COVID-19 and cryptocurrency volatility: Evidence from asymmetric modelling.

This paper analyzes the role of COVID-19 pandemic crisis in determining and forecasting conditional volatility returns for a set of eight cryptocurrencies through an asymmetric GARCH modeling approach. The findings report that the COVID-19 pandemic exerts a positive effect on the conditional volatility of those returns, while explicitly considering the pandemic event improves volatility predictions.

Introduction

The COVID-19 pandemic has been a disruptive force to the global economy, as well as to financial markets. As a result, there has evolved an extensive literature on the impact of the pandemic on financial, and especially, cryptocurrency markets. Cryptocurrencies play the role of a hedging mechanism during financial market turmoil, giving rise to major concerns coming from certain market stakeholders, such as market participants, regulators and policymakers (Foley et al., 2019). The literature has established that cryptocurrencies are better hedging assets over other financial assets, such as stocks and US dollar (Dyhrberg, 2016). During the COVID-19 pandemic crisis, investors highly attempt to diversify their portfolio toward cryptocurrencies to experience short-term gains, thus consider them as safe-haven assets and potentially entering a herd-type of behavior. In contrast, during the same period, their value suffered, potentially indicating the presence of a fear sentiment across investors (Chen et al., 2020; Corbet et al., 2020).

Financial stability conditions are more than a necessity, given that the presence of high and persistent volatility in various assets can generate unstable markets with negative spillovers to the real economy (Mnif et al., 2020). Salisu and Ogbonna (2021) document that fear-induced news, due to the COVID-19 pandemic crisis, increases the return volatility of cryptocurrencies compared to the pre-pandemic period, while the incorporation of news effects forecasts volatility better than benchmark forecasts. More specifically, crises events, such as financial crises and/or pandemic crises tend to induce panic and concerns amidst investors, mainly through raises in price volatility, thus contributing to social mindsets, such as the herding behavior (Mnif et al. 2020; Kizys et al., 2021; Espinosa-Méndez and Arias, 2021). Moreover, Hong et al. (2021) argue that the pandemic event is closely associated with market inefficiency, offering substantial rewards to dealers and opportunists. In addition, others discuss that COVID-19 news affects asset prices because fear caused by the mass media is related with growing price volatility (Haroon and Rizvi 2020), while Chundakkadan and Nedumparambil (2021) provide evidence that the hysteria with the pandemic generated a pessimistic reaction between market players and weakened the stock exchanges, a typical attitude in behavioral finance. The hypothesis of safe-haven assets can also explain higher volatility during health crises. The literature supports this approach that pandemic events promote efficient diversification and risk alleviation, especially when it comes to cryptocurrencies (Huang et al., 2021; Mariana et al., 2021; Disli et al., 2021). Finally, the impact can be explained through the channel of investor attention, according to which, when investors are more attentive to news events, the associated information is faster reflected onto asset prices, leading to higher volatility (Smales, 2021). In this case, the hypothesis of ‘investor sentiment’ can be tested in relevance to the mood-biased information reflected onto asset prices, since higher levels of investor attention exacerbate the effect of investors’ sentiment on asset prices. The theories associated with investor attention, the choice asymmetry (Barber and Odean, 2008) and the information discovery (Tantaopas et al., 2016) provide the theoretical background for the empirical findings.

Our work is close to this piece of evidence, but significantly differs in a sense of using an asymmetric volatility model that reflects better the cryptocurrency behavior, while it explicitly introduces COVID-19 data into the conditional volatility model. This paper is an addition to the (limited) literature that investigates the impact of epidemics on financial markets and, particularly the market of cryptocurrencies. In terms of cryptocurrencies during the pandemic period, Goodell and Goutte (2021) find that the presence of COVID-19 has caused rises in Bitcoin prices, while Corbet et al. (2020) provide adequate evidence on the growth of returns and the trading volume of cryptocurrencies, suggesting that (particularly) large cryptocurrencies act as a store of value during the pandemic. Their returns are found to be significantly influenced by negative sentiments associated with COVID-19. As a result, they provide diversification benefits for investors, indicating that they can act as safe-haven assets. Wasiuzzaman et al. (2021) also provide solid evidence of increased volatility of gold-back cryptocurrencies during the COVID-19 pandemic, but the increase is insignificant to suggest that gold-backed cryptocurrencies serve as a safe-haven asset. Geuder et al. (2019) also provide new evidence that confirms the presence of certain bubble periods in terms of the Bitcoin prices. They also explore the causes of such bubbles, with their results documenting that such factors are associated with institutional changes, such as the introduction of Bitcoin futures, the use of Bitcoin for web-based transactions, governments restrictions on the use of cryptocurrencies and other regulatory changes. Moreover, Conlon et al. (2020), Ji et al. (2020), Sifat (2021), Wang and Wang (2021) discover that cryptocurrencies’ volatility is not influenced by any global sentiment proxies, and mostly those associated with the COVID-19 pandemic. In other words, the majority of cryptocurrencies can be treated as an independent asset class and as a safe haven asset with diversification benefits. Mariana et al. (2021) also find that the two most influential cryptocurrencies, that is Bitcoin and Ethereum, can act as short-term safe-haven assets, with the latter acting as a better safe-haven than the former. Nevertheless, both cryptocurrencies illustrate high volatilities during the pandemic crisis. By contrast, Conlon and McGee (2020) document that Bitcoin does not serve as a safe-haven asset as its price decreases in concert with the S&P500 stock index, reflecting increases in downside risks as the COVID-19 pandemic develops. Yarovaya et al. (2021) also explore whether the COVID-19 crisis serves as a black swan event on cryptocurrencies, resulting in behavioral anomalies, i.e., investor herding. Their findings do not provide any supportive evidence that the pandemic serves in amplifying herding in the cryptocurrency markets.

Data and methodology

We study the effect of COVID-19 on a group of eight major cryptocurrencies’ returns and their volatility, spanning the period February 1, 2020 through October 31, 2021 using daily data. The cryptocurrencies in our analysis include Bitcoin, Dash, Ethereum, Litecoin, XRP, NEM, DigiByte, and Dogecoin, since their volume of transactions comes close to 80% of total cryptocurrency volume. Data were retrieved from Datastream. We also employ two proxies for the COVID-19 event: (i) worldwide confirmed cases, and (ii) worldwide cases of death cases, with data being obtained from Datastream. Moreover, data on total assets (Liquidity) for certain central banks, i.e., US, UK, ECB, Japan, Canada, and China, were obtained from the FRB of Saint Louis, while data on the market sentiment index were sourced from the FRB of San Francisco. Finally, data on the volume of transactions in the cryptocurrency market were obtained from Datastream. Continuously compounded daily cryptocurrency returns are computed as follows:where P and P are cryptocurrency prices at time t and t-1, respectively. Table 1 presents summary statistics. Panel A reports the original variables in their levels, while Panel B presents the abnormal volumes associated with the cryptocurrencies under consideration. The numbers clearly illustrate that XRP is the most volatile cryptocurrency over the COVID-19 period, followed by the Dash. By contrast, Ethereum experienced the highest average returns, followed by Bitcoin. In terms of the skewness metric, all cryptocurrencies display an asymmetric distribution; finally, in terms of kurtosis, these cryptocurrencies deviate from the normal distribution, with all of them following a leptokurtic distribution, indicating that the return series are characterized by thicker tails versus the normal distribution, a sign of a risky investment.

Table 1

Descriptive statistics.

Variables	Mean	SD	Min	Max	Skewness	Kurtosis
Panel A
Bitcoin	0.0026	0.0206	-0.2018	0.0741	-2.7891	26.1994
Dash	0.0013	0.028	-0.1995	0.1789	-0.1448	13.6082
Ethereum	0.0029	0.0268	-0.2392	0.1509	-1.6094	17.4482
Litecoin	0.0017	0.0248	-0.195	0.1105	-1.2673	12.9015
XRP	0.0011	0.0321	-0.2136	0.2691	0.1608	15.8094
NEM	0.001	0.0217	-0.0002	0.0028	0.2873	17.0672
DigiByte	0.0008	0.0058	-0.0003	0.0019	0.5471	19.0063
Dogecoin	0.0012	0.0032	-0.0005	0.0023	0.1885	16.9061
WCOVID-19 cases	0.0101	0.0144	-0.0463	0.1519	3.9781	27.7114
WCOVID-19 deaths	0.0095	0.0182	-0.0561	0.1806	4.6591	25.6135
Sentiment	-0.2729	0.2129	-0.6522	0.0614	-0.2498	-1.432
Panel B
Abnormal volume
Bitcoin	-0.6348	0.2381	-0.0468	1.6735	4.6109	17.6025
Abnormal volume
Dash	-0.9619	0.4592	-1.5997	0.8765	0.5218	-0.9137
Abnormal volume
Ethereum	-0.085	1.8584	-0.0339	1.4598	10.9447	118.5068
Abnormal volume
Litecoin	-2.8843	2.6754	-3.4067	4.4619	1.4239	1.3194
Abnormal volume
XRP	-0.0072	4.9019	-0.0028	5.6982	0.5568	-0.2519
Abnormal volume
NEM	-0.0239	2.3894	-0.0142	4.8903	1.8835	1.5592
Abnormal volume
DigiByte	-0.3471	3.4792	-0.1744	5.0541	2.0918	1.3382
Abnormal volume
Dogecoin	-0.6753	4.0038	-1.5732	3.9937	1.4382	7.8905
No. of daily obs.	639 ×8 = 5112
Liquidity (US $)	5008,416	10,016,248	17,230	188,015,994	7.6344	64.3092
(in mil.)
No. of weekly obs.	84 ×8 = 672

Notes: The time span is: February 1, 2020 through October 31, 2021. This table presents descriptive statistics for the data. WCOVID-19 cases and WCOVID-19 deaths denotes COVID-19 world confirmed cases and deaths, respectively. Liquidity shows the total assets value (in US dollars) of certain central banks, i.e., US, UK, ECB, Japan, Canada, and China. SD shows standard deviation, while the figures of cryptocurrencies indicate statistics of returns.

To examine the impact of the COVID-19 pandemic on cryptocurrency returns and their volatility, the analysis explicitly considers the evidence provided by Iqbal et al. (2021) who evaluate the top 10 cryptocurrencies and provide evidence on the presence of a non-linear relationship between cryptocurrency returns, along the COVID-19 outbreak. Bouri et al. (2021) also examine the non-linearity-based connectedness of cryptocurrencies to provide evidence that both returns and volatility connectedness strengthen with shock size for both positive and negative shocks, indicating that shocks propagate more intensely during extreme events, such as pandemic crises. Similar evidence on the non-linearity feature of cryptocurrency volatility has been also provided by Baur and Dimpfl (2018) and Stavroyiannis (2018) who explore how cryptocurrencies’ conditional volatility is affected by past positive and negative shocks.

The baseline methodology follows the TGARCH(1, 1) model recommended by Glosten et al. (1993). We also allow the variable of COVID-19 to enter the model. The mean (returns) equation uses an autoregressive model of order one (AR(1)) to detect serial correlation across all cryptocurrencies under investigation. Based on the contributions by Kinateder et al. (2017) and Batten et al. (2019), the mean equation yields:where Liquidity denotes the monetary policy liquidity variable (total assets) of certain central banks, Sentiment is the market sentiment index, AVOL shows the abnormal volume defined as the difference between the actual and detrended volume (Batten et al. 2019), and Δ is the difference operator; in terms of the conditional variance equation, the analysis also adds the COVID-19 variable into the conditional variance equation, which yields:where I(.)is an indicator function taking 1 ifut-1< 0, and 0 otherwise. The parameters ω2 and ω3 are restricted to be positive, and the parameter ω4 takes values between -1 and 1. Moreover, given the asymmetric assumption of the modeling process, the estimates also need to satisfy the following restriction: (i.e., the stationary variance process condition).

Empirical results

We begin with tests of unit roots using the generalized least squares (GLS) test (Elliott et al., 1996), as shown in Table 2 . The results indicate that the respective returns for cryptocurrencies are stationary, while the COVID proxies related to COVID-19 cases and deaths is first-difference stationary.

Table 2

GLS unit root tests.

Variables	Levels First differences
Bitcoin returns	-6.96(1)⁎⁎⁎
Dash returns	-6.90(2)⁎⁎⁎
Ethereum returns	-7.25(2)⁎⁎⁎
Litecoin returns	-6.97(1)⁎⁎⁎
XRP returns	-6.85(2)⁎⁎⁎
NEM returns	-6.37(2)⁎⁎⁎
DigiByte returns	-5.94(3)⁎⁎⁎
Dogecoin returns	-6.38(2)⁎⁎⁎
Liquidity	-1.33(3)	-6.84(2)⁎⁎⁎
Sentiment	-1.36(4)	-7.16(2)⁎⁎⁎
Abnormal volume Bitcoin	-6.25(2)⁎⁎⁎
Abnormal volume Dash	-6.63(1)⁎⁎⁎
Abnormal volume Ethereum	-6.15(2)⁎⁎⁎
Abnormal volume Litecoin	-6.44(2)⁎⁎⁎
Abnormal volume XRP	-6.67(1)⁎⁎⁎
Abnormal volume NEM	-6.51(2)⁎⁎⁎
Abnormal volume DigiByte	-6.38(2)⁎⁎⁎
Abnormal volume Dogecoin	-6.04(1)⁎⁎⁎
WCOVID19-cases	-1.29(2)	-6.97(1)⁎⁎⁎
WCOVID19-deaths	-1.36(2)	-6.94(1)⁎⁎⁎

Notes: The time span is: February 1, 2020 through October 31, 2021. The table provides unit root test results based on the GLS method. WCOVID19-cases and WCOVID19-deaths denote worldwide confirmed cases and deaths, respectively. Liquidity is the sum of total assets in US dollars of certain central banks, i.e., US, UK, ECB, Japan, Canada, and China. Sentiment is the market sentiment index. The abnormal volume (AVOL) is calculated as the difference between actual volume and the detrended volume (through a trend regression). The rejection of the null hypothesis indicates stationarity. Figures in parentheses denote the number of lags included in the test and were determined through the Akaike information criterion.

p ≤ 0.01.

Next, the analysis provides the estimates of the parameters of the TGARCH model in Table 3 . Focusing on the primary coefficient of interest, the world pandemic metrics, the results provide strong evidence that the COVID-19 factor exerts a significant negative impact on the mean of cryptocurrency returns, with the findings being held across both COVID-19 measures and with the negative impact getting more pronounced when the world confirmed deaths proxy the effect of the pandemic. The results in the conditional volatility equation document that in terms of the asymmetric coefficient ω4, they support the presence of a positive parameter, implying that negative shocks increase conditional volatility more than positive shocks. Moreover, the COVID-19 metrics have a positive and statistically significant effect on the conditional volatility of cryptocurrency returns, with these effects being stronger with the consideration of the world number of deaths as a proxy for COVID-19. Finally, certain diagnostics denote the absence of serial correlation and autocorellation in the residuals, implying that the TGARCH models are well specified.

Table 3

TGARCH estimates: COVID-19 and cryptocurrency returns.

TOTAL CONFIRMED CASESMean equation	Bitcoin	Dash	Ethereum	Litecoin XRP NEM DigiByte Dogecoin
Constant	0.014	0.012	0.007	0.006 0.010 0.006 0.014 0.012
	[0.55]	[0.58]	[0.62]	[0.65] [0.60] [0.68] [0.55] [0.59]
Cryptocurrency returns(-1)	0.526⁎⁎⁎	0.546⁎⁎⁎	0.561⁎⁎⁎	0.625⁎⁎⁎ 0.599⁎⁎⁎ 0.562⁎⁎⁎ 0.613⁎⁎⁎ 0.525⁎⁎⁎
	[0.00]	[0.00]	[0.00]	[0.00] [0.00] [0.00] [0.00] [0.01]
Liquidity 1.603⁎⁎⁎ 1.122⁎⁎⁎ 1.752⁎⁎⁎ 1.577⁎⁎⁎ 1.604⁎⁎⁎ 1.462⁎⁎⁎ 1.536⁎⁎⁎ 1.228⁎⁎⁎[0.00] [0.00] [0.00] [0.00] [0.00] [0.00] [0.00] [0.01]Sentiment 0.911⁎⁎⁎ 0.749⁎⁎ 0.968⁎⁎⁎ 1.007⁎⁎⁎ 0.854⁎⁎⁎ 0.673⁎⁎⁎ 0.826⁎⁎⁎ 0.694⁎⁎⁎[0.00] [0.02] [0.01] [0.00] [0.01] [0.01] [0.00] [0.01]Abnormal volume -0.448⁎⁎ -0.339* -0.504⁎⁎ -0.519⁎⁎ -0.389* -0.352* -0.416* -0.363*[0.05] [0.08] [0.05] [0.05] [0.10] [0.10] [0.07] [0.10]
ΔCOVID-19	-2.384⁎⁎⁎	-2.126⁎⁎⁎	-2.367⁎⁎⁎	-2.946⁎⁎⁎ -2.258⁎⁎⁎ -2.117⁎⁎⁎ -2.184⁎⁎⁎ -2.459⁎⁎⁎
	[0.00]	[0.00]	[0.00]	[0.00] [0.00] [0.00] [0.00] [0.00]
Conditional volatility equation
Cosntant	0.0020	0.0021	0.0015	0.0007 0.0008 0.0003 0.0002 0.0010
	[0.16]	[0.16]	[0.20]	[0.28] [0.27] [0.31] [0.35] [0.25]
h(-1)	0.637⁎⁎⁎	0.488⁎⁎⁎	0.549⁎⁎⁎	0.536⁎⁎⁎ 0.545⁎⁎⁎ 0.509⁎⁎⁎ 0.473⁎⁎⁎ 0.504⁎⁎⁎
	[0.00]	[0.00]	[0.00]	[0.00] [0.00] [0.00] [0.01] [0.00]
u2(-1)	0.356⁎⁎⁎	0.412⁎⁎⁎	0.429⁎⁎⁎	0.437⁎⁎⁎ 0.458⁎⁎⁎ 0.416⁎⁎⁎ 0.385⁎⁎⁎ 0.409⁎⁎⁎
	[0.00]	[0.00]	[0.00]	[0.00] [0.00] [0.00] [0.00] [0.00]
u2t-1 I (ut-1<0)	0.0047*	0.0388*	0.0039*	0.0395⁎⁎ 0.0046 0.0029 0.0017 0.0031
	[0.08]	[0.06]	[0.09]	[0.05] [0.12] [0.19] [0.28] [0.18]
ΔCOVID-19	0.179⁎⁎⁎	0.194⁎⁎⁎	0.180⁎⁎⁎	0.205⁎⁎⁎ 0.173⁎⁎⁎ 0.146⁎⁎⁎ 0.129⁎⁎ 0.138⁎⁎⁎
	[0.00]	[0.00]	[0.00]	[0.00] [0.00] [0.01] [0.02] [0.01]
Diagnostics
Log-likelihood	4159.3	3617.7	3908.5	3963.1 3880.6 3439.6 3158.4 3439.5
LM test for Heteroscedasticity	[0.56]	[0.65]	[0.64]	[0.68] [0.60] [0.52] [0.48] [0.55]
AR(12) test for Autocorrelation	[0.32]	[0.39]	[0.28]	[0.44] [0.37] [0.33] [0.30] [0.34]
TOTAL CONFIRMED DEATHS
Mean equation
Constant	0.023	0.013	0.010	0.005 0.011 0.009 0.004 0.012
	[0.44]	[0.49]	[0.52]	[0.57] [0.50] [0.53] [0.60] [0.50]
Cryptocurrency returns(-1)	0.564⁎⁎⁎	0.617⁎⁎⁎	0.620⁎⁎⁎	0.618⁎⁎⁎ 0.633⁎⁎⁎ 0.592⁎⁎⁎ 0.536⁎⁎⁎ 0.571⁎⁎⁎
	[0.00]	[0.00]	[0.00]	[0.00] [0.00] [0.00] [0.00] [0.00]
Liquidity	1.683⁎⁎⁎	1.082⁎⁎⁎	1.719⁎⁎⁎	1.684⁎⁎⁎ 1.769⁎⁎⁎ 1.471⁎⁎⁎ 1.064⁎⁎⁎ 1.362⁎⁎⁎
	[0.00]	[0.00]	[0.00]	[0.00] [0.00] [0.00] [0.00] [0.00]
Sentiment	1.028⁎⁎⁎	0.855⁎⁎⁎	1.053⁎⁎⁎	1.148⁎⁎⁎ 1.102⁎⁎⁎ 1.043⁎⁎⁎ 0.895⁎⁎ 1.074⁎⁎⁎
	[0.00]	[0.01]	[0.00]	[0.00] [0.00] [0.00] [0.02] [0.00]
Abnormal volume	-0.446⁎⁎	-0.358*	-0.511⁎⁎	-0.549⁎⁎ -0.407* -0.358* -0.316* -0.350*
	[0.05]	[0.08]	[0.04]	[0.03] [0.06] [0.08] [0.09] [0.08]
ΔCOVID-19	-2.648⁎⁎⁎	-3.259⁎⁎⁎	-3.674⁎⁎⁎	-3.926⁎⁎⁎ -3.553⁎⁎⁎ -2.784⁎⁎⁎ -2.139⁎⁎⁎ -2.299⁎⁎⁎
	[0.00]	[0.00]	[0.00]	[0.00] [0.00] [0.00] [0.01] [0.00]
Conditional volatility equation
Constant	0.0019	0.0017	0.0018	0.0006 0.0011 0.0009 0.0004 0.0013
	[0.17]	[0.20]	[0.17]	[0.28] [0.14] [0.16] [0.24] [0.18]
h(-1)	0.484⁎⁎⁎	0.471⁎⁎⁎	0.470⁎⁎⁎	0.499⁎⁎⁎ 0.608⁎⁎⁎ 0.519⁎⁎⁎ 0.462⁎⁎⁎ 0.509⁎⁎⁎
	[0.00]	[0.00]	[0.00]	[0.00] [0.00] [0.00] [0.01] [0.00]
u2(-1)	0.411⁎⁎⁎	0.405⁎⁎⁎	0.417⁎⁎⁎	0.423⁎⁎⁎ 0.398⁎⁎⁎ 0.327⁎⁎⁎ 0.293⁎⁎ 0.347⁎⁎⁎
	[0.00]	[0.00]	[0.00]	[0.00] [0.00] [0.00] [0.02] [0.00]
u2t-1 I (ut-1<0)	0.0036*	0.0313*	0.0035*	0.0026 0.0032* 0.0024 0.0017 0.0029
	[0.09]	[0.08]	[0.10]	[0.17] [0.10] [0.18] [0.23] [0.21]
ΔCOVID-19	0.183⁎⁎⁎	0.230⁎⁎⁎	0.194⁎⁎⁎	0.235⁎⁎⁎ 0.187⁎⁎⁎ 0.153⁎⁎⁎ 0.128⁎⁎ 0.147⁎⁎⁎
	[0.00]	[0.00]	[0.00]	[0.00] [0.00] [0.00] [0.02] [0.00]
Diagnostics
Log-likelihood	4265.0	4126.4	4297.7	4387.2 4258.1 3894.3 3459.2 3774.6
LM test for Heteroscedasticity	[0.65]	[0.77]	[0.79]	[0.80] [0.73] [0.76] [0.78] [0.68]
AR(12) test for Autocorrelation	[0.42]	[0.48]	[0.41]	[0.53] [0.48] [0.52] [0.56] [0.50]

Notes: The table reports the estimates of the TGARCH model described in Eqs. (1) and (2). The first panel reports the results with respect to the world conformed cases, while the second panel reports the results with respect to the world conformed deaths. LM is a heteroskedasticity test, while AR(12) is an autocorrelation test at 12 lags. The time span is: February 1, 2020 through October 31, 2021. Figures in brackets denote p-values.

p ≤ 0.10.

p ≤ 0.05.

p ≤ 0.01.

In light of the results reported, the next step evaluates the forecasting performance of the TGARCH (1, 1) model in terms of volatility. In doing so, the analysis estimates the respective models from February 2, 2020 to March 31, 2021 with the out-of-sample forecasting horizon covering the period April 1, 2021 to October 31, 2021. The forecasting process calculates one-day-ahead volatility forecasts through a rolling-window scheme. The forecasting performance is compared between the model without and that with the COVID-19 metrics. Table 4 reports the results which highlight that the model with the COVID-19 factors (Panel A with respect to the world confirmed cases and Panel B with respect to the world confirmed deaths) outperforms the forecasts vis-à-vis the model that ignores them.

Table 4

Forecasting performance of the TGARCH(1, 1) model with COVID-19.

Forecasting Horizon	A. Cases					B. Deaths
(Days)	Without COVID-19		With COVID-19		(Days)	Without COVID-19		With COVID-19
	MAFE	MSFE	MAFE	MSFE		MAFE	MSFE	MAFE	MSFE
Bitcoin
1	0.1564	0.0674	0.1026	0.0403	1	0.1483	0.0583	0.0925	0.0302
4	0.1592	0.0699	0.1084	0.0428	4	0.1509	0.0609	0.1002	0.0340
8	0.1629	0.0737	0.1121	0.0451	8	0.1548	0.0638	0.1030	0.0385
15	0.1671	0.0768	0.1158	0.0576	15	0.1592	0.0694	0.1085	0.0418
DM test		Clark/West test			DM test		Clark/West test
MAFE: [0.00], MSFE: [0.00]		MAFE: [0.00], MSFE: [0.00]			MAFE: [0.00], MSFE: [0.00]		MAFE: [0.00], MSFE: [0.00]
Dash
1 0.1568 0.0541			0.1084	0.0414	1 0.1526		0.0618	0.0972	0.0311
4 0.1594 0.0590			0.1149	0.0450	4 0.1583		0.0659	0.1043	0.0358
8 0.1630 0.0628			0.1189	0.0495	8 0.1639		0.0693	0.1082	0.0395
15 0.1687 0.0685			0.1246	0.0538	15 0.1695		0.0735	0.1141	0.0435
DM test		Clark/West test			DM test		Clark/West test
MAFE: [0.00], MSFE: [0.00]		MAFE: [0.00], MSFE: [0.00]			MAFE: [0.00]. MSFE: [0.00]		MAFE: [0.00], MSFE: [0.00]
Ethereum
1 0.1587 0.0511			0.1077	0.0406	1 0.1482		0.0482	0.0983	0.0302
4 0.1630 0.0552			0.1102	0.0449	4 0.1511		0.0524	0.1029	0.0333
8 0.1672 0.0593			0.1149	0.0515	8 0.1554		0.0565	0.1065	0.0385
15 0.1739 0.0652			0.1195	0.0548	15 0.1589		0.0604	0.1106	0.0442
DM test		Clark/West test			DM test		Clark/West test
MAFE: [0.00], MSFE: [0.00]		MAFE: [0.00], MSFE: [0.00]			MAFE: [0.00], MSFE: [0.00]		MAFE: [0.00], MSFE: [0.00]
Litecoin
1 0.1512 0.0489			0.1016	0.0385	1 0.1484		0.0453	0.0943	0.0275
4 0.1560 0.0529			0.1069	0.0424	4 0.1522		0.0492	0.1004	0.0330
8 0.1607 0.0580			0.1122	0.0467	8 0.1549		0.0534	0.1040	0.0365
15 0.1664 0.0611			0.1169	0.0493	15 0.1609		0.0571	0.1078	0.0419
DM test		Clark/West test			DM test:		Clark/West test
MAFE: [0.00], MSFE: [0.00]		MAFE: [0.00], MSFE: [0.00]			MAFE: [0.00], MSFE: [0.00]		MAFE: [0.00], MSFE: [0.00]
XRP
1 0.1616 0.0525			0.1106	0.0404	1 0.1495		0.0503	0.1005	0.0309
4 0.1649 0.0557			0.1133	0.0442	4 0.1529		0.0534	0.1034	0.0334
8 0.1694 0.0594			0.1178	0.0465	8 0.1561		0.0560	0.1062	0.0368
15 0.1726 0.0640			0.1213	0.0503	15 0.1589		0.0586	0.1088	0.0401
DM test		Clark/West test			DM test			Clark/West test
MAFE: [0.00], MSFE: [0.00]		MAFE: [0.01], MSFE: [0.00]			MAFE: [0.00], MSFE: [0.00]			MAFE: [0.00], MSFE: [0.00]
NEM
1 0.1523 0.0452			0.1062	0.0348	1 0.1257		0.0426	0.0904	0.0258
4 0.1561 0.0491			0.1094	0.0381	4 0.1294		0.0469	0.1002	0.0294
8 0.1590 0.0530			0.1123	0.0427	8 0.1336		0.0502	0.1045	0.0332
15 0.1637 0.0579			0.1175	0.0494	15 0.1385		0.0541	0.1081	0.0381
DM test		Clark/West test			DM test			Clark/West test
MAFE: [0.00], MSFE: [0.00]		MAFE: [0.01], MSFE: [0.00]			MAFE: [0.00], MSFE: [0.00]			MAFE: [0.00], MSFE: [0.00]
DigiByte
1 0.1368 0.0401			0.1005	0.0316	1 0.1158		0.0392	0.0886	0.0344
4 0.1401 0.0449			0.1041	0.0340	4 0.1194		0.0427	0.0952	0.0393
8 0.1472 0.0482			0.1095	0.0388	8 0.1247		0.0481	0.1006	0.0417
15 0.1498 0.0517			0.1132	0.0416	15 0.1290		0.0520	0.1069	0.0462
DM test		Clark/West test			DM test			Clark/West test
MAFE: [0.00], MSFE: [0.00]		MAFE: [0.01], MSFE: [0.00]			MAFE: [0.00], MSFE: [0.00]			MAFE: [0.00], MSFE: [0.00]
Dogecoin
1 0.1185 0.0429			0.1067	0.0355	1 0.1183		0.0416	0.0861	0.0357
4 0.1249 0.0472			0.1109	0.0386	4 0.1246		0.0458	0.0885	0.0399
8 0.1290 0.0508			0.1158	0.0427	8 0.1291		0.0489	0.0942	0.0430
15 0.1335 0.0558			0.1196	0.0473	15 0.1325		0.0534	0.1002	0.0478
DM test		Clark/West test			DM test			Clark/West test
MAFE: [0.00], MSFE: [0.00]		MAFE: [0.01], MSFE: [0.00]			MAFE: [0.00], MSFE: [0.00]			MAFE: [0.00], MSFE: [0.00]

Notes: The table presents empirical sizes for two tests for equality of MAFE and MSFE against the alternative in terms of the TGARCH model. The out-of-sample time span is: April 1, 2021 to October 31, 2021. MAFE and MSFE represent mean absolute forecast error and mean squared forecast error, respectively. Clark/West is the Clark and West (2007) forecasting accuracy test. DM is the Diebold-Mariano test statistic. Figures in brackets denote p-values. The results are based on 15-day out-of-sample forecasts and are reported on specific days.

The mean absolute forecast error (MAFE) and the mean squared forecast error (MSFE) are used to assess forecast accuracy. The model which includes the COVID-19 variables displays smaller MAFE and MSFE metrics versus that without those metrics. It is also imperative to assess whether any reductions in the two measures are statistically significant (Harris and Sollis, 2003). Two measures of assessing the out-of-sample forecasting performance have been used, that of the Diebold and Mariano (1995) test and the Clark and West (2007) approach. The latter test has the advantage of being approximately normal, which permits the tabulation of asymptotic critical values applicable under multistep forecasting and conditional heteroskedasticity. The results in Table 4 reject the null hypothesis of equal forecasting accuracy in both COVID-19 definitions, in both testing methodologies, and across all five cryptocurrency returns.

The final empirical step performs some robustness analysis. Given the abundance of alternative asymmetric GARCH models, we make use of the GJR-GARCH model recommended by Glosten et al. (1993). In this case, Eq. (2) turns into:where I(u < 0)gives 1 whenut-1< 0, and 0 otherwise. The new estimates are presented in Table 5 and provide robust support to those in Table 3. Finally, Table 6 repeats the associated forecasting case, with the results lending again support to the superiority of the model that contains the COVID-19 measures (as in Table 4).

Table 5

GJR-GARCH estimates: COVID-19 and cryptocurrency returns.

TOTAL CONFIRMED CASES Mean equation	Bitcoin	Dash	Ethereum	Litecoin XRP NEM DigiByte Dogecoin
Constant	0.015	0.012	0.010	0.007 0.007 0.004 0.001 0.011
	[0.48]	[0.49]	[0.56]	[0.62] [0.53] [0.59] [0.66] [0.52]
Cryptocurrency returns(-1)	0.561⁎⁎⁎	0.616⁎⁎⁎	0.634⁎⁎⁎	0.652⁎⁎⁎ 0.638⁎⁎⁎ 0.584⁎⁎⁎ 0.511⁎⁎⁎ 0.548⁎⁎⁎
	[0.00]	[0.00]	[0.00]	[0.00] [0.00] [0.00] [0.00] [0.00]
Liquidity	1.425⁎⁎⁎	1.304⁎⁎⁎	1.682⁎⁎⁎	1.654⁎⁎⁎ 1.403⁎⁎⁎ 1.117⁎⁎⁎ 0.952⁎⁎ 1.109⁎⁎⁎
	[0.00]	[0.00]	[0.00]	[0.00] [0.00] [0.00] [0.02] [0.00]
Sentiment	0.815⁎⁎⁎	0.636⁎⁎	0.792⁎⁎⁎	0.847⁎⁎⁎ 0.782⁎⁎⁎ 0.669⁎⁎ 0.614⁎⁎ 0.654⁎⁎
	[0.00]	[0.02]	[0.00]	[0.00] [0.01] [0.02] [0.03] [0.02]
Abnormal volume	-0.413*	-0.337*	-0.452⁎⁎	-0.486⁎⁎ -0.435* -0.384* -0.325* -0.375*
	[0.07]	[0.09]	[0.05]	[0.05] [0.06] [0.08] [0.09] [0.08]
ΔCOVID-19	-2.696⁎⁎⁎	-2.775⁎⁎⁎	-3.216⁎⁎⁎	-3.928⁎⁎⁎ -3.085⁎⁎⁎ -2.691⁎⁎⁎ -2.037⁎⁎⁎ -2.140⁎⁎⁎
	[0.00]	[0.00]	[0.00]	[0.00] [0.00] [0.00] [0.01] [0.01]
Conditional volatility equation
Constant	0.0018	0.0021	0.0015	0.0007 0.0015 0.0010 0.0004 0.0016
	[0.19]	[0.14]	[0.24]	[0.38] [0.20] [0.26] [0.35] [0.30]
h(-1)	0.636⁎⁎⁎	0.499⁎⁎⁎	0.602⁎⁎⁎	0.577⁎⁎⁎ 0.596⁎⁎⁎ 0.511⁎⁎⁎ 0.448⁎⁎⁎ 0.498⁎⁎⁎
	[0.00]	[0.00]	[0.00]	[0.00] [0.00] [0.00] [0.01] [0.00]
u2(-1)	0.337⁎⁎⁎	0.398⁎⁎⁎	0.411⁎⁎⁎	0.430⁎⁎⁎ 0.448⁎⁎⁎ 0.394⁎⁎⁎ 0.326⁎⁎⁎ 0.375⁎⁎⁎
	[0.00]	[0.00]	[0.00]	[0.00] [0.00] [0.01] [0.01] [0.00]
u2t-1 I(ut-1<0)	0.0094⁎⁎	0.0184⁎⁎	0.0109⁎⁎	0.0316⁎⁎ 0.0065* 0.0039* 0.0021 0.0034*
	[0.05]	[0.04]	[0.05]	[0.02] [0.07] [0.08] [0.12] [0.09]
ΔCOVID-19	0.197⁎⁎⁎	0.209⁎⁎⁎	0.195⁎⁎⁎	0.242⁎⁎⁎ 0.193⁎⁎⁎ 0.158⁎⁎⁎ 0.126⁎⁎ 0.141⁎⁎
	[0.00]	[0.00]	[0.00]	[0.00] [0.00] [0.01] [0.02] [0.02]
Diagnostics
Log-likelihood	4266.2	4036.5	4128.9	4371.5 4188.0 3672.1 3261.7 3472.8
LM test for Heteroscedasticity	[0.65]	[0.70]	[0.75]	[0.78] [0.69] [0.73] [0.76] [0.67]
AR(12) test for Autocorrelation	[0.39]	[0.46]	[0.37]	[0.51] [0.44] [0.48] [0.53] [0.45]
TOTAL CONFIRMED DEATHS
Mean equation
Constant	0.019	0.013	0.010	0.005 0.011 0.007 0.004 0.010
	[0.45]	[0.48]	[0.49]	[0.55] [0.50] [0.56] [0.61] [0.52]
Cryptocurrency returns(-1)	0.602⁎⁎⁎	0.650⁎⁎⁎	0.637⁎⁎⁎	0.648⁎⁎⁎ 0.670⁎⁎⁎ 0.593⁎⁎⁎ 0.538⁎⁎⁎ 0.584⁎⁎⁎
	[0.00]	[0.00]	[0.00]	[0.00] [0.00] [0.00] [0.00] [0.00]
Liquidity	1.483⁎⁎⁎	1.432⁎⁎⁎	1.529⁎⁎⁎	1.566⁎⁎⁎ 1.509⁎⁎⁎ 1.394⁎⁎⁎ 1.094⁎⁎⁎ 1.274⁎⁎⁎
	[0.00]	[0.00]	[0.00]	[0.00] [0.00] [0.00] [0.00] [0.00]
Sentiment	0.855⁎⁎⁎	0.744⁎⁎	0.918⁎⁎⁎	0.868⁎⁎⁎ 0.819⁎⁎⁎ 0.752⁎⁎⁎ 0.638⁎⁎⁎ 0.692⁎⁎⁎
	[0.01]	[0.02]	[0.00]	[0.01] [0.01] [0.01] [0.01] [0.00]
Anormal volume	-0.483⁎⁎	-0.419*	-0.525⁎⁎	-0.560⁎⁎ -0.409* -0.358* -0.316* -0.383*
	[0.05]	[0.08]	[0.04]	[0.03] [0.08] [0.09] [0.10] [0.08]
ΔCOVID-19	-2.696⁎⁎⁎	-3.428⁎⁎⁎	-3.549⁎⁎⁎	-4.466⁎⁎⁎ -3.536⁎⁎⁎ -2.947⁎⁎⁎ -2.461⁎⁎⁎ -2.773⁎⁎⁎
	[0.00]	[0.00]	[0.00]	[0.00] [0.00] [0.00] [0.00] [0.00]
Conditional volatility equation
Constant	0.0017	0.0019	0.0020	0.0005 0.0010 0.0007 0.0002 0.0009
	[0.16]	[0.15]	[0.13]	[0.24] [0.19] [0.22] [0.29] [0.21]
h(-1)	0.530⁎⁎⁎	0.509⁎⁎⁎	0.521⁎⁎⁎	0.537⁎⁎⁎ 0.529⁎⁎⁎ 0.491⁎⁎⁎ 0.436⁎⁎ 0.488⁎⁎⁎
	[0.00]	[0.00]	[0.00]	[0.00] [0.00] [0.01] [0.02] [0.01]
u2(-1)	0.435⁎⁎⁎	0.418⁎⁎⁎	0.423⁎⁎⁎	0.437⁎⁎⁎ 0.409⁎⁎⁎ 0.379⁎⁎ 0.341⁎⁎ 0.371⁎⁎
	[0.00]	[0.01]	[0.00]	[0.00] [0.01] [0.02] [0.03] [0.02]
u2t-1 I(ut-1<0)	0.0137*	0.0228⁎⁎	0.0117*	0.0085* 0.0069* 0.0045 0.0029 0.0039
	[0.06]	[0.05]	[0.07]	[0.09] [0.10] [0.12] [0.16] [0.13]
ΔCOVID-19	0.229⁎⁎⁎	0.265⁎⁎⁎	0.234⁎⁎⁎	0.277⁎⁎⁎ 0.224⁎⁎⁎ 0.209⁎⁎⁎ 0.173⁎⁎ 0.202⁎⁎⁎
	[0.00]	[0.00]	[0.00]	[0.00] [0.00] [0.00] [0.02] [0.01]
Diagnostics
Log-likelihood	4516.0	4605.4	4573.2	4511.5 4437.9 4128.7 3873.6 4248.9
LM test for Heteroscedasticity	[0.67]	[0.74]	[0.79]	[0.77] [0.72] [0.75] [0.79] [0.76]
AR(12) test for Autocorrelation	[0.42]	[0.46]	[0.40]	[0.53] [0.48] [0.53] [0.56] [0.54]

Notes: The table reports the estimates of the GJR-GARCH model described in Eqs. (1) and (3). The first panel reports the results with respect to the world conformed cases, while the second panel reports the results with respect to the world conformed deaths. LM is a heteroskedasticity test, while AR(12) is an autocorrelation test at 12 lags. The time span is: February 1, 2020 through October 31, 2021. Figures in brackets denote p-values.

p ≤ 0.10.

p ≤ 0.05.

p ≤ 0.01.

Table 6

Forecasting performance of the GJR-GARCH model with COVID-19.

Forecasting Horizon	A. Cases					B. Deaths
(Days)	Without COVID-19		With COVID-19		(Days)	Without COVID-19		With COVID-19
	MAFE	MSFE	MAFE	MSFE		MAFE	MSFE	MAFE MSFE
Bitcoin
1	0.1546	0.0692	0.1051	0.0401	1	0.1489	0.0554	0.0955 0.0301
4	0.1582	0.0733	0.1079	0.0424	4	0.1526	0.0590	0.0986 0.0327
8	0.1614	0.0761	0.1103	0.0457	8	0.1551	0.0627	0.1035 0.0351
15	0.1650	0.0785	0.1140	0.0573	15	0.1610	0.0662	0.1071 0.0390
DM test		Clark/West test			DM test		Clark/West test
MAFE: [0.00], MSFE: [0.00]		MAFE: [0.00], MSFE: [0.00]			MAFE: [0.00], MSFE: [0.00]		MAFE: [0.00], MSFE: [0.00]
Dash
1 0.1516 0.0541			0.1103	0.0417	1 0.1533		0.0603	0.0943 0.0307
4 0.1559 0.0575			0.1135	0.0440	4 0.1578		0.0636	0.1005 0.0348
8 0.1601 0.0608			0.1169	0.0485	8 0.1610		0.0685	0.1042 0.0390
15 0.1627 0.0639			0.1202	0.0519	15 0.1652		0.0704	0.1086 0.0422
DM test		Clark/West test			DM test		Clark/West test
MAFE: [0.00], MSFE: [0.00]		MAFE: [0.00], MSFE: [0.00]			MAFE: [0.00]. MSFE: [0.00]		MAFE: [0.00], MSFE: [0.00]
Ethereum
1 0.1548 0.0476			0.1006	0.0409	1 0.1422		0.0431	0.0927 0.0279
4 0.1593 0.0508			0.1049	0.0436	4 0.1469		0.0476	0.0968 0.0304
8 0.1632 0.0547			0.1095	0.0477	8 0.1503		0.0507	0.1006 0.0362
15 0.1671 0.0593			0.1130	0.0513	15 0.1541		0.0553	0.1039 0.0401
DM test		Clark/West test			DM test		Clark/West test
MAFE: [0.00], MSFE: [0.00]		MAFE: [0.00], MSFE: [0.00]			MAFE: [0.00], MSFE: [0.00]		MAFE: [0.01], MSFE: [0.00]
Litecoin
1 0.1502 0.0433			0.1004	0.0379	1 0.1518		0.0430	0.0932 0.0284
4 0.1541 0.0475			0.1042	0.0416	4 0.1547		0.0462	0.0975 0.0305
8 0.1594 0.0514			0.1085	0.0485	8 0.1563		0.0495	0.1017 0.0358
15 0.1626 0.0568			0.1125	0.0514	15 0.1598		0.0527	0.1052 0.0396
DM test		Clark/West test			DM test:		Clark/West test
MAFE: [0.00], MSFE: [0.00]		MAFE: [0.00], MSFE: [0.00]			MAFE: [0.00], MSFE: [0.00]		MAFE: [0.01], MSFE: [0.00]
XRP
1 0.1572 0.0501			0.1074	0.0389	1 0.1488		0.0496	0.0954 0.0304
4 0.1610 0.0548			0.1103	0.0424	4 0.1519		0.0529	0.1017 0.0338
8 0.1663 0.0589			0.1151	0.0450	8 0.1562		0.0553	0.1049 0.0375
15 0.1704 0.0614			0.1186	0.0486	15 0.1597		0.0587	0.1076 0.0402
DM test		Clark/West test			DM test			Clark/West test
MAFE: [0.00], MSFE: [0.00]		MAFE: [0.01], MSFE: [0.00]			MAFE: [0.00], MSFE: [0.00]			MAFE: [0.00], MSFE: [0.00]
ΝΕΜ
1 0.1621 0.0529			0.1091	0.0397	1 0.1503		0.0461	0.0843 0.0385
4 0.1663 0.0561			0.1147	0.0438	4 0.1544		0.0495	0.0905 0.0427
8 0.1701 0.0596			0.1192	0.0479	8 0.1580		0.0530	0.0968 0.0486
15 0.1758 0.0644			0.1246	0.0513	15 0.1604		0.0564	0.1004 0.0511
DM test		Clark/West test			DM test			Clark/West test
MAFE: [0.00], MSFE: [0.00]		MAFE: [0.01], MSFE: [0.00]			MAFE: [0.00], MSFE: [0.00]			MAFE: [0.00], MSFE: [0.00]
DigiByte
1 0.1711 0.0543			0.1235	0.0413	1 0.1533		0.0477	0.0903 0.0415
4 0.1762 0.0585			0.1278	0.0460	4 0.1574		0.0503	0.0955 0.0448
8 0.1798 0.0627			0.1329	0.0495	8 0.1605		0.0562	0.0994 0.0493
15 0.1837 0.0669			0.1374	0.0528	15 0.1648		0.0596	0.1036 0.0528
DM test		Clark/West test			DM test			Clark/West test
MAFE: [0.00], MSFE: [0.00]		MAFE: [0.01], MSFE: [0.00]			MAFE: [0.00], MSFE: [0.00]			MAFE: [0.00], MSFE: [0.00]
Dogecoin
1 0.1764 0.0531			0.1269	0.0422	1 0.1514		0.0454	0.0925 0.0452
4 0.1795 0.0570			0.1295	0.0458	4 0.1559		0.0489	0.0962 0.0490
8 0.1830 0.0604			0.1333	0.0488	8 0.1588		0.0527	0.0998 0.0503
15 0.1869 0.0655			0.1382	0.0536	15 0.1637		0.0577	0.1047 0.0554
DM test		Clark/West test			DM test			Clark/West test
MAFE: [0.00], MSFE: [0.00]		MAFE: [0.01], MSFE: [0.00]			MAFE: [0.00], MSFE: [0.00]			MAFE: [0.00], MSFE: [0.00]

Notes: Similar to those in Table 4.

Conclusion

This paper undertook an analysis of the role of COVID-19 in determining and predicting the conditional volatility of five important cryptocurrencies (i.e., Bitcoin, Dash, Ethereum, Litecoin and XRP). Through the employment of an asymmetric TGARCH(1, 1) model, the empirical results documented the significant role of the pandemic metrics in predicting the conditional volatilities across all five cryptocurrencies. Overall, the results could be of substantial significance for identifying potential vulnerabilities associated with the cryptocurrency market during the pandemic crisis period, while offering substantial information to market participants in terms of reaching rational investment decisions. More specifically, given that many investors have decided to include cryptocurrencies in their investment portfolio, our findings have substantial implications in adopting the right trading strategies. In other words, the findings could provide significant information to investors/portfolio managers who optimize their trading transactions, while seeking extra caution to be taken in adding to portfolio risk during stressful periods with high volatility levels. Further implications could be there for policymakers as a warning in the case of substantial losses for investors during crises periods with high volatility.

Author statement

Please, be informed that in relevance to my (single-authored) revised submission entitled: to be potentially considered for publication by Finance Research Letters, the author has no conflicts of interest.