ghaderi SF, Sohrabkhani S (2007) Forecasting electrical consumption by integration of Neural Network, time series and ANOVA. Appl Math Comput 186(2):1753–1761
Baek C, Elbeck M (2015) Bitcoins as an investment or speculative vehicle? A first look. Appl Econ Lett 22(1):30–34
Bahloul S, Mroua M, Naifar N, Naifar N (2021) Are Islamic indexes, Bitcoin and gold, still “safe-haven” assets during the COVID-19 pandemic crisis? Int J Islam Middle East Financ Manag 15(2):372–385
Baur DG, Dimpfl T, Kuck K (2018a) Bitcoin, gold and the US dollar: a replication and extension. Financ Res Lett 25:103–110
Baur DG, Hong K, Lee AD (2018b) Bitcoin: medium of exchange or speculative assets? J Int Finan Markets Inst Money 54:177–189
Baur DG, Lucey BM (2010) Is gold a hedge or a safe haven? An analysis of stocks, bonds and gold. Financ Rev 45(2):217–229
Będowska-Sójka B, Kliber A (2021) Is there one safe-haven for various turbulences? The evidence from gold, Bitcoin and Ether. The North American J Econ Finance 56. https://doi.org/10.1016/j.najef.2021.101390
Bouri E, Das M, Gupta R, Roubaud D (2018) Spillovers between Bitcoin and other assets during bear and bull Markets. Appl Econ 50(55):5935–5949
Bouri E, Molnar P, Azzi G, Roubaud D, Hagfors LI (2017) On the hedge and safe haven properties of bitcoin: is it really more than a diversifier? Financ Res Lett 20:192–198
Bouri E, Shahzad SJH, Roubaud D (2020a) Cryptocurrencies as hedges and safe-havens for US equity sectors. Q Rev Econ Finance 75:294–307
Bouri E, Shahzad SJH, Roubaud D, Kristoufek L, Lucey B (2020b) Bitcoin, gold, and commodities as safe havens for stocks: new insight through wavelet analysis. Q Rev Econ Finance 77:156–164
Brandvold M, Molnár P, Vagstad K, Andreas Valstad OC (2015) Price discovery on Bitcoin exchanges. J Int Finan Markets Inst Money 36:18–35
Briere M, Oosterlinck K, Szafarz A (2015) Virtual currency, tangible return: portfolio diversification with bitcoin. J Asset Manag 16(6):365–373
Brock WA, Dechert WD, Scheinkman J (1987) A test for independence based on the correlation dimension. Department of Economics, University of Wisconsin, University of Houston and University of Chicago
Chen C, Liu L, Zhao N (2020) Fear sentiment, uncertainty, and bitcoin price dynamics: the case of COVID-19. Emerg Mark Financ Trade 56(10):2298–2309
Chemkha R, BenSaïda A, Ghorbel A, Tayachi T (2021) Hedge and safe haven properties during COVID-19: evidence from Bitcoin and gold. Q Rev Econ Finance 82:71–85
Chkili W, Ben Rejeb A, Arfaoui M (2021) Does bitcoin provide hedge to Islamic stock markets for pre- and during COVID-19 outbreak? A comparative analysis with gold. Resour Policy 74. https://doi.org/10.1016/j.resourpol.2021.102407
Ciaian P, Rajcaniova M, Kancs A (2016) The economics of BitCoin price formation. Appl Econ 48(19):1799–1815
Das D, LieslLe Roux C, Jana RK, Dutta A (2019) Does Bitcoin hedge crude oil implied volatility and structural shocks? A comparison with gold, commodity and the US Dollar. Finance Res Lett. 36. https://doi.org/10.1016/j.frl.2019.101335
Derbali A, Naoui K, Jamel L (2021) COVID-19 news in USA and in China: which is suitable in explaining the nexus among Bitcoin and Gold? Pac Account Rev 33(5):578–595
Diniz-Maganini N, Diniz EH, Rasheed AA (2021) Bitcoin’s price efficiency and safe haven properties during the COVID-19 pandemic: a comparison. Res Int Bus Finance 58. https://doi.org/10.1016/j.ribaf.2021.101472
Engle R (2002) Dynamic conditional correlation (A simple class of multivariate generalized autoregressive conditional heteroskedasticity models). J Bus Econ Stat 20(3):339–350
Episcopos A, Davis J (1996) Predicting returns on Canadian exchange rates with artificial neural networks and EGARCH-M models. Neural Comput Appl 4(3):168–174
Fang F, Ventre C, Basios M, Kanthan L, Martinez-Rego D, Wu F, Li L (2022) Cryptocurrency trading: a comprehensive survey. Financ Innov 8:13. https://doi.org/10.1186/s40854-021-00321-6
García-Medina A, Luu Duc Huynh T (2021) What drives bitcoin? An approach from continuous local transfer entropy and deep learning classification models. Entropy 23(12):1582
Ghazani MM, Jafari MA (2021) Cryptocurrencies, gold, and WTI crude oil market efficiency: a dynamic analysis based on the adaptive market hypothesis. Financ Innov 7:29. https://doi.org/10.1186/s40854-021-00246-0
Giudici G, Milne A, Vinogradov D (2020) Cryptocurrencies: market analysis and perspectives. J Ind Bus Econ 47:1–18
Göçken M, Özçalıcı M, Boru A, Dosdoğru AT (2016) Integrating metaheuristics and artificial neural networks for improved stock price prediction. Expert Syst Appl 44:320–331
Göçken M, Özçalıcı M, Boru A, Dosdoğru AT (2019) Stock price prediction using hybrid soft computing models incorporating parameter tuning and input variable selection. Neural Comput Appl 31(2):577–592
Grobys K (2021) When Bitcoin has the flu: on Bitcoin’s performance to hedge equity risk in the early wake of the COVID-19 outbreak. Appl Econ Lett 28(10):860–865
Guo X, Lu F, Wei Y (2021) Capture the contagion network of bitcoin: evidence from pre and mid COVID-19. Res Int Bus Finance 58. https://doi.org/10.1016/j.ribaf.2021.101484
Hajizadeh E, Seifi A, Zarandi MF, Turksen IB (2012) A hybrid modeling approach for forecasting the volatility of S&P 500 index return. Expert Syst Appl 39(1):431–436
Hakim das Neves R (2020) Bitcoin pricing: impact of attractiveness variables. Financ Innov 6:21. https://doi.org/10.1186/s40854-020-00176-3
Hoon Kang S, Min Yoon S, Bekiros S, Uddin GS (2019) Bitcoin as hedge or safe haven: evidence from stock, currency, bond and derivatives markets. Comput Econ 56:529–545
Hui ECM, Chan KKK (2022) How does Covid-19 affect global equity markets? Financ Innov 8:25. https://doi.org/10.1186/s40854-021-00330-5
Jakub B (2015) Does Bitcoin follow the hypothesis of efficient market ? Int J Econ Sci 4(2):10–23
Jareno F, de la O Gonzalez M, Tolentino M, Sierra K (2020) Bitcoin and gold price returns: a quantile regression and NARDL analysis. Resour Policy 67. https://doi.org/10.1016/j.resourpol.2020.101666
Jeribi A, Ghorbel A (2021) Forecasting developed and BRICS stock markets with cryptocurrencies and gold: generalized orthogonal generalized autoregressive conditional heteroskedasticity and generalized autoregressive score analysis. Int J Emerg Mark 17(9):2290–2320
Jiang S, Li Y, Lu Q, Wang S, Wei Y (2022) Volatility communicator or receiver? Investigating volatility spillover mechanisms among Bitcoin and other financial markets. Res Int Bus Finance 59. https://doi.org/10.1016/j.ribaf.2021.101543
Jin J, Yu J, Hu Y, Shang Y (2019) Which one is more informative in determining price movements of hedging assets? Evidence from Bitcoin, gold and crude oil markets. Physica A: Stat Mech Appl 527. https://doi.org/10.1016/j.physa.2019.121121
Kakinuma Y (2021) Nexus between Southeast Asian stock markets, bitcoin and gold: spillover effect before and during the COVID-19 pandemic. J Asia Bus Stud 16(4):693–711
Kapar B, Olmo J (2019) An analysis of price discovery between Bitcoin futures and spot markets. Econ Lett 174:62–64
Kayal P, Rohilla P (2021) Bitcoin in the economics and finance literature: a survey. SN Bus Econ 1(88):1–21
Kim W, Lee J, Kang K (2019) The effects of the introduction of Bitcoin futures on the volatility of Bitcoin returns. Finance Res Lett 33. https://doi.org/10.1016/j.frl.2019.06.002
Kou G, Chao X, Peng Y, Alsaadi FE, Herrera-Viedma E (2019) Machine learning methods for systemic risk analysis in financial sectors. Technol Econ Dev Econ 25(5):716–742
Kou G, Olgu Akdeniz Ö, Dinçer H, Yüksel S (2021a) Fintech investments in European banks: a hybrid IT2 fuzzy multidimensional decision-making approach. Financ Innov 7:39. https://doi.org/10.1186/s40854-021-00256-y
Kou G, Peng Y, Wang G (2014) Evaluation of clustering algorithms for financial risk analysis using MCDM methods. Inf Sci 275:1–12
Kou G, Xu Y, Peng Y, Shen F, Chen Y, Chang K, Kou S (2021b) Bankruptcy prediction for SMEs using transactional data and two-stage multiobjective feature selection. Decis Support Syst. 140. https://doi.org/10.1016/j.dss.2020.113429
Kou G, Yüksel S, Dinçer H (2022) Inventive problem-solving map of innovative carbon emission strategies for solar energy-based transportation investment projects. Appl Energy 311. https://doi.org/10.1016/j.apenergy.2022.118680
Kristjanpoller W, Minutolo MC (2015) Gold price volatility: a forecasting approach using the artificial neural network–GARCH model. Expert Syst Appl 42(20):7245–7251
Kristoufek L (2020) Bitcoin and its mining on the equilibrium path. Energy Econ. 85. https://doi.org/10.1016/j.eneco.2019.104588
Kwak W, Shi Y, Kou G (2012) Bankruptcy prediction for Korean firms after the 1997 financial crisis: using a multiple criteria linear programming data mining approach. Rev Quant Financ Acc 38:441–453
Kwon JH (2020) Tail behavior of Bitcoin, the dollar, gold and the stock market index. J Int Financ Markets Inst Money 67. https://doi.org/10.1016/j.intfin.2020.101202
Kwon JH (2021) On the factors of Bitcoin’s value at risk. Financ Innov 7:87. https://doi.org/10.1186/s40854-021-00297-3
Kyriazis NA (2021) Investigating the nexus between European major and sectoral stock indices, gold and oil during the COVID-19 pandemic. SN Bus Econ 1(57):1–12
Kyrtsou C, Terraza V (2000) Volatility behaviour in emerging markets: a case study of the Athens stock exchange, using daily and intra-daily data. Eur Res Stud J 3(3–4):3–16
Lahiani A, Jeribi A, Boukef Jlassi N (2021) Nonlinear tail dependence in cryptocurrency-stock market returns: the role of Bitcoin futures. Res Int Bus Finance 56. https://doi.org/10.1016/j.ribaf.2020.101351
Lahmiri S, Boukadoum M (2015) An ensemble system based on hybrid EGARCH-ANN with different distributional assumptions to predict S&P 500 intraday volatility. Fluct Noise Lett 14(1). https://doi.org/10.1142/S0219477515500017
Lardic S, Terraza V (2019) Financial ratios analysis in determination of bank performance in the German banking sector. Int J Econ Financ Issues 9(3):22–47
Le Tran V, Leirvik T (2020) Efficiency in the markets of crypto-currencies. Finance Res Lett 35. https://doi.org/10.1016/j.frl.2019.101382
Li T, Kou G, Peng Y, Yu PS (2022a) An integrated cluster detection, optimization, and interpretation approach for financial data. IEEE Trans Cybern 52(12):13848–13861
Li Y, Jiang S, Li X, Wang S (2022b) Hybrid data decomposition-based deep learning for Bitcoin prediction and algorithm trading. Financ Innov 8:31. https://doi.org/10.1186/s40854-022-00336-7
Lorenzo L, Arroyo J (2022) Analysis of the cryptocurrency market using different prototype-based clustering techniques. Financ Innov 8:7. https://doi.org/10.1186/s40854-021-00310-9
Lu X, Que D, Cao G (2016) Volatility forecast based on the hybrid artificial neural network and GARCH-type models. Procedia Comput Sci 91:1044–1049
Ma D, Tanizaki H (2022) Intraday patterns of price clustering in Bitcoin. Financ Innov 8:4. https://doi.org/10.1186/s40854-021-00307-4
Mademlis DK, Dritsakis N (2021) Volatility forecasting using hybrid GARCH neural network models: the case of the Italian stock market. Int J Econ Financ Issues 11(1):49–60
Makarov I, Schoar A (2020) Trading and arbitrage in cryptocurrency markets. J Financ Econ 135(2):293–319
Malladi RK, Dheeriya PL (2021) Time series analysis of Cryptocurrency returns and volatilities. J Econ Finance 45:75–94
Matkovskyy R, Jalan A (2019) From financial markets to Bitcoin markets: a fresh look at the contagion effect. Financ Res Lett 31:93–97
Mizerka J, Szajek AS, Mizerka P (2020) The role of Bitcoin on developed and emerging markets – on the basis of a Bitcoin users graph analysis. Finance Res Lett 35. https://doi.org/10.1016/j.frl.2020.101489
Moghaddam AH, Moghaddam MH, Esfandyari M (2016) Stock market index prediction using artificial neural network. J Econ Finance Admin Sci 21(41):89–93
Mokni K, Noomen Ajmi A, Bouri E, Vinh Vo X (2020) Economic policy uncertainty and the Bitcoin-US stock nexus. J Multinatl Financ Manag 57–58. https://doi.org/10.1016/j.mulfin.2020.100656
Moreno EA, Garcia Medina A (2023) LSTM-GARCH hybrid model for the prediction of volatility in cryptocurrency portfolios. Comput Econ. https://doi.org/10.1007/s10614-023-10373-8
Nasir MA, Huynh TLD, Nguyen SP, Duong D (2019) Forecasting cryptocurrency returns and volume using search engines. Financ Innov 5:2. https://doi.org/10.1186/s40854-018-0119-8
Nelson D (1991) Conditional Heteroskedasticity in asset returns: a new approach. Econometrica 59(2):347–370
Noda A (2020) On the evolution of cryptocurrency market efficiency. Appl Econ Lett 28(6):433–439
Omane-Adjepong M, Paul Alagidede I (2021) Exploration of safe havens for Africa's stock markets: a test case under COVID-19 crisis. Finance Res Lett 38. https://doi.org/10.1016/j.frl.2020.101877
Owusu Junior P, Adam AM, Tweneboah G (2020) Connectedness of cryptocurrencies and gold returns: evidence from frequency-dependent quantile regressions. Cogent Econ Finance 8(1). https://doi.org/10.1080/23322039.2020.1804037
Özdemir O (2022) Cue the volatility spillover in the cryptocurrency markets during the COVID-19 pandemic: evidence from DCC-GARCH and wavelet analysis. Financ Innov 8:12. https://doi.org/10.1186/s40854-021-00319-0
Peng Y, Wang G, Kou G, Shi Y (2011) An empirical study of classification algorithm evaluation for financial risk prediction. Appl Soft Comput 11(2):2906–2915
Philippas D, Rjiba H, Guesmi K, Goutte S (2019) Media attention and Bitcoin prices. Financ Res Lett 30:37–43
Platanakis E, Urquhart A (2019) Should investors include Bitcoin in their portfolios? A portfolio theory approach. Br Account Rev 52(4). https://doi.org/10.1016/j.bar.2019.100837
Rounaghi MM, Nasirzadeh F (2016) Investigation of market efficiency and financial stability between S&P 500 and London stock exchange: monthly and yearly forecasting of time series stock returns using ARMA model. Physica A 456:10–21
Sebastião H, Godinho P (2021) Forecasting and trading cryptocurrencies with machine learning under changing market conditions. Financ Innov 7:3. https://doi.org/10.1186/s40854-020-00217-x
Selvamuthu D, Kumar V, Mishra A (2019) Indian stock market prediction using artificial neural networks on tick data. Financ Innov 5:16. https://doi.org/10.1186/s40854-019-0131-7
Shahzad SJH, Bouri E, Kristoufek L, Saeed T (2021) Impact of the COVID-19 outbreak on the US equity sectors: evidence from quantile return spillovers. Financ Innov 7:14. https://doi.org/10.1186/s40854-021-00228-2
Shahzad SJH, Bouri E, Roubaud D, Kristoufek L (2020) Safe haven, hedge and diversification for G7 stock markets: Gold versus bitcoin. Econ Model 87:212–224
Shahzad SJH, Bouri E, Roubaud D, Kristoufek L, Lucey B (2019) Is Bitcoin a better safe-haven investment than gold and commodities? Int Rev Financ Anal 63:322–330
Shaikh I (2020) Policy uncertainty and Bitcoin returns. Borsa Istanbul Rev 20(3):257–268
Shehzad K, Bilgili F, Zaman U, Kocak E, Kuskaya S (2021) Is gold favourable than bitcoin during the COVID-19 outbreak? Comparative analysis through wavelet approach. Resour Policy 73. https://doi.org/10.1016/j.resourpol.2021.102163
Sikiru AA, Salisu AA (2021) Hedging with financial innovations in the Asia-Pacific markets during the COVID-19 pandemic: the role of precious metals. Quant Finance Econ 5(2):352–372
Singh A (2021) Investigating the dynamic relationship between litigation funding, gold, bitcoin and the stock market: the case of Australia. Econ Model 97:45–57
Stensas A, Frostholm Nygaard M, Kyaw K, Treepongkaruna S (2019) Can Bitcoin be a diversifier, hedge or safe haven tool? Cogent Econ Finance, 7(1). https://doi.org/10.1080/23322039.2019.1593072
Symitsi E, Chalvatzis KJ (2019) The economic value of Bitcoin: a portfolio analysis of currencies, gold, oil and stocks. Res Int Bus Financ 48:97–110
Tiwari AK, Jana RK, Das D, Roubaud D (2018) Informational efficiency of Bitcoin: an extension. Econ Lett 163:106–109
Toque C, Terraza V (2011) Time series factorial models with uncertainty measures: applications to ARMA processes and financial data. Commun Stat - Theory Methods 40(9):1533–1544
Toque C, Terraza V (2014) Histogram-valued data on value at risk measures: a symbolic approach for risk attribution. Appl Econ Lett 21(17):1243–1251
Vardar G, Aydogan B (2019) Return and volatility spillovers between Bitcoin and other asset classes in Turkey: evidence from VAR-BEKK-GARCH approach. EuroMed J Bus 14(3):209–220
Wang P, Zhang H, Yang C, Guo Y (2021) Time and frequency dynamics of connectedness and hedging performance in global stock markets: Bitcoin versus conventional hedges. Res Int Business Finance 58. https://doi.org/10.1016/j.ribaf.2021.101479
Wang Q, Liu L (2022) Pandemic or panic? A firm-level study on the psychological and industrial impacts of COVID-19 on the Chinese stock market. Financ Innov 8:36. https://doi.org/10.1186/s40854-022-00335-8
Wei WC (2018) Liquidity and market efficiency in cryptocurrencies. Econ Lett 168:21–24
Xu M, Chen X, Kou G (2019) A systematic review of blockchain. Financ Innov 5:27. https://doi.org/10.1186/s40854-019-0147-z
Yarovaya L, Matkovskyy R, Jalan A (2022) The COVID-19 black swan crisis: reaction and recovery of various financial markets. Res Int Bus Finance 59. https://doi.org/10.1016/j.ribaf.2021.101521
Yousaf I, Ali S (2020) Discovering interlinkages between major cryptocurrencies using high-frequency data: new evidence from COVID-19 pandemic. Financ Innov 6:45. https://doi.org/10.1186/s40854-020-00213-1
Youssef M, Mokni K, Ajmi AN (2021) Dynamic connectedness between stock markets in the presence of the COVID-19 pandemic: does economic policy uncertainty matter? Financ Innov 7:13. https://doi.org/10.1186/s40854-021-00227-3
Zhang H, Wang P (2020) Does Bitcoin or gold react to financial stress alike? Evidence from the U.S. and China. Int Rev Econ Financ 71:629–648
Acknowledgements
The authors would like to acknowledge the support of our study by the Department of Economics and Management, University of Luxembourg.
Funding
This work was supported by the Department of Economics and Management, University of Luxembourg. Mohammad Mahdi Rounaghi would like to acknowledge financial support from the Department of Economics and Management, University of Luxembourg.
Author information
Authors and Affiliations
Contributions
V.T. contributed to supervision, conceptualization, methodology, software, visualization, investigation, writing-original draft, validation, project administration, writing review & editing, and formal analysis of the paper. A.B.İ. contributed to conceptualization, methodology, software, visualization, investigation, writing-original draft, validation, project administration, writing-review & editing, and formal analysis of the paper. M.M.R. contributed to data curation, conceptualization, writing- original draft, investigation, validation, writing-review & editing, and formal analysis of the paper. All authors read and approved the final version of the manuscript.
Corresponding author
Ethics declarations
Competing interests
The authors declare that they have no competing interests.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Appendix: Further analysis
Appendix: Further analysis
Appendix A: The BDS test results
Appendix A shows the full estimation result of the BDS test. These results are given in Tables
8,
9,
10,
11,
12,
13,
14,
15,
16,
17.
Appendix B: The Ljung box test results
Appendix B shows tests for autocorrelation in the returns using the Ljung Box test.
Tables
18 and
19 report the Q-Statistic and P-value for Bitcoin, gold, and the stock market indexes.
Appendix C: The Lagrange multiplier test
Appendix C shows autocorrelation in the squared of the returns using the Lagrange Multiplier test for 2 periods (see Tables
20,
21,
22,
23,
24,
25,
26,
27,
28,
29).
Appendix D: The VAR (1) models
Tables
30 and
31 report the estimation of VAR (1) models for 2 periods. Tables 32 and 33 report the Ljung Box test on the standardized residuals of the VAR-DCC-EGARCH models for 2 periods.
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Terraza, V., Boru İpek, A. & Rounaghi, M.M. The nexus between the volatility of Bitcoin, gold, and American stock markets during the COVID-19 pandemic: evidence from VAR-DCC-EGARCH and ANN models. Financ Innov 10, 22 (2024). https://doi.org/10.1186/s40854-023-00520-3
Received:
Accepted:
Published:
DOI: https://doi.org/10.1186/s40854-023-00520-3