Exploring Calendar Anomalies and Volatility Dynamics in Cryptocurrencies: A Comparative Analysis of Day-of-the-Week Effects before and during the COVID-19 Pandemic

Abstract

This study investigates calendar anomalies and their impact on returns and volatility patterns in the cryptocurrency market, focusing on day-of-the-week effects before and during the COVID-19 pandemic. Using advanced statistical models from the GARCH family, we analyze the returns of Binance USD, Bitcoin, Binance Coin, Cardano, Dogecoin, Ethereum, Solana, Tether, USD Coin, and Ripple. Our findings reveal significant shifts in volatility dynamics and day-of-the-week effects on returns, challenging the notion of market efficiency. Notably, Bitcoin and Solana began exhibiting day-of-the-week effects during the pandemic, whereas Cardano and Dogecoin did not. During the pandemic, Binance USD, Ethereum, Tether, USD Coin, and Ripple showed multiple days with significant day-of-the-week effects. Notably, positive returns were generally observed on Sundays, whereas a shift to negative returns on Mondays was evident during the COVID-19 period. These patterns suggest that exploitable anomalies persist despite the market’s continuous operation and increasing maturity. The presence of a long-term memory in volatility highlights the need for robust trading strategies. Our research provides valuable insights for investors, traders, regulators, and policymakers, aiding in the development of effective trading strategies, risk management practices, and regulatory policies in the evolving cryptocurrency market.

1. Introduction

The study of anomalies in financial time-series datasets that occur on specific dates dates back more than a century. Seasonal and psychological factors affect these anomalies, also referred to as calendar anomalies, which represent patterns or effects that conventional asset pricing models cannot explain (Chatzitzisi et al. 2021). These anomalies challenge the Efficient Market Hypothesis (EMH) by suggesting that predictable trends in asset prices can be exploited for abnormal returns, facilitating the development of effective trading techniques (Kumar 2023).

Cryptocurrencies present new challenges for the study of calendar anomalies. With over 22,235 cryptocurrencies listed on CoinMarketCap, the emergence of digital assets has introduced significant changes to traditional monetary systems, prompting a reevaluation of established standards (Weber 2016; Baek and Elbeck 2014). As cryptocurrencies gain popularity, retail investors are increasingly including them in their portfolios (Zhao and Zhang 2021). This evolving trend involves extending the research on calendar anomalies to encompass the rapidly growing cryptocurrency industry.

The Adaptive Market Hypothesis (AMH) contradicts established financial theories by arguing that market efficiency and inefficiency can coexist, allowing investors and participants to adjust to changing market conditions (Enow 2022). This hypothesis suggests that market participants modify their strategies based on their changing knowledge and market dynamics, resulting in more accurate pricing models and trading strategies (Naz et al. 2023). Miralles-Quirós and Miralles-Quirós (2022) found evidence of calendar anomalies in cryptocurrencies, including the day-of-the-week effect, which showed predictable patterns in returns based on specific days. AMH’s emphasis on market adaptability is consistent with the reported anomalies in cryptocurrency markets, where investors may modify trading methods based on calendar impacts (Khuntia and Pattanayak 2021). Understanding these anomalies is crucial for developing effective investment strategies and regulatory frameworks.

To improve risk management, regulatory implications, and forecasting accuracy, it is critical to model volatility and day-of-the-week effects in cryptocurrencies using advanced statistical models. Symmetric and asymmetric generalized autoregressive conditional heteroscedasticity (GARCH) models are suitable for this purpose. They help regulators analyze crypto risk and volatility (Ngunyi et al. 2019), facilitate market monitoring (Omari and Ngunyi 2021), provide insights into market risks (Aggarwal and Jha 2023), and influence crypto regulatory policies (Ampountolas 2022).

This study investigates whether the cryptocurrency market exhibits calendar effects given its unique 24/7 operations, including holidays and weekends. Unlike traditional financial markets with set trading hours, cryptocurrency markets immediately reflect any published information in prices. This continuous operation suggests that returns should be uniform across days and times. However, the potential for varying returns throughout the year and week makes studying calendar effects in cryptocurrencies difficult. We specifically explore the day-of-the-week effects by analyzing the returns of the top ten cryptocurrencies by market capitalization, extending the focus beyond Bitcoin and Ethereum. Using statistical models such as GARCH, EGARCH, GJR-GARCH, and FIGARCH, we provide a comprehensive analysis of these effects.

Additionally, this study addresses a notable gap in the literature regarding a comparative analysis of the day-of-the-week effects in the cryptocurrency market before and during the COVID-19 pandemic. The pandemic’s seismic shifts in global financial markets prompted us to investigate how cryptocurrency efficiency and volatility evolved during this period and how temporal patterns and anomalies shifted. By analyzing the top ten cryptocurrencies, this study offers valuable insights for investors, traders, regulators, and policymakers. The use of asymmetric GARCH models enhances our understanding of how different types of news impact the day-of-the-week effects. Testing for long-term memory using the FIGARCH model reveals the persistence of volatility over time, which is crucial for the development of robust trading strategies. The continuous and global trading nature of cryptocurrencies highlights the importance of non-stop market operations in analyzing these effects.

The remainder of this paper is structured as follows: Section 2 reviews the pertinent literature; Section 3 expounds on our data and methodology; Section 4 presents the empirical data analysis and discussion; and Section 5 concludes our study.

2. Literature Review

Studying anomalies and volatility is crucial for developing smart investment strategies, effective risk management, and market stability (Tadepalli and Jain 2018). Anomalies challenge the efficient market hypothesis, which suggests that regular asset price patterns can be exploited for abnormal returns (Dong et al. 2021). These anomalies may vary over time owing to changing market conditions, necessitating a detailed analysis of their dynamics. Researchers have noted calendar anomalies in various markets, including the Russian bond and stock markets (Compton et al. 2013), Turkish markets (Aydoğan and Booth 2003), US markets (Plastun et al. 2019), Asia-Pacific stock markets (Aziz and Ansari 2017), Thai stock markets (Wuthisatian 2021), Gulf Cooperation Council stock exchanges (Siriopoulos and Youssef 2019), Nigerian stock markets (Adaramola and Adekanmbi 2020), and Swedish stock markets (Eidinejad and Dahlem 2021).

Empirical studies primarily focus on the effects of the day of the week and month of the year, categorizing them into religious and non-religious anomalies (Sejati et al. 2022). Religious anomalies include festive religious days, such as the Yom Kippur, Diwali, and Ramadan effects (Kliger and Qadan 2019), whereas non-religious anomalies encompass the day of the week, month of the year, Halloween, turn-of-the-month, and turn-of-the-year effects (Mehta and Chander 2009). While calendar impacts on stock markets are well documented, our understanding of calendar effects on cryptocurrency markets remains limited, especially among cryptocurrencies other than Bitcoin (Robiyanto et al. 2019).

Various authors have suggested factors that explain calendar anomalies in cryptocurrency markets, attributing them to market sentiment, liquidity, and other external factors (Naz et al. 2023; Caporale and Plastun 2019). The sentiment analysis of social media data and liquidity dynamics plays a crucial role in cryptocurrency markets and can influence the occurrence of calendar anomalies (Valencia et al. 2019; Wan et al. 2023). Understanding these dynamics is essential for comprehending the underlying factors driving calendar anomalies in cryptocurrency markets.

The COVID-19 pandemic has profoundly affected global financial markets, including cryptocurrencies (Lahmiri and Bekiros 2020). Several studies have investigated these effects across different markets, highlighting their significant impact on both the equity and cryptocurrency markets (Sahoo 2021). The pandemic has transformed the global role of cryptocurrencies and has adversely affected various economies (Lee et al. 2022). Despite the initial shocks, cryptocurrencies such as Bitcoin, Ethereum, and Litecoin demonstrated resilience but suffered significant negative return shocks during the initial wave of the pandemic (Marobhe 2022).

Researchers have widely adopted GARCH models, including asymmetric GARCH models, to study calendar anomalies and volatility in the cryptocurrency markets (Kim et al. 2021; Ampountolas 2022). These models are crucial for capturing the time-varying nature of volatility, a prominent characteristic of cryptocurrency markets. Asymmetric GARCH models, such as the Exponential GARCH (EGARCH) and Glosten-Jagannathan-Runkle GARCH (GJR-GARCH), are particularly well suited for modeling volatility and cryptocurrency anomalies because they can capture asymmetric volatility patterns (Naimy et al. 2021). This asymmetry is significant, as it reflects the different reactions of market volatility to positive and negative shocks, often observed in highly speculative and sentiment-driven cryptocurrency markets.

These models offer valuable insights into cryptocurrency market dynamics, such as the impact of macroeconomic announcements, market sentiment, and regulatory news on volatility. By accurately modeling these dynamics, asymmetric GARCH models enhance risk management and forecasting capabilities, providing investors and policymakers with tools to better understand and mitigate the risks associated with cryptocurrency investments. Predicting volatility patterns helps develop robust trading strategies, optimize portfolio allocations, and improve overall market efficiency.

Furthermore, the Fractionally Integrated Generalized Autoregressive Conditional Heteroskedasticity (FIGARCH) model is particularly advantageous for analyzing the day-of-the-week effect in the cryptocurrency market for several reasons (Ampountolas 2024). FIGARCH models capture long-term memory in volatility, which is crucial given that past volatility in cryptocurrencies can have a prolonged impact on future volatility. This model’s flexibility allows for a more accurate representation of volatility dynamics, which is essential for detecting patterns over different days of the week. Additionally, FIGARCH models account for autocorrelation in returns, a significant factor influencing day-of-the-week effects.

FIGARCH models are robust to non-stationarity, accommodating the changing statistical properties often observed in cryptocurrency markets. They effectively utilize daily data, making them suitable for detecting periodic volatility patterns that may occur weekly. This comprehensive framework ensures a sophisticated understanding of how day-of-the-week effects manifest in volatile and often unpredictable cryptocurrency markets.

Kinateder and Papavassiliou (2021) investigated seasonality and calendar effects in cryptocurrencies, specifically focusing on how the day of the week influences returns and volatility. Their study utilized daily data from major cryptocurrencies to identify patterns and anomalies that could impact trading strategies. Aharon and Qadan (2019) provide empirical evidence of the day-of-the-week effect, highlighting distinct patterns in price movements and volatility on certain days. They analyze the daily returns of Bitcoin and Ethereum, showing that Mondays and Fridays exhibit higher volatility than other days. Dangi (2020) explored the implications of these calendar effects and offered insights into the unique behaviors of cryptocurrency markets. This study examines a broad range of cryptocurrencies and finds that certain weekdays consistently show abnormal returns, suggesting potential opportunities for traders. İmre and Ölçen (2022) further analyze these effects, demonstrating how understanding day-of-the-week patterns can inform investment strategies and risk management. They use a comprehensive dataset spanning several years and multiple cryptocurrencies, revealing that day-of-the-week effects are significant and can be exploited for better portfolio management.

Analyzing cryptocurrency data from pre-COVID-19 (1 January 2017 to 19 March 2020) and during COVID-19 (20 March 2020 to 5 May 2023) provides a comprehensive perspective on market dynamics and anomalies. This period encompasses significant events and developments within the cryptocurrency market, offering rich insights into market behavior and efficiency. Dividing the data into pre-COVID-19 and during the COVID-19 periods is a strategic approach to analyzing the cryptocurrency market, given the profound impact of the pandemic on financial markets.

The pre-COVID-19 period includes the 2017 cryptocurrency boom, the 2018 market correction, and a gradual recovery up to early 2020. This period reflects a market driven primarily by retail investors, speculative trading, and initial regulatory development. In contrast, the COVID-19 period captures the market crash and rapid recovery in March 2020, significant bull runs, increased institutional adoption, and the rise of Decentralized Finance (DeFi). This period also includes the third Bitcoin halving in May 2020, which is historically correlated with price increases. Additionally, economic stimulus measures, low interest rates, and inflation concerns during the pandemic have influenced market dynamics. This division allows for a comprehensive examination of how the COVID-19 pandemic has affected the cryptocurrency market. This extended period encompasses significant events and developments within the cryptocurrency market, offering rich insights into market behavior and efficiency. This understanding enables informed decision-making and the development of strategies to effectively navigate the market.

The literature review highlights critical aspects of cryptocurrency anomalies and volatility, emphasizing the importance of calendar effects in these markets. It is evident that traditional and cryptocurrency markets exhibit calendar anomalies, which challenge the EMH and support the AMH. The use of advanced statistical models, particularly GARCH and its variants, is crucial for capturing the time-varying nature of volatility and for providing valuable insights into market dynamics.

This study aims to fill the gap in the literature by focusing on the day-of-the-week effects in the cryptocurrency market, particularly before and during the COVID-19 pandemic. By analyzing the top ten cryptocurrencies by market capitalization, we aim to provide a general understanding of how the market operates. Employing advanced models such as GARCH, EGARCH, GJR-GARCH, and FIGARCH, this study provides a comprehensive analysis of these effects, offering valuable insights for investors, traders, regulators, and policymakers. Understanding these anomalies and volatility patterns is essential for developing effective trading strategies, risk management practices, and regulatory frameworks, particularly in the rapidly evolving cryptocurrency market.

3. Data and Methodology

3.1. Data Description

In our empirical investigation, we analyzed a dataset of daily closing prices in US dollars obtained from CoinMarketCap (https://coinmarketcap.com/coins/ accessed on 16 February 2024). We focused on the following top cryptocurrencies in terms of diffusion and market capitalization: Binance USD, Bitcoin, Binance Coin, Cardano, Dogecoin, Ethereum, Solana, Tether, USD Coin, and Ripple.

Cryptocurrency exchanges operate continuously without formal closing times. Thus, data providers typically determine the “closing price” based on a specific point in time each day, usually at the end of the UTC day. Each exchange might calculate the closing price differently; some use the last trade price before midnight UTC, while others use an average price over the last few minutes of the day. Higher liquidity exchanges tend to have more stable prices, whereas lower liquidity exchanges may experience greater volatility and price discrepancies.

The “closing auction process” in cryptocurrency trading establishes the closing price of digital assets at the end of the trading session. During this process, buy and sell orders are matched to determine the equilibrium price, which serves as the official closing price for the asset. CoinMarketCap aggregates prices from multiple exchanges to determine the daily closing price, averaging prices across different exchanges weighted by trading volume. This methodology provides a representative closing price. Differences in the methodologies used by data providers can lead to slight variations in the reported closing prices.

3.2. Data Preparation

Our investigation began by checking the database for normality using the Jacque–Bera (JB) and Anderson–Darling (AD) tests. We then calculate the returns, defined as the natural logarithm of the ratio between two consecutive prices, using the following formula:

$$R\mathrm{n}=In\left(CP\mathrm{n}\right)-In\left(C{P}_{\mathrm{n}-1}\right)\times 100$$

(1)

where R_n denotes returns on an nth day in percentage; $C{P}_{\mathrm{n}}$ denotes closing price on an nth day; $C{P}^{\left({\mathrm{n}}^{-1}\right)}$ denotes the closing price on the previous trading day; and In is a natural log.

We used log returns in the subsequent models because they allow for continuous compounding and tend to exhibit stationarity, making them more suitable for statistical analysis. We assessed the return series for all ten coins using both the Augmented Dickey–Fuller (ADF) and Phillips–Perron tests, confirming their stationarity.

3.3. Parametric and Non-Parametric Tests

We applied a diverse set of quantitative approaches encompassing both parametric and non-parametric tests. Specifically, we use the conventional regression model with dummy variables and Analysis of Variance (ANOVA) as parametric tests (Basdas 2011). To address potential biases arising from dummy variables, especially in the presence of abrupt fluctuations, we incorporated non-parametric testing techniques such as the mood Median Test (Mood’s Median Test), following the recommendations of Chien et al. (2002).

3.4. Regression Analysis

We apply GARCH models to check for volatility. Initially, we employed a dummy regression model that assumed a constant return variance for cryptocurrencies. The ordinary least squares (OLS) regression equation was as follows:

Return_t = β₁MONDAY_t + β₂TUESDAY_t + β₃WEDNESDAY_t + β₄THURSDAY_t + β₅FRIDAY_t + β₆SATURDAY_t + β₇SUNDAY_t + ε_t

(2)

where MONDAY, TUESDAY, WEDNESDAY, THURSDAY, FRIDAY, SATURDAY, and SUNDAY are dummy variables for each day of the week returns (e.g., if the day is Monday, then the dummy variable Monday will be 1 and 0 otherwise); β₁, β₂, β₃, β₄, β₅, β₆, and β₇ are coefficients; and ε_t is error term. The coefficients of these seven dummy variables represent the returns for each day of the week. To prevent perfect multicollinearity, we excluded the intercept term and included dummy variables for all seven days of the week.

3.5. Volatility Modelling

We checked the residuals from the least-squares regression equation for autoregressive conditional heteroscedasticity using the ARCH test. If the ARCH effect becomes apparent in the residuals, we apply the GARCH family model.

To capture the leptokurtic distributions, volatility clustering, leverage effects, and long-term memory properties of cryptocurrencies, we applied symmetric, asymmetric, and fractionally integrated volatility models. We use the widely employed GARCH (p, q) model to model symmetric volatility. The conditional variance equation of the GARCH (p, q) model is as follows:

$${\mathsf{\sigma }}_{\mathrm{t}}^2= +{\sum }_{i=1}^p{\mathsf{\alpha }}_i{\mathsf{\epsilon }}_{t-i}^2+{\sum }_{j=1}^q\mathsf{\beta }\mathrm{j}{\mathsf{\sigma }}_{t-j}^2$$

(3)

where, ${\mathsf{\alpha }}_i$, and $\mathsf{\beta }\mathrm{j}$ are coefficients, ε²_t−i is the previous-period ARCH term, and s²_t−j is the previous-period GARCH term.

To capture the asymmetric effect, also known as the leverage effect, we apply the EGARCH and GJR-GARCH models. The conditional variance equation of the EGARCH (p, q) model is as follows:

$$log\left({\sigma }_t^2\right)=\omega +{\sum }_{i=1}^p\left[{\alpha }_i\left({\displaystyle \frac{\left|{\epsilon }_{t-i}\right|}{{\sigma }_{t-i}}}-\sqrt{{\displaystyle \frac{2}{\pi }}}\right)+{\gamma }_i\left({\displaystyle \frac{{\epsilon }_{t-i}}{{\sigma }_{t-i}}}\right)\right]+{\sum }_{j=i}^q{\beta }_{j}log\left({\sigma }_{t-j}^2\right)$$

(4)

${\alpha }_i$ measures the magnitude of the shock_, ${\beta }_j$ measures the persistence of the conditional volatility of the shocks to the market; and γ_ι is the asymmetric pattern that measures the leverage effect.

The conditional variance equation of the GJR-GARCH (p, q) model is as follows:

$${\sigma }_t^2=\omega +{\sum }_{i=1}^p\left({\alpha }_i+{\gamma }_i{I}_{t-i}\right){\epsilon }_{t-i}^2+{\sum }_{j=1}^q{\beta }_j{\sigma }_{t-j}^2$$

(5)

where, ω ≥ 0, ${\alpha }_i$ ≥ 0, ${\beta }_j$ ≥ 0, ${\alpha }_i$ + γ_ι ≥ 0.

To account for the long-term memory properties in volatility, we apply the FIGARCH model. The conditional variance equation of the FIGARCH (p, d, q) model is as follows:

$${(1-ꞵ(L\left)\right){\left(1-L\right)}^d\sigma }_t^2=\omega +\alpha \left(L\right){\epsilon }^2ₜ$$

(6)

where ${\sigma }_t^2$ is the conditional variance at time t, L is the lag operator, β(L) is a polynomial in the lag operator L with parameters ${\beta }_i$, representing the autoregressive component of the conditional variance, ${\left(1-L\right)}^d$ is the fractional differencing operator with parameter and (where 0 ≤ d ≤ 10), capturing long memory in the volatility process.

The FIGARCH (1, d, 1) model captures the long-term memory and persistence of volatility observed in cryptocurrency returns. By accommodating long-range dependence, the FIGARCH model addresses the limitations of traditional GARCH models and provides a more accurate representation of volatility dynamics. The fractional differencing parameter d in the FIGARCH model quantifies the degree of long-term memory, offering deeper insights into the volatility behavior of cryptocurrencies before and during the COVID-19 pandemic.

To assess the presence of long-term memory in the residuals of the FIGARCH (1, d, 1) model, we applied Lo’s modified R/S test. We first calculated the modified R/S statistic for the residuals using a specified number of lags based on an autocorrelation function (ACF) plot. To determine the critical values, we conducted a Monte Carlo simulation, generating 10,000 white noise time series of the same length as the actual data. For each simulated series, we computed the modified R/S statistic, which allowed us to build a distribution of the statistic under the null hypothesis of no long-term memory. We then extracted the critical values corresponding to 1%, 5%, and 10% significance levels from this distribution. Finally, we compared the calculated modified R/S statistic for the residuals with these critical values. If the calculated statistic exceeds the critical value at the 5% significance level, we reject the null hypothesis and conclude that long-term memory is present in the time series. Conversely, if the calculated statistic is below the critical value, we do not find any evidence of long-term memory.

3.6. Model Adequacy and Selection

To ensure the adequacy of the GARCH models, we applied the Ljung–Box and Lagrange multiplier (LM) tests (Engle 2001) to check for autocorrelation or volatility clustering in the residuals. We then used the Akaike Information Criterion (AIC) to select the best GARCH models. The AIC is designed to minimize the expected estimated Kullback–Leibler (K-L) information loss and balance the model fit and complexity (Burnham and Anderson 2004). This criterion is particularly useful for our large sample size and complex model structures, ensuring that we select models that provide a good fit to the data without being overly complex.

4. Empirical Data Analysis and Discussion

We begin our analysis with fundamental statistics and parametric/non-parametric tests. We conducted a descriptive analysis of the ten selected cryptocurrencies, as outlined in

Table 1. Daily descriptive statistics of ten cryptocurrencies in the pre-COVID-19 period.

Descriptive Statistics	Bitcoin	Binance Coin	Cardano	Dogecoin	Ethereum	Tether	USD Coin	Ripple
Mean	12.015%	58.287%	2.719%	20.358%	−12.189%	−0.017%	−0.110%	31.179%
Maximum	2870.990%	32,699.360%	8721.609%	4553.488%	2625.760%	1265.370%	253.691%	8812.683%
Minimum	−2251.580%	−10,024.390%	−2698.714%	−4781.982%	−2185.820%	−2833.380%	−209.640%	−4962.824%
Standard Deviation	4.393	15.609	7.708	6.921	5.152	1.486	0.475	7.703
Coefficient of Variation	36.563	26.780	283.529	33.996	−42.271	−9004.824	−431.951	24.706
Skewness	0.076	10.643	2.920	0.829	−0.201	−5.635	0.186	2.437
Kurtosis	7.796	237.267	31.126	12.965	5.857	148.928	9.022	27.515

Source: Elaborated by the author.

and

Table 2. Daily descriptive statistics of ten cryptocurrencies during the COVID-19 periods.

Descriptive Statistics	Binance USD	Bitcoin	Binance Coin	Cardano	Dogecoin	Solana	Ethereum	Tether	USD Coin	Ripple
Mean	−0.025%	9.981%	29.489%	24.346%	−11.627%	37.451%	23.580%	0.005%	−0.033%	8.463%
Maximum	650.371%	1760.260%	5526.562%	2691.957%	7324.953%	3844.862%	2194.057%	250.046%	192.579%	4233.534%
Minimum	−649.448%	−4337.140%	−5590.344%	−5244.024%	−4667.967%	−4521.549%	−5630.799%	−197.281%	−158.485%	−5495.483%
Standard Deviation	0.428	3.874	5.700	5.859	7.457	7.792	5.209	0.292	0.282	6.276
Coefficient of Variation	−1697.480	38.813	19.330	24.065	−64.137	20.806	22.092	5760.118	−854.539	74.162
Skewness	−0.107	−1.429	−0.185	−0.442	1.464	−0.058	−1.464	0.159	0.045	−0.205
Kurtosis	106.763	19.683	24.491	11.051	24.921	6.640	18.420	15.488	9.884	17.856

Source: Elaborated by the author.

. Before the COVID-19 pandemic, Binance Coin exhibited the highest average return, followed by Ripple. During the COVID-19 period, Binance Coin clearly led in average returns, followed by Cardano, which showed significant growth in popularity and value. Among the ten cryptocurrencies, USD Coin had the least fluctuation during both the pre-COVID-19 and COVID-19 periods. The distribution of returns during the pre-COVID-19 period skewed leftward favorably for Binance USD, Ethereum, and Tether and positively for the remaining coins. During the COVID-19 period, most cryptocurrencies, including Binance USD, Bitcoin, Binance Coin, Cardano, Solana, Ethereum, and Ripple, exhibited a leftward skew.

To ensure robustness, we followed Caporale and Plastun’s (2019) recommendation by employing both parametric and non-parametric models. To investigate variations across days of the week, we conducted one-way ANOVA and Mood Median tests. We applied the Jarque–Bera and Anderson–Darling tests for normality to all ten cryptocurrencies. The results indicate that in both the pre- and during the COVID-19 periods, the null hypothesis of normality in returns should be rejected at the 5% significance level, consistent with Szczygielski et al. (2019) and Agyei et al. (2022) (see

Table A1. Results of the parametric and non-parametric tests on cryptocurrencies in pre- and during the COVID-19 periods.

	Normality Test		Central Tendency Test				Variance Test
	Anderson Darling Test p-Values		Mood Median Test p-Values		One-Way ANOVA p-Values		Levene’s Test p-Values		Bartlett’s Test p-Values
	Pre	During	Pre	During	Pre	During	Pre	During	Pre	During
Binance USD	-	<0.05	-	0.402	-	0.885	-	0.588	-	0.61
Bitcoin	<0.05	<0.05	0.249	0.733	0.645	0.676	0.026	0.000	0.101	0.000
Binance Coin	<0.05	<0.05	0.346	0.992	0.673	0.955	0.243	0.000	0.62	0.001
Cardano	<0.05	<0.05	0.058	0.762	0.137	0.331	0.048	0.001	0.148	0.003
Dogecoin	<0.05	<0.05	0.482	0.368	0.481	0.728	0.559	0.009	0.953	0.036
Solana	-	<0.05	-	0.941	-	0.741	-	0.011	-	0.033
Ethereum	<0.05	<0.05	0.042	0.674	0.302	0.675	0.049	0.000	0.044	0.001
Tether	<0.05	<0.05	0.024	0.444	0.156	0.449	0.959	0.592	0.947	0.545
USD Coin	<0.05	<0.05	0.960	0.147	0.983	0.462	0.943	0.456	0.950	0.604
Ripple	<0.05	<0.05	0.129	0.857	0.826	0.888	0.004	0.001	0.033	0.002

Source: Elaborated by the author.

in Appendix A).

Upon scrutinizing the one-way ANOVA results at a 95% confidence level, we observed no significant differences in mean returns among days of the week for all coins during both the pre- and during COVID-19 periods. We employ Mood’s median test, a robust non-parametric test, to examine the median equality for log returns across the seven days. In the pre-COVID-19 period, Ethereum and Tether exhibited p-values < 0.05, suggesting a day-of-week effect. However, during the COVID-19 period, no coins yielded significant p-values, indicating no observed day-of-week effects, consistent with Kaiser’s (2019) findings.

Furthermore, we tested for equal variances between days of the week to assess the variability and potential day-of-week effects. For the pre-COVID-19 period, Bitcoin, Cardano, Ethereum, and Ripple rejected the null hypothesis at the 95% confidence level. During the COVID-19 period, Bitcoin, Binance Coin, Cardano, Dogecoin, Solana, Ethereum, and Ripple rejected the null hypothesis at 95% confidence, indicating significant differences in variances among days.

While parametric and non-parametric tests confirm the presence of day-of-the-week effects, we further validate these findings by incorporating dummy variables into GARCH models. This approach allows for the modeling of time-varying volatility patterns, leading to more accurate forecasts and a better understanding of how specific days of the week impact financial returns and volatility. This transition to GARCH models enhances our ability to capture the dynamic nature of cryptocurrency markets and provides deeper insights into day-of-the-week effects.

To ensure the robustness of our GARCH model, it is essential to confirm the stationarity of the data. We rigorously examined stationarity through unit root tests employing both the Augmented Dickey–Fuller (ADF) and Phillips–Perron (PP) tests, which are standard tools in time-series analyses. The results, displayed in

Table A2. Augmented Dickey–Fuller test results before and during the COVID-19 pandemic.

Augmented Dickey–Fuller Test Statistics
Pre-COVID-19 Period
	Binance USD	Bitcoin	Binance Coin	Cardano	Dogecoin	Solana	Ethereum	Tether	USD Coin	Ripple
t-Statistic	−12.454	−33.183	−31.552	−16.336	−20.820	N/A	−28.069	−25.340	−14.962	−20.492
p-value	0.000	0.000	0.000	0.000	0.000		0.000	0.000	0.000	0.000
During the COVID-19 Period
t-Statistic	−26.466	−33.829	−21.147	−33.867	−25.908	−32.832	−34.677	−24.210	−23.482	−32.970
p-value	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000

Source: Elaborated by the author.

and

Table A3. Phillips–Perron test results before and during the COVID-19 period.

Phillips–Perron Test Statistic
Pre-COVID-19 Period
	Binance USD	Bitcoin	Binance Coin	Cardano	Dogecoin	Solana	Ethereum	Tether	USD Coin	Ripple
t-Statistic	−16.307	−33.201	−31.727	−27.945	−31.612	N/A	−28.245	−68.989	−33.266	−33.572
p-value	0.000	0.000	0.000	0.000	0.000		0.000	0.000	0.000	0.000
During the COVID-19 Period
t-Statistic	−30.657	−33.784	−43.953	−34.209	−32.753	−33.492	−29.931	−74.346	−41.548	−35.457
p-value	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000

Source: Elaborated by the author.

, consistently revealed p-values below 0.05 for all ten cryptocurrencies studied. This compelling evidence led to the rejection of the null hypothesis at the 95% confidence level, confirming the stationarity of our time-series data.

After confirming stationarity, we used dummy variables in an ordinary least squares (OLS) regression and conducted Engle’s ARCH test. This test reveals the presence of volatility clustering both before and after the COVID-19 pandemic (see

Table A4. Test results for Engle’s Arch test.

1	Binance USD	During COVID-19	F-statistic	236.151	Prob. F	0.000
			Obs*R-squared	324.169	Prob. Chi-Square	0.000
2	Bitcoin	Pre-COVID-19	F-statistic	19.672	Prob. F	0.000
			Obs*R-squared	38.077	Prob. Chi-Square	0.000
		During COVID-19	F-statistic	0.142	Prob. F	0.049
			Obs*R-squared	0.284	Prob. Chi-Square	0.049
3	Binance Coin	Pre-COVID-19	F-statistic	0.038	Prob. F	0.963
			Obs*R-squared	0.076	Prob. Chi-Square	0.963
		During COVID-19	F-statistic	23.340	Prob. F	0.000
			Obs*R-squared	44.775	Prob. Chi-Square	0.000
4	Cardano	Pre-COVID-19	F-statistic	26.171	Prob. F	0.000
			Obs*R-squared	49.309	Prob. Chi-Square	0.000
		During COVID-19	F-statistic	8.806	Prob. F	0.000
			Obs*R-squared	17.365	Prob. Chi-Square	0.000
5	Dogecoin	Pre-COVID-19	F-statistic	16.792	Prob. F	0.000
			Obs*R-squared	32.669	Prob. Chi-Square	0.000
		During COVID-19	F-statistic	24.146	Prob. F	0.000
			Obs*R-squared	44.661	Prob. Chi-Square	0.000
6	Solana	During COVID-19	F-statistic	18.776	Prob. F	0.000
			Obs*R-squared	36.201	Prob. Chi-Square	0.000
7	Ethereum	Pre-COVID-19	F-statistic	6.232	Prob. F	0.002
			Obs*R-squared	12.313	Prob. Chi-Square	0.002
		During COVID-19	F-statistic	3.724	Prob. F	0.025
			Obs*R-squared	7.416	Prob. Chi-Square	0.025
8	Tether	Pre-COVID-19	F-statistic	7.657	Prob. F	0.001
			Obs*R-squared	15.133	Prob. Chi-Square	0.001
		During COVID-19	F-statistic	234.791	Prob. F	0.000
			Obs*R-squared	322.888	Prob. Chi-Square	0.000
9	USD Coin	Pre-COVID-19	F-statistic	37.645	Prob. F	0.000
			Obs*R-squared	64.870	Prob. Chi-Square	0.000
		During COVID-19	F-statistic	122.120	Prob. F	0.000
			Obs*R-squared	197.782	Prob. Chi-Square	0.000
10	Ripple	Pre-COVID-19	F-statistic	52.853	Prob. F	0.000
			Obs*R-squared	96.619	Prob. Chi-Square	0.000
		During COVID-19	F-statistic	23.880	Prob. F	0.000
			Obs*R-squared	45.766	Prob. Chi-Square	0.000

Source: Elaborated by the author.

in Appendix A). The presence of ARCH effects was confirmed as all p-values were less than 0.05. These results support the use of GARCH frameworks for modeling volatility.

To incorporate the leptokurtic nature of cryptocurrencies, we implement a Normal Inverse Gaussian (NIG) distribution for the error element in the GARCH model. This distribution can capture the additional skewness and kurtosis in the residual return series (Osterrieder et al. 2017). We first identify the best GARCH (p, q) model to accurately model the volatility of ten cryptocurrencies. To ensure the reliability of our chosen GARCH (p, q) models, all the coefficients (ω, αi, and βj) in the GARCH (p, q) model must be non-negative and satisfy the condition αi + βj < 1. Higher αi values suggest greater volatility responses to market shocks, whereas larger βj coefficients indicate the occurrence of market shocks.

As indicated in

Table 3. Summary of GARCH (p,q) model parameters and diagnostics (pre-COVID-19 period).

	Bitcoin	Binance Coin	Cardano	Dogecoin	Ethereum	Tether	USD Coin	Ripple
Best GARCH (p,q) Model	GARCH (1,2)	GARCH (1,1)	GARCH (1,1)	GARCH (1,1)	GARCH (1,1)	GARCH (1,1)	GARCH (1,1)	GARCH (1,2)
ω	1.539	6.653	0.558	0.658	9.588	0.003	0.090	2.550
ω (p-value)	0.000	0.018	0.049	0.004	0.018	0.003	0.010	0.000
α1	0.139	0.348	0.055	0.376	0.455	0.305	0.090	0.392
α1 (p-value)	0.000	0.006	0.002	0.000	0.031	0.000	0.001	0.000
β1	0.055	0.623	0.936	0.555	0.524	0.667	0.900	0.200
β1 (p-value)	0.032	0.000	0.000	0.000	0.000	0.000	0.000	0.040
β2	0.757							0.419
β2 (p-value)	0.032							0.000
Volatility persistence	0.951	0.971	0.992	0.931	0.979	0.972	0.990	1.011
AIC Value	5.405	6.541	6.304	5.964	5.999	0.805	0.433	5.980
Ljung box test p-value	0.146	0.742	0.232	0.149	0.538	0.606	0.344	0.089
ARCH LM-Test p-value	0.673	0.671	0.640	0.977	0.713	0.800	0.298	0.760

Source: Elaborated by the author.

and

Table 4. Summary of GARCH (p,q) model parameters and diagnostics (during the COVID-19 period).

	Binance USD	Bitcoin	Binance Coin	Cardano	Dogecoin	Solana	Ethereum	Tether	USD Coin	Ripple
Best GARCH (p,q) Model	GARCH(1,2)	GARCH(1,1)	GARCH(1,1)	GARCH(1,1)	GARCH(1,1)	GARCH(1,1)	GARCH(1,1)	GARCH(1,2)	GARCH(1,1)	GARCH(1,1)
ω	0.000	0.321	0.974	2.383	8.317	2.557	1.076	0.000	0.000	1.676
ω (p-value)	0.021	0.041	0.001	0.001	0.016	0.003	0.005	0.132	0.176	0.002
α1	1.282	0.096	0.181	0.211	0.833	0.146	0.117	0.615	0.377	0.237
α1 (p-value)	0.049	0.001	0.000	0.000	0.016	0.000	0.000	0.003	0.000	0.000
β1	0.307	0.900	0.806	0.747	0.537	0.820	0.849	0.258	0.608	0.719
β1 (p-value)	0.014	0.000	0.000	0.000	0.000	0.000	0.000	0.036	0.000	0.000
β2	0.315							0.466
β2 (p-value)	0.003							0.000
Volatility persistence	1.904	0.997	0.988	0.958	1.370	0.966	0.966	1.339	0.985	0.955
AIC Value	−0.600	5.155	5.580	5.983	5.931	6.617	5.741	−0.796	−0.615	5.745
Ljung box test p-value	0.486	0.425	0.637	0.830	0.500	0.786	0.995	0.689	0.208	0.963
ARCH LM-Test p-value	0.669	0.978	0.465	0.622	0.787	0.105	0.788	0.839	0.000	0.682

Source: Elaborated by the author.

(period preceding COVID-19 and period during COVID-19), the fact that the coefficients ꞵ₁ + ꞵ₂ > α₁ indicates that when attempting to forecast present volatility, attention is directed towards the enduring consequences of past shocks rather than recent occurrences. Furthermore, we evaluate the volatility persistence by summing the values of α₁, β₁, and β₂. The sum of these parameters, which is a critical indicator of the model stability, must not exceed one. The high value of coefficient β₁ suggests the presence of volatility clustering.

Ripple shows a heightened susceptibility to negative leaps and eruptive behavior, as indicated by the equation α₁ + β₁ + β₂ > 1, during both periods. This pattern suggests a decline in volatility, which aligns with the findings of Idrees and Akhtar (2023). Consistent with the findings of Queiroz and David (2023), the GARCH (1,1) model performs well in predicting volatility across most cryptocurrencies during both the pre-COVID-19 and during the COVID-19 periods, leaving only Bitcoin and Ripple during the pre-COVID-19 period and Binance USD and Tether during the COVID-19 period, for which GARCH (1,2) provides a better fit.

We also examine the EGARCH and GJR-GARCH asymmetric GARCH models for ten distinct cryptocurrencies before and during the COVID-19 pandemic. To account for heavy tails and high kurtosis, these models capture inherent volatility asymmetry, specifically, as they relate to positive and negative returns in an effective manner. The optimal p-q model with the lowest AIC score was then selected.

Table 5. Summary of asymmetric GARCH (p,q) model parameters and diagnostics (pre-COVID-19 period).

	Bitcoin	Binance Coin	Cardano	Dogecoin	Ethereum	Tether	USD Coin	Ripple
Best GARCH (p,q) Model	No asymmetric model is a good fit	EGARCH (1,1)	EGARCH (1,1)	EGARCH (2,1)	No asymmetric model is a good fit	No asymmetric model is a good fit	No asymmetric model is a good fit	EGARCH (2,1)
ω		−0.036	−0.053	−0.109				−0.072
ω (p-value)		0.033	0.039	0.000				0.006
α1		0.294	0.163	0.500				0.679
α1 (p-value)		0.000	0.000	0.000				0.000
α2				−0.260				−0.498
α2 (p-value)				0.002				0.000
γi		−0.032	−0.008	0.049				0.056
γi (p-value)		0.028	0.007	0.046				0.028
β1		0.971	0.985	0.982				0.985
β1 (p-value)		0.000	0.000	0.000				0.000
AIC Value		6.539	6.314	6.005				5.987
Ljung box test p-value		0.762	0.140	0.167				0.320
ARCH LM-Test p-value		0.951	0.435	0.813				0.416

Source: Elaborated by the author.

and

Table 6. Summary of asymmetric GARCH (p,q) model parameters and diagnostics (during the COVID-19 period).

	Binance USD	Bitcoin	Binance Coin	Cardano	Dogecoin	Solana	Ethereum	Tether	USD Coin	Ripple
Best GARCH (p,q) Model	No asymmetric model is a good fit	EGARCH (1,2)	No asymmetric model is a good fit	No asymmetric model is a good fit	No asymmetric model is a good fit	No asymmetric model is a good fit	GJR-GARCH (1,1)	EGARCH (1,2)	No asymmetric model is a good fit	No asymmetric model is a good fit
ω		0.040					0.778	−0.381
ω (p-value)		0.004					0.000	0.000
α1		0.087					0.108	0.511
α1 (p-value)		0.000					0.000	0.000
α2		−0.039						0.117
α2 (p-value)		0.000						0.021
γi		1.469					0.046	0.617
γi (p-value)		0.000					0.009	0.000
β1		−0.507					0.848	0.358
β1 (p-value)		0.000					0.000	0.020
AIC Value		5.489					5.880	−0.818
Ljung box test p-value		0.844					0.829	2.254
ARCH LM-Test p-value		0.450					0.633	0.156

Source: Elaborated by the author.

(pre-COVID-19 and during COVID-19) illustrate the optimal selection of the asymmetric models.

Our findings indicate a significant shift in the leverage effect dynamics before and during the COVID-19 period. In the pre-COVID period, Binance Coin, Cardano, Dogecoin, and Ripple exhibited leverage effects, meaning that negative returns led to greater increases in volatility than positive returns of the same magnitude. However, during the COVID-19 pandemic, this dynamic changed substantially. Only Bitcoin, Ethereum, and Tether continued to show leverage effects, whereas the previously mentioned cryptocurrencies did not exhibit the same behavior.

This shift can be attributed to the changing market conditions and investor behavior during the pandemic, where Bitcoin, Ethereum, and Tether became more prominent as stable and reliable assets, leading to different volatility dynamics compared to other cryptocurrencies. This analysis highlights the importance of considering the market context and the evolving nature of leverage effects in financial markets.

We conducted a FIGARCH (1, d, 1) model to capture the long-term memory and persistence in volatility observed in cryptocurrency returns, as shown in

Table 7. Summary of FIGARCH (1,d,1) model parameters and diagnostics (pre-COVID-19 period).

	Bitcoin	Binance Coin	Cardano	Dogecoin	Ethereum	Tether	USD Coin	Ripple
ω	0.385	11.313	0.284	0.582	23.714	0.003	−0.003	0.271
ω (p-value)	0.064	0.009	0.395	0.014	0.000	0.000	0.755	0.114
α	0.277	−0.166	0.752	0.314	0.860	0.156	−0.057	0.792
α (p-value)	0.053	0.368	0.000	0.002	0.000	0.031	0.714	0.000
β	0.791	0.224	0.897	0.728	0.595	0.773	0.071	0.891
β (p-value)	0.000	0.292	0.000	0.000	0.000	0.000	0.665	0.000
d	0.726	0.699	0.397	0.760	0.618	1.001	0.385	0.549
d (p-value)	0.004	0.000	0.002	0.000	0.000	0.000	0.003	0.000
AIC Value	5.406	6.531	6.287	5.963	6.077	0.817	0.553	5.959
Ljung box test p-value	0.132	0.098	0.286	0.208	0.591	0.524	0.590	0.155
ARCH LM-Test p-value	0.890	0.321	0.953	0.787	0.254	0.852	0.308	0.630

Source: Elaborated by the author.

and

Table 8. Summary of FIGARCH (1,d,1) model parameters and diagnostics (during the COVID-19 period).

	Binance USD	Bitcoin	Binance Coin	Cardano	Dogecoin	Solana	Ethereum	Tether	USD Coin	Ripple
ω	0.000	0.800	0.960	2.387	1.519	0.820	4.316	−0.001	0.000	1.717
ω (p-value)	0.461	0.168	0.308	0.111	0.076	0.064	0.001	0.090	0.904	0.155
α	0.206	0.120	−0.105	0.195	0.671	0.472	−0.190	0.156	0.234	−0.090
α (p-value)	0.001	0.044	0.046	0.037	0.000	0.351	0.017	0.376	0.015	0.797
β	0.807	0.781	0.161	0.427	0.505	0.011	0.078	0.391	0.611	0.027
β (p-value)	0.000	0.000	0.020	0.010	0.004	0.008	0.041	0.514	0.000	0.942
d	0.943	0.718	0.394	0.457	0.249	0.231	0.360	0.478	0.658	0.399
d (p-value)	0.000	0.016	0.000	0.002	0.035	0.004	0.000	0.074	0.163	0.060
AIC Value	−0.533	5.156	5.569	5.981	5.914	6.659	5.746	0.074	−0.598	5.758
Ljung box test p-value	0.324	0.433	0.481	0.820	0.550	0.965	0.857	0.611	0.059	0.854
ARCH LM-Test p-value	0.739	0.815	0.035	0.609	0.818	0.128	0.991	0.633	0.130	0.977

Source: Elaborated by the author.

(pre-COVID period and during the COVID-19 period). The results show that in the pre-COVID period, only Bitcoin and USD Coin do not have significant p-values for the fractional differencing parameter d at the 95% confidence level. During the COVID period, Tether, USD Coin, and Ripple also did not show significant d p-values at the 95% confidence level.

To further confirm the presence of long-range dependence, we applied Lo’s modified R/S test at the 95% confidence level. We compared the resulting test statistic Q_n with the critical values at the 1%, 5%, and 10% significance levels, as shown in

Table 9. Summary Lo’s modified R/S test results (pre-COVID-19 period).

	Calculated Lo’s Modified R/S Statistic Qn	Critical Value (1%)	Critical Value (5%)	Critical Value (10%)	Interpretation
Bitcoin	57.105	64.894	57.348	53.288	No long-term memory detected
Binance Coin	73.294	68.748	56.386	54.987	Long-term memory detected
Cardano	59.978	57.803	51.957	48.356	Long-term memory detected
Dogecoin	59.445	54.675	50.857	47.348	Long-term memory detected
Ethereum	68.429	64.944	57.242	53.268	Long-term memory detected
Tether	64.657	62.559	55.463	51.572	Long-term memory detected
USD Coin	37.329	41.739	37.458	34.949	No long-term memory detected
Ripple	59.384	58.886	51.952	48.556	Long-term memory detected

Source: Elaborated by the author.

for the pre-COVID period and

Table 10. Summary Lo’s modified R/S test results (during the COVID-19 period).

Currency	Calculated Lo’s Modified R/S Statistic	Critical Value (1%)	Critical Value (5%)	Critical Value (10%)	Interpretation
Binance USD	59.106	54.984	51.987	49.681	Long-term memory detected
Bitcoin	65.194	65.652	58.275	54.301	Long-term memory detected
Binance Coin	69.924	66.133	58.243	54.170	Long-term memory detected
Cardano	66.927	65.652	58.275	54.301	Long-term memory detected
Dogecoin	64.839	64.937	57.293	54.628	Long-term memory detected
Solana	68.746	65.258	57.543	53.251	Long-term memory detected
Ethereum	69.201	65.912	54.836	53.228	Long-term memory detected
Tether	57.188	65.893	58.396	54.532	No long-term memory detected
USD Coin	51.208	66.097	58.345	54.284	No long-term memory detected
Ripple	57.299	65.893	58.396	54.532	No long-term memory detected

Source: Elaborated by the author.

for the COVID period. The consistency of Lo’s test results with our FIGARCH findings reaffirms the presence of long-range dependence in the dataset, thus validating the robustness of our initial FIGARCH results. These results are consistent with those of previous studies on Bitcoin and Ethereum by Soylu et al. (2020) and Sheraz et al. (2022), which also showed long-term memory in these cryptocurrencies. However, our results differ from those of Sheraz et al. (2022) regarding Ripple, which did not exhibit long-term memory during the COVID-19 period.

After conducting all the tests, we first selected the best GARCH (p, q) model for each cryptocurrency. Next, we identify the best asymmetric model by choosing between EGARCH (p, q) and GJR-GARCH (p, q). Finally, we determined the best FIGARCH (1,d,1) model. Among these, we selected the optimal model based on the lowest Akaike Information Criterion (AIC).

We performed Q-Q plot tests on the residuals from the best-fitted GARCH models, including GARCH, EGARCH, GJR-GARCH, and FIGARCH, as shown in Figure 1 (pre-COVID) and Figure 2 (during COVID-19). By comparing the Q-Q plots of the residuals against the theoretical NIG distribution, we evaluated which model residuals most closely followed this expected pattern. Figure 1 and Figure 2 also indicate which GARCH model provides the best fit for each cryptocurrency. We then used this best-fit model to model the volatility of the top ten cryptocurrencies, incorporating dummy variables to determine whether a day-of-the-week effect exists.

From the best-fitted GARCH model, we scrutinized the significant anomalies and observed a notable trend on Sundays, where the majority of cryptocurrencies exhibited positive returns during both the pre-COVID-19 and COVID-19 periods. All coefficients of cryptocurrencies are positive, indicating higher average returns on that day. A day with a positive coefficient may be seen as a good day to hold or sell if you look to capitalize on higher returns. Traders might prefer to sell on these days to maximize profits. This finding deviates from the previously reported negative Sunday effect by Dorfleitner and Lung (2018) but corroborates the findings of Naz et al. (2023).

In addition, a noticeable shift occurred in Monday returns. During the pre-COVID-19 period, cryptocurrencies displayed positive returns, consistent with the findings of Ma and Tanizaki (2019), Hamurcu (2022), López-Martín (2023), and Naz et al. (2023). However, during the COVID-19 period, this trend reversed, and all the coins had negative coefficients, indicating lower average returns on that day. This aligns with the findings of Baur et al. (2019) and Hinny and Szabó (2022). Days with negative coefficients may be seen as better days to buy, as prices tend to be lower. This provides a buying opportunity for traders looking to purchase at lower prices and sell at higher prices on subsequent days with positive coefficients like Thursday, Friday, and Sunday. This alignment supports the adaptive market hypothesis.

Table 11. Coefficients and p-values (pre-COVID-19 period) for day-of-week effects from the best-fit GARCH model.

		Monday	Tuesday	Wednesday	Thursday	Friday	Saturday	Sunday
Bitcoin	Coefficient	0.306	0.037	0.129	0.320	−0.130	0.419	0.184
	p-value	0.183	0.838	0.521	0.130	0.529	0.055	0.448
Binance Coin	Coefficient	0.110	−0.188	−0.276	−0.476	−0.081	0.801	0.023
	p-value	0.772	0.580	0.434	0.193	0.815	0.029	0.955
Cardano	Coefficient	0.347	−0.640	−0.444	−0.454	−1.307	0.596	0.380
	p-value	0.374	0.082	0.250	0.250	0.002	0.143	0.423
Dogecoin	Coefficient	0.055	−0.432	−0.357	−0.006	−0.717	0.237	−0.069
	p-value	0.823	0.037	0.121	0.978	0.004	0.354	0.795
Ethereum	Coefficient	0.365	−0.228	−0.163	−0.277	−0.395	0.751	0.169
	p-value	0.214	0.384	0.563	0.359	0.182	0.014	0.579
Tether	Coefficient	0.005	−0.031	−0.003	0.002	0.020	−0.007	0.018
	p-value	0.687	0.012	0.833	0.892	0.163	0.586	0.230
USD Coin	Coefficient	0.027	0.001	0.014	0.023	0.023	−0.018	0.000
	p-value	0.206	0.953	0.586	0.316	0.355	0.433	0.996
Ripple	Coefficient	0.075	−0.593	−0.090	−0.227	−1.073	0.220	0.223
	p-value	0.642	0.001	0.497	0.100	0.000	0.213	0.192

Source: Elaborated by the author. Note: The p-values in bold indicate statistically significant day-of-the-week effects at the 95% significance level for specific days.

and

Table 12. Coefficients and p-values (during the COVID-19 period) for day-of-week effects from the best-fit GARCH model.

		Monday	Tuesday	Wednesday	Thursday	Friday	Saturday	Sunday
Binance USD	Coefficient	−0.017	−0.009	−0.003	−0.001	0.016	0.011	−0.008
	p-value	0.001	0.116	0.587	0.833	0.006	0.032	0.201
Bitcoin	Coefficient	−0.132	0.666	−0.059	0.224	0.071	−0.038	0.214
	p-value	0.511	0.000	0.741	0.222	0.714	0.860	0.323
Binance Coin	Coefficient	−0.446	0.445	−0.142	0.185	0.188	0.124	0.622
	p-value	0.052	0.051	0.517	0.393	0.404	0.631	0.008
Cardano	Coefficient	−0.554	0.274	−0.267	0.001	0.158	−0.379	0.521
	p-value	0.077	0.336	0.339	0.997	0.594	0.241	0.119
Dogecoin	Coefficient	−0.372	−0.057	−0.408	−0.060	−0.088	−0.067	0.359
	p-value	0.138	0.809	0.099	0.800	0.719	0.777	0.180
Solana	Coefficient	−0.538	0.568	−0.967	−0.029	0.285	−0.478	0.831
	p-value	0.222	0.154	0.017	0.944	0.492	0.278	0.083
Ethereum	Coefficient	−0.128	0.790	−0.139	0.605	0.281	−0.105	0.530
	p-value	0.666	0.002	0.593	0.021	0.283	0.718	0.091
Tether	Coefficient	−0.012	−0.010	−0.002	−0.014	0.015	0.024	0.001
	p-value	0.044	0.149	0.712	0.030	0.035	0.000	0.915
USD Coin	Coefficient	−0.021	−0.012	−0.004	0.000	0.026	0.021	0.013
	p-value	0.000	0.102	0.465	0.941	0.000	0.000	0.001
Ripple	Coefficient	−0.238	0.932	−0.089	0.297	0.769	−0.245	0.225
	p-value	0.328	0.005	0.787	0.367	0.024	0.488	0.529

Source: Elaborated by the author. Note: The p-values in bold indicate statistically significant day-of-the-week effects at the 95% significance level for specific days.

present the coefficients and p-values for the day-of-the-week effects, further detailing the observed trends.

Binance Coin, Ethereum, Tether, USD Coin, and Ripple continued to exhibit anomalies throughout the observed period. During the COVID-19 period, Bitcoin, Ethereum, and Ripple experienced a shift in anomalies to Tuesdays, with positive coefficients indicating higher returns for investors. Ripple consistently maintained its anomalies on Tuesdays and Fridays, with positive returns on these days during the COVID-19 period. Bitcoin showed a day-of-the-week effect with positive returns on Tuesday, in line with the study by Aharon and Qadan (2019), which contradicts their finding of a Monday effect on Bitcoin. Binance Coin’s effect was observed on Sundays. Solana exhibited a day-of-the-week effect with negative returns on Wednesdays, which is consistent with the findings of López-Martín (2023). Notably, Cardano and Dogecoin did not show any anomalies during the COVID-19 period.

Binance Coin, Ethereum, Tether, and USD Coin displayed anomalies on multiple days. Binance Coin showed anomalies on Mondays, Fridays, and Saturdays, with Mondays having a negative coefficient and Fridays and Saturdays having positive coefficients. This pattern suggests that investors in Binance Coin could benefit from buying on Mondays and selling on Fridays or Saturdays. Ethereum exhibits a day-of-the-week effect with positive coefficients on Tuesday and Friday, indicating that these days are optimal for selling to gain higher returns. Tether had a day-of-the-week effect, with negative coefficients on Monday and Thursday making these days better for buying, while positive coefficients on Friday and Saturday indicated better days for selling. Similarly, USD Coin’s pattern suggests that investors should consider buying on Monday and selling on Fridays, Saturdays, and Sundays.

The effect of market sentiment is implicitly observed in our analysis of day-of-the-week anomalies and shifts in return patterns during the COVID-19 period. Market sentiment significantly influences cryptocurrency prices, often leading to herding behavior, where investors follow the actions of others rather than their own independent analysis. This behavior amplifies price movements and contributes to the observed day-of-the-week effects. The shifts in returns and anomalies during the COVID-19 period likely reflect changes in market sentiment as investors react to the rapidly evolving economic and social conditions.

While this study offers significant insights, its limitations include the following: future research could benefit from incorporating intraday data to provide more detailed insights. While market sentiment significantly influences cryptocurrency prices, we did not include specific variables to quantify sentiment. Future research should consider incorporating sentiment analysis from social media trends, news sentiments, and investor surveys to provide a more detailed understanding of market dynamics. Furthermore, our model is backward-looking, meaning that the day-of-the-week effects detected in historical data may not persist under current market conditions. Market dynamics evolve, and past patterns may not necessarily hold true today. A post-pandemic analysis can reveal if trends have changed since COVID-19.

5. Conclusions

This study delves into calendar anomalies and volatility patterns within the cryptocurrency market, focusing on day-of-the-week effects before and during the COVID-19 pandemic. We leverage advanced statistical models, including GARCH, EGARCH, GJR-GARCH, and FIGARCH, to analyze the top ten cryptocurrencies by market capitalization. The continuous 24/7 operation of cryptocurrency markets, which includes holidays and weekends, offers a unique context for this investigation that is distinct from traditional financial markets.

Our findings reveal notable shifts in volatility dynamics and day-of-the-week effects due to the pandemic. The pre-COVID period shows pronounced leverage effects in Binance Coin, Cardano, Dogecoin, and Ripple, with negative returns leading to greater increases in volatility. However, during the COVID-19 period, this behavior was observed only in Bitcoin, Ethereum, and Tether, indicating significant changes in market dynamics and investor behavior. These shifts underscore the importance of considering the evolving market context when analyzing financial anomalies.

We find compelling evidence of day-of-the-week anomalies, particularly in the returns of all studied coins, except for Cardano and Dogecoin, during the COVID-19 period. Bitcoin, which did not show any day-of-the-week effect pre-COVID-19, began to exhibit such effects during the pandemic. This finding challenges the notion of market efficiency in the cryptocurrency space, suggesting that exploitable anomalies persist despite a market’s continuous operation and increasing maturity.

The use of FIGARCH models provides deeper insights into long-term memory and the persistence of volatility in cryptocurrency returns. The presence of long-term memory in most cryptocurrencies before and during the COVID-19 period highlights the need for robust trading strategies that account for prolonged volatility effects. Our application of Lo’s modified R/S test further validates these findings, confirming long-range dependence in the dataset.

Our analysis also demonstrated day-of-the-week effects on cryptocurrency returns, with different patterns emerging before and during the pandemic. Positive returns are generally observed on Sundays, whereas a shift to negative returns on Mondays is evident during the COVID-19 period. These patterns suggest strategic opportunities for investors, such as buying on days with negative coefficients and selling on days with positive coefficients, to maximize returns.

Several macroprudential strategies can enhance investor confidence and mitigate fear and uncertainty, especially in the face of anomalies and exogenous shocks, such as crises and pandemics. Enhanced transparency and reporting, including real-time reporting of trading volumes and significant trades, helps investors make informed decisions and reduce uncertainty. Establishing market stabilization funds to intervene during periods of extreme volatility can help stabilize prices and prevent panic selling. Investor education programs on market anomalies and risk management techniques empower better investment decisions, reduce fear, and promote confidence. Regular stress testing and scenario analysis of major exchanges ensure preparedness for potential shocks and inform market-stability strategies. Developing comprehensive regulatory frameworks that address the unique aspects of cryptocurrency markets provides a stable environment for investors.

In conclusion, our study provides valuable insights for investors, traders, regulators, and policymakers to navigate the complexities of the cryptocurrency market. The identified volatility patterns and day-of-the-week effects inform the development of effective trading strategies, risk-management practices, and regulatory frameworks. As the cryptocurrency market continues to evolve, analysis and adaptation are essential to capitalize on emerging opportunities and mitigate associated risks.