Long memory in the high frequency cryptocurrency markets using fractal connectivity analysis: The impact of COVID-19
Graphical Abstract
Introduction
Since their creation, started by Bitcoin in 2008, cryptocurrencies have gathered a keen interest among investors, risk managers, and policymakers. This new class of assets becomes more and more interesting and occupies an important place in the financial system, due to their beneficial investment as well as their ability to act as a hedge and safe haven against traditional assets’ fluctuations and increased uncertainty (Fang et al., 2022, Mokni et al., 2020, Mokni and Ajmi, 2021, Urquhart and Zhang, 2019, Wang et al., 2019; Conlon et al., 2020). Particularly, the cryptocurrency market has boomed over the last few years, with the propagation of the COVID-19 pandemic, when the different cryptocurrencies’ prices showed a strong increase. This upward trend is not necessarily obvious from a theoretical perspective but is due to the increased demand for hedging and risk-reducing purposes in response to the augmented uncertainty related to this health crisis.
The COVID-19 restricts several activities of human beings, ultimately affecting the financial markets and economies. Many of the financial markets sharply declined at the start of the COVID-19 pandemic, including stocks (Baker et al., 2020, Ding et al., 2021), bonds (Halling et al., 2020, Gupta et al., 2021), commodities (Salisu et al., 2020, Ji et al., 2020), real estate (Ling et al., 2020, Qian et al., 2021). In the context of the cryptocurrency market, several studies have highlighted the consequence of the COVID-19 crisis on this new market (Goodell and Goutte, 2021; Yousaf and Ali, 2020a, Yousaf and Ali, 2020b, among others). However, during the later phase of COVID-19, the prices of several highly capitalized cryptocurrencies unprecedently increased and touched their all-time high peaks, especially after April 2020. Moreover, the prices and volatilities of these cryptocurrencies are much higher during the COVID-19 than during the pre-COVID-19 period (see. Fig. 1). Therefore, investors need to adjust their portfolios of cryptocurrencies during this health crisis. In this way, some questions should be asked such as the efficiency and the long memory property characterizing cryptocurrencies’ prices. In this way, the success of investing in cryptocurrencies concerning their roles in providing high returns and hedging opportunities depends on whether the cryptocurrency market is efficient.
According to the Efficient Market Hypothesis (EMH), futures prices fully reflect all public information, and traders will not be able to create trading strategies to make excess profits or beat the market returns (Fama, 1970). In this context, long memory processes are popular in modeling persistence, and therefore in testing the efficiency, observed in financial markets (see for example Assaf et al., 2021; Abuzayed et al., 2018; Charfeddine, 2016; Baillie and Morana, 2009).
The presence of long-range dependence on financial assets raises many issues in regard to modeling, statistical testing, and efficiency. The long memory feature has been found in the returns and volatilities of various financial assets and markets (Cheung and Lai, 1993, Ding et al., 1993; Bollerslev and Mikkelsen, 1996; Ding and Granger, 1996; Mighri et al., 2010; Cheah et al., 2018, Oral and Unal, 2019) and report some causes of long memory in these markets. In the context of the cryptocurrency market, shocks such as hacking or bankruptcies of multiple cryptocurrencies, the introduction of Bitcoin futures, the outbreak of the COVID-19 pandemic, the collapse of the cryptocurrency market, and the ban and regulations imposed on some of those assets are all having an impact on their behavior, individually and as a group of assets, can be the origin of structural breaks, which can be the main source of long memory. Therefore, it is of great importance to determine how these shocks affect the behavior of cryptocurrency prices; and whether these shocks have any permanent or transitory effect on their dynamics over time.
To our knowledge, this is the first attempt to examine the long memory structure among the high-frequency cryptocurrency returns using a multivariate long memory model, and studying the impact of the COVID-19 pandemic on that structure. The study of fractal networks within the long memory model is important for the study of the evolutionary and adaptive nature of market structure after a shock, such as the COVID-19 pandemic crisis, and investors should be aware that such shocks can alter the long-memory properties of the assets under study. These shocks may lead to a change in the long-run correlation among cryptocurrencies, which will increase the portfolio risk and that may imply that some cryptocurrencies do not provide diversification benefits to investors during downturns or crisis periods, like the COVID-19 pandemic (see for example Matkovskyy et al., 2021, Yarovaya et al., 2022 and Conlon and McGee, 2020).
In the current study we, firstly, examine the impact of COVID-19 on the long memory property of the major cryptocurrencies using high-frequency data. For this purpose, we estimate the long memory (in returns) of the seven highly capitalized cryptocurrencies before and over the COVID-19 periods. The long memory analysis is useful for detecting market efficiency, which provides valuable information to investors about the forecasting power of cryptocurrencies. More specifically, the presence of long memory offers evidence against weak form efficiency, indicating the ability to forecast future returns through past returns. Secondly, we investigate the long-range correlations between the seven cryptocurrencies before and during COVID-19. These correlations are insightful for investors in the context of hedging and diversification strategies. As the dynamics of cryptocurrencies vary intensively during COVID-19 (Yousaf and Ali, 2020a), we can expect the different long-range correlations between cryptocurrencies during the COVID-19 compared to the pre-COVID-19 period, which forces the investors to change their portfolio allocation in cryptocurrencies accordingly. Thirdly, we look at the clustering or community similarities among the different cryptocurrencies before and during COVID-19. This clustering analysis provides valuable information to investors about the group of cryptocurrencies whose structures are similar or different from each other, and this information is helpful in portfolio diversification before and during crisis periods. Fourth, our study conducts also a testing procedure for changes in persistence over the sample period.
Accordingly, in this paper, we contribute to the existing literature in the following ways. First, we study the long-range correlations and clustering dynamics among the high-frequency cryptocurrencies during and before the COVID-19 period; an issue that is not considered previously in the literature. Second, our study uses high-frequency data in the empirical analysis. In this context, limited studies use high-frequency data for long memory analysis in the literature (Zhang et al., 2019, Mensi et al., 2019a, Mensi et al., 2019b; Naeem et al., 2021; Aslan and Sensoy, 2020). High-frequency data provides more stylized facts and a more detailed picture than low-frequency data in the long memory analysis (Bollerslev and Wright, 2000). Third, we investigate whether the long memory parameter estimates have changed over time. Particularly, the impact of the COVID-19 pandemic on the dynamics of long memory estimates is analyzed. Moreover, we investigate how the multivariate fractality and connectivity of these assets behave before and during the COVID-19 pandemic. We contribute to the existing literature in several aspects. Recent studies explore the impact of COVID-19 from different aspects. Mnif et al. (2020) find an increase in the cryptocurrency market efficiency during the COVID-19 pandemic period. However, Naeem (2021) shows that COVID-19 has a negative impact on the efficiency of major cryptocurrencies while they recover from inefficiency at the end of March 2020.
In the context of the cryptocurrency market, Lahmiri and Bekiros, 2020a, Lahmiri and Bekiros, 2020b show higher instability and irregularity during the pandemic compared to the equities implying that they are riskier and more unpredictable. The impact of COVID-19 on the hedging properties of Bitcoin is widely explored (Corbet et al., 2020b, Corbet et al., 2020c; Conlon et al., 2020; Demir et al., 2020; Goodell, 2020; Iqbal et al., 2021). Although a strand of the literature considers the effect of the pandemic on the cryptocurrency market, to our knowledge, we are the first to examine the long memory parameter estimates in the COVID-19 pandemic period. Moreover, we explore how the multivariate fractality and connectivity of cryptocurrencies change in the COVID-19 period compared to the pre-COVID-19 period.
Initially, we apply two long memory tests to deal with the spurious long memory. The two tests are proposed by Qu (2011) and Sibbertsen et al. (2018). The first test is a univariate version, while Sibbertsen et al. (2018) has a multivariate form, whereas both are based on the local Whittle likelihood function. Based on Qu (2011)'s univariate test, the true long memory is rejected with the bandwidth of 0.60 and 0.65, yet with higher bandwidths of 0.70 and 0.75, the null hypothesis of true long memory cannot be rejected for all series except for Litecoin at 0.70 bandwidth. Our results indicate the presence of true long memory in most considered cryptocurrencies, and there are no low-frequency contaminations, such as random level shifts or breaks, underlying their returns variation. Then, by applying the MLWS test statistic, the results indicate that the null hypothesis of true long memory is rejected for all series, implying that the persistence in the high-frequency cryptocurrency returns is not real and might be a spurious one, associated with some regime change during the sample period (i.e., the effect of COVID-19).
Second, we complement our analysis by estimating the long-run correlation matrix of returns by relying on the multivariate long memory estimator, which is wavelet-based and suggested by Achard and Gannaz (2016) and Achard et al. (2008). For the whole period, our results reveal some evidence of a long-run correlation structure among the hourly returns of Bitcoin (BTC), Ethereum (ETH), Litecoin (LTC), Monero (XMR), Stellar (XLM), Tron (TRX), and EOS token (EOS). However, the clustering matrix indicates a strong long-run correlation among our sample, except for Stellar (XLM). Then, considering the impact of COVID-19 on our results, the evidence provided shows, except for Stellar (XLM), the remaining six crypto returns exhibit significant long-run correlations among each other. The fractal connectivity clustering indicates a similarity in fractal structure among Ethereum (ETH) and Litecoin (LTC), Monero (XMR), Bitcoin (BTC), and EOC token (EOS), while Stellar (XLM) is clustered away from the remaining six crypto returns, indicating the absence of any interdependence with other crypto returns.
Then, studying the fractal structure among the seven cryptos during the COVID-19 period, XLM exhibits a weaker correlation with EOS coin and TRX (Tron). Similarly, the EOS coin, Litecoin, Bitcoin, and Ethereum form a cluster revealing the similarity in the fractal structure of the EOS coin with that of Litecoin, Bitcoin, and Ethereum. The same can be found for Bitcoin (BTC), Ethereum (ETH), and Litecoin (LTC). Again, our evidence indicates the disentanglement of Stellar (XLM) from the network of six other crypto returns during the COVID19 period. Overall, shocks arising from the COVID-19 crisis have led to changes in the long-run correlation structure.
Finally, to support further our results, we apply a change in persistence testing methods. Specifically, we apply the ratio tests of Busetti and Taylor (2004), Leybourne and Taylor (2004), and Harvey et al. (2006), then complement that with the modified ratio test proposed by Martins and Rodrigues (2014). Overall, the evidence obtained indicates a decrease in the persistence for the majority of the return series, except for the Stellar cryptocurrency. Then, we try to localize the breakpoint of change in persistence. The results indicate the presence of a break in persistence at a sample data point of 14403 coinciding with 8/23/2020 at 2:00 AM, where the cryptos return being integrated with different orders within two regimes.
Our results of the presence of long memory are related to the characteristics of cryptocurrencies in terms of their administration and speed of transactions (for example, Bitcoin and Ethereum are two decentralized cryptocurrencies that operate on public blockchain ledgers), and can be attributed to the macro-economic and financial factors of the real economy (Cheah, Mishra, Parhi, and Zhang, 2018), and to behavioral factors like the composition of investors and market conditions (Khuntia and Pattanayak, 2018), under which these assets go through. In terms of regulatory measures, Shanaev, Sharma, Ghimire, and Shuraeva (2020) have studied 120 regulatory measures relating to cryptocurrencies and examined their impact on efficiency. The cryptocurrency market, in general, is found to be efficient in reflecting the cryptocurrencies' regulatory information on the one hand or is burdened by too much undesirable regulation on other hand.
In addition, Phillip et al. (2019) related the presence of long memory in cryptocurrencies to the completion time or transaction speed of each crypto. They studied the volatility oscillation memory ratios (VOMR) in a large number of cryptocurrencies. Cryptocurrencies use Blockchain technology that can be explained as a clearing house for transactions, that are meant to be instantaneous and have a negligible bid-ask spread, as opposed to fiat currencies that have those frictions. Phillip et al. (2019) explain the intuitive relationship of VOMR with completion time and how the day-to-day volatility correlation is dependent on completion times and more liquidity. They looked at the top six Cryptocurrencies, keeping in mind that BTC, ETH, and XMR have long completion times, compared to LTC, DASH, and XRP which have shorter completion times. For example, BTC takes up to two days to transact, whereas XRP takes only seconds. This implies that transaction speeds are an important factor in the role of these cryptocurrencies and are associated with the oscillatory long-run autocorrelation structure of their volatility measures.1
In terms of transaction speed, BTC receives the biggest criticism as its infrastructure set-up was not designed to handle such a large volume of trades that it currently experiences. As such, critics argue that it is not a sustainable Cryptocurrency, since it now has extremely slow transaction speeds and is therefore not a long-term viable solution. Another interesting finding is the VOMR of ETH being again close to one. ETH claims to have embedded “Smart Contracts” to circumvent the slow transaction fallacy of BTC. However, in reality, the transaction time of ETH has also increased considerably due to a lack of infrastructure upgrades to deal with growing pains. XMR is a coin that mainly focuses itself on security and privacy, but not on speed. These three Cryptocurrencies as a group are in sharp contrast to LTC and DASH who pride themselves on having faster transactions.
The rest of the paper is structured as follows: Section 2 provides the literature review. Section 3 describes the empirical methodology. Section 4 presents the data set of the study. The results are presented in Section 5. The last section concludes the paper and provides the implications.
Section snippets
Literature review
Bitcoin (BTC) and in general, cryptocurrencies have been attracting considerable attention among researchers, practitioners, investors, and regulatory bodies and have been experiencing large fluctuations during the past few years. With the introduction of other cryptocurrencies after Bitcoin, an enormous stream of literature has been devoted to exploring the dynamic properties of the newly introduced currencies. The literature surveys conducted by Yli-Huumo et al. (2016), Corbet et al. (2019),
Empirical methodology
The spectral density function of a long memory process which displays a persistent slow power-law decaying autocorrelations takes the formasymptotically as the frequency , whereand represents the Gamma function, and the parameter known as the Hurst exponent, is the most popular measure for the presence of long memory. For long memory processes, . The constant is obtained from the equivalent asymptotic autocovariance function written
Data
We use hourly historical time series data of seven cryptocurrencies including Bitcoin (BTC), Ethereum (ETH), Litecoin (LTC), Monero (XMR), Stellar (XLM), Tron (TRX), and EOS (EOS) as of January 20, 2021. The dataset is for the period from 1 January 2019–20 January 2021 for the hourly data having 18001 observations for all cryptocurrencies. The data is obtained from Kaiko Digital Asset Store. We specifically use Bitfinex Exchange since it includes the most liquid order book and offers different
Empirical Findings
The rise of cryptocurrencies that started in 2008 as a means of payment brought with it many answered questions. In contrast to traditional financial assets, they evolved into complex and high-yield assets. Cryptocurrencies are not (mostly) traded on organized markets and do not abide by the legal framework. That resulted in their extreme volatility and fluctuations over time caused by investors’ sentiments and events that call for such an investigation. In this paper, we study the
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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