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12
Market Eciency and Calendar
Anomalies Post-COVID: Insights from
Bitcoin and Ethereum
Eciencia del mercado y anomalías de
calendario pos-COVID: perspectivas
de bitcoin y ethereum
Received: March 3, 2024.
Approved: May 22, 2024.
Sonal Sahu
Tecnológico de
Monterrey, Campus
Guadalajara, Mexico
13
Abstract
This study investigates day-of-the-week eects in the digital market, with a focus on Bitcoin
and Ethereum, spanning from July 1st, 2020, to December 31st, 2023, in the post-COVID-19
period. Employing parametric and non-parametric tests alongside the GARCH (1,1) model,
market dynamics was analized. The ndings indicate the presence of a day-of-the-week eect
in Ethereum, characterized by notable return variations across dierent days, while Bitcoin
exhibits no discernible calendar anomalies, suggesting enhanced market eciency. Ethereum’s
susceptibility to these eects underscores ongoing market complexities. Disparities in calendar
anomalies stem from evolving market dynamics, methodological dierences, and the speculative
nature of cryptocurrency trading. Furthermore, the decentralized and global market complicates
the accurate identication of market-wide eects. This study provides experimental ndings on
day-of-the-week eects in the digital market, facilitating investors in rening trading strategies
and risk management. Further research is warranted to explore underlying mechanisms and
monitor regulatory and technological developments for investor insights.
Keywords: Cryptocurrencies, calendar anomalies, GARCH model, trading strategy, ANOVA.
JEL Classication: G14, G10, G41.
Resumen
Este estudio investiga los efectos del día de la semana en el mercado digital, con un enfoque
en bitcoin y ethereum, abarcando desde el 1º de julio de 2020 hasta el 31 de diciembre de
2023, en el período posterior al COVID-19. Empleando pruebas paramétricas y no paramétricas
junto con el modelo GARCH (1,1), se analizó la dinámica del mercado. Los hallazgos indican un
efecto signicativo del día de la semana en ethereum, caracterizado por notables variaciones
de rendimiento entre diferentes días, mientras que bitcoin no muestra anomalías de calendario
discernibles, lo que sugiere una mayor eciencia del mercado. La susceptibilidad de ethereum
a estos efectos subraya las complejidades actuales del mercado. Las disparidades en las
anomalías del calendario surgen de la evolución de la dinámica del mercado, las diferencias
metodológicas y la naturaleza especulativa del comercio de criptomonedas. Además, el
mercado descentralizado y global complica la identicación precisa de los efectos en todo
el mercado. Este estudio proporciona evidencia empírica sobre los efectos del día de la semana
en el mercado de criptomonedas, lo que facilita a los inversionistas renar las estrategias
comerciales y la gestión de riesgos. Se justica realizar más investigaciones para explorar los
mecanismos subyacentes y monitorear los desarrollos regulatorios y tecnológicos para obtener
información de los inversionistas.
Palabras clave: criptomonedas, anomalías de calendario, modelo GARCH, estrategia de
trading, ANOVA.
Clasicación JEL: G14, G10, G41.
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14
1. Introduction
The cryptocurrency market has witnessed remarkable growth, establishing itself as
a signicant player within the nancial landscape. This growth is evident through
the soaring market capitalization of cryptocurrencies such as Bitcoin, Ethereum, and
Dogecoin, which have surged to unprecedented levels (Stavrova, 2021). Key factors
contributing to this surge include the decentralized nature of cryptocurrencies
and the innovative blockchain technology underpinning them (Chen et al., 2019).
Moreover, the integration of cryptocurrencies with traditional nance has sparked
increased interest among investors (Volosovych et al., 2023).
The distinct decentralized structure of the cryptocurrency market, facilitated by
blockchain technology, sets it apart from traditional nancial markets. This structure
enables peer-to-peer transactions without the need for intermediaries like banks
(Andolfatto & Martin, 2022). Additionally, rapid technological innovation within
the cryptocurrency sphere attracts diverse participants, consequently expanding the
market infrastructure (Volosovych et al., 2023).
The regulatory landscape surrounding cryptocurrencies continues to evolve, adding
layers of complexity to the market. Governments and regulatory bodies worldwide
are increasingly focused on regulating cryptocurrencies to safeguard investor
interests and ensure nancial stability (Singh, 2021). As Pantielieieva et al. (2021)
argue, regulatory scrutiny actively shapes the future adoption of virtual currencies.
Furthermore, various factors inuence price movements, volatility, and investor
sentiment within the cryptocurrency market. Heightened investor interest has led
to increased market activity and trading volumes, with studies emphasizing the
signicance of comprehending price deviations and capital controls for exploiting
arbitrage opportunities (Makarov & Schoar, 2020).
Volatility remains as a dening characteristic of the cryptocurrency market, with
studies scrutinizing volatility co-movements among major cryptocurrencies such as
Bitcoin and Ether (Katsiampa, 2019). External factors like the COVID-19 pandemic
contribute to uctuations in prices and market sentiment (Washington et al., 2023).
Additionally, researchers have explored the inuence of news media on virtual
currency prices, analyzing the impact of news discourses on market dynamics
(Coulter, 2022).
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Market Eciency and Calendar Anomalies Post-COVID: Insights from Bitcoin and Ethereum
Eciencia del mercado y anomalías de calendario pos-COVID: perspectivas de bitcoin y ethereum
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Given the inherent volatility in the cryptocurrency market, understanding and
managing associated risks are imperative for investors. While oering the potential
for substantial gains, the market also poses risks of signicant losses (Zhao & Zhang,
2021). Challenges in forecasting cryptocurrency volatility persist due to market
uniqueness and external factors such as the COVID-19 pandemic (Ftiti et al., 2021).
Therefore, understanding and modelling cryptocurrency volatility are crucial for
informed decision-making, with advanced techniques such as machine learning and
GARCH models aiding in forecasting (Joshi & Sharma, 2022).
In traditional nancial markets, investors note the day-of-the-week impact, which
refers to discernible patterns in stock returns corresponding to specic days of the
week, inuencing their trading strategies and risk management (Tran, 2023). These
patterns, inuenced by psychological factors, underscore the intricacies of nancial
markets, necessitating investors to consider both fundamental and technical analysis
(Țilică, 2021).
Investigating the day-of-the-week eect in the digital currency market holds
signicance amidst increasing investor interest. Recognizing these patterns can
empower investors to tailor trading strategies and develop advanced algorithms
and risk management strategies (Caporale & Plastun, 2019).
The present study aims to explore the implications of identied day-of-the-week
eects for cryptocurrency investors. By understanding how returns and volatility
vary across dierent days, investors can potentially capitalize on favorable market
conditions and mitigate risks. Additionally, the study seeks to provide empirical
evidence of the day-of-the-week pattern in the cryptocurrency market post-COVID-19,
shedding light on evolving market dynamics. Focusing on Bitcoin and Ethereum
from July 2020 to December 2023, this paper aims to investigate the day-of-the-
week eect in these prominent cryptocurrencies, considering their signicance in
the market and the period post-COVID-19.
The subsequent sections of this paper are structured as follows: Section 2
reviews the theoretical framework; Section 3 presents the data and methodology;
Section 4 analyzes empirical data and discusses ndings; and Section 5 provides
conclusions.
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2. Theoretical Framework
Olivares-Sánchez et al. (2022) assert that market eciency, a fundamental concept
in nance, determines the extent to which asset prices reect available information.
The Ecient Market Hypothesis (EMH) states that asset prices fully integrate
available information, rendering consistent outperformance of the market by
investors impossible (Harabida et al., 2023). This theory describes three forms of
market eciency: weak eciency, semi-strong eciency, and strong eciency, each
dening the extent to which information is incorporated into asset prices (Souza &
De França Carvalho, 2023).
Weak eciency implies that all historical trading information is already
incorporated into current equity prices, making achieving excess returns through
historical data analysis challenging (Rossi & Gunardi 2018). In semi-strong
eciency, this idea extends to cover all information accessible to the public,
suggesting that neither fundamental nor technical analysis can reliably produce
outperformance (Liu et al., 2022). In the most stringent form, strong eciency
indicates that all information, regardless of its public or private nature, already
factors into asset prices, making it impossible to gain an advantage even with
insider information (Apergis, 2022).
Various empirical studies have evaluated the eciency of traditional nancial
markets. However, the debate on market eciency in cryptocurrency markets
remains ongoing. Some studies support the weak-form eciency of cryptocurrency
markets, while others emphasize the impact of external factors, such as the pandemic
COVID-19, on cryptocurrency market eciency (Scherf et al., 2022). This ongoing
discussion reects the dynamic nature of cryptocurrency markets, with studies
exploring factors like market liquidity, volatility, and the impact of geopolitical events
on market eciency (Fama, 1997).
To address these complexities, the adaptive market hypothesis (AMH) was proposed,
which extends beyond the EMH by recognizing the limitations of the assumption
of market eciency and incorporating the role of behavioral biases and bounded
rationality in market participants (Rehan & Gül, 2023). The AMH acknowledges that
markets can be inecient at times due to factors like investor sentiment, herding
behavior, and information cascades (Okorie & Lin, 2021). By integrating insights from
behavioral nance and evolutionary biology, the AMH provides a more nuanced
understanding of market dynamics, highlighting the importance of adaptation,
Sonal Sahu
Market Eciency and Calendar Anomalies Post-COVID: Insights from Bitcoin and Ethereum
Eciencia del mercado y anomalías de calendario pos-COVID: perspectivas de bitcoin y ethereum
17
learning, and the interplay between rational and irrational behavior in shaping
nancial markets (Shahid, 2022).
Lo (2004) proposed the Adaptive Markets Hypothesis (AMH), which oers a valuable
framework for understanding the dynamics of cryptocurrency markets. In the
context of cryptocurrency trading, the presence of adaptive market participants
is particularly pronounced. Cryptocurrency markets are characterized by high
volatility and rapid price uctuations, leading to a dynamic environment where
market participants continuously adapt their strategies based on changing market
conditions. The decentralized nature of cryptocurrencies and the absence of a
central authority contribute to the adaptive behavior of market participants, who
respond to news, regulatory developments, and technological advancements in
real-time (Khuntia & Pattanayak, 2021).
Technological advancements play a signicant role in shaping market behavior in
cryptocurrency trading. The use of blockchain technology, algorithmic trading, and
articial intelligence has revolutionized the way transactions are conducted and
information is processed in cryptocurrency markets (Davidson et al. 2018). These
technological innovations have enabled faster execution of trades, increased market
transparency, and facilitated the development of sophisticated trading strategies
that respond to market signals and trends (Mikhaylov, 2020). However, they have
also introduced new challenges related to market manipulation and cybersecurity
(Ogunyolu & Adebayo, 2022).
The day-of-the-week eect is observed in capital markets where certain days exhibit
distinct patterns in terms of volatility and returns (Luxianto et al., 2020). Researchers
and investors have been interested in this eect as it can oer insights into market
dynamics and potentially impact trading strategies (Zilca, 2017). Studies have shown
that specic days of the week may experience higher or lower levels of market
activity and price movements, indicating the day-of-the-week eect in both volatility
and return equations (Chaouachi & Dhaou, 2020; Paital & Panda, 2018).
The day-of-the-week eect in the cryptocurrency market has garnered signicant
attention from researchers exploring anomalies within the realm of digital assets.
Studies have demonstrated that specic days of the week may witness uctuations
in market activity and price movements, inuencing both volatility and return
equations. Caporale and Plastun (2019) conducted a thorough investigation into
the day-of-the-week eect in the cryptocurrency market, shedding light on potential
patterns and trends in price movements across dierent trading days. Theiri et al.
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(2022) contributed to this area of research by focusing on cryptocurrency liquidity
during the Russia-Ukraine war, underscoring the crucial role of market liquidity in
comprehending the day-of-the-week eect.
Tosunoğlu et al. (2023) advanced the literature by employing articial neural
networks to analyze the day-of-the-week anomaly in cryptocurrencies, oering
insights into the predictability of various currencies. Furthermore, Bae and Kim
(2022) explored robust anomaly scores in cryptocurrencies, highlighting the impact
of network factors on cryptocurrency returns. Grobys and Junttila (2020) delved into
speculation and lottery-like demand in cryptocurrency markets, shedding light on
the short-term reversal eects observed in the cross-section of cryptocurrencies.
These studies collectively contribute to our comprehension of the day-of-the-week
eect and its implications for cryptocurrency markets.
The implications of the day-of-the-week eect for investors and trading strategies
in cryptocurrency markets are signicant. Understanding how specic days of the
week inuence market volatility and returns can help investors optimize their trading
decisions and risk management strategies (Dangi, 2020). By leveraging insights from
the day-of-the-week eect, investors may be able to identify potential opportunities
for prot and adjust their trading activities accordingly. Furthermore, the day-of-the-
week eect can inform the development of trading algorithms and strategies that
incorporate the cyclicality and patterns observed in cryptocurrency market behavior
(Miralles-Quirós & Miralles-Quirós, 2022).
In this paper, we also conducted both Parametric, Nonparametric, and OLS Regression
models to nd the eect of the day of the week on cryptocurrency market. This paper
adds to the current literature by applying non-parametric tests alongside parametric
tests, making it unique. By addressing the behavioral aspects driving the day-of-
the-week eect in virtual currency markets, this paper provides deeper insights
into investor sentiment and market dynamics, lling a gap in the existing literature.
Additionally, the GARCH (1,1) model is commonly used for studying the day-of-the-
week eect in cryptocurrencies. This model has been applied in various nancial
markets, including cryptocurrencies, to analyze volatility and the impact of specic
days of the week on asset returns and market dynamics. Studies have shown that
GARCH (1,1) models eectively capture time-varying volatility and examine the day-
of-the-week eect in various markets (Katsiampa, 2017; Chu et al., 2017; Aggarwal &
Jha, 2023; Ampountolas, 2022; Naimy et al., 2021).
Sonal Sahu
Market Eciency and Calendar Anomalies Post-COVID: Insights from Bitcoin and Ethereum
Eciencia del mercado y anomalías de calendario pos-COVID: perspectivas de bitcoin y ethereum
19
3. Data and Methodology
Utilizing the daily closing prices of Bitcoin and Ethereum sourced from CoinMarketCap
(https://coinmarketcap.com/coins/), this study covers the period from July 1st, 2020,
to December 31st, 2023, enabling an examination of the post-COVID-19 period’s
impact.
Dierent quantitative methods, including both parametric and non-parametric tests,
were applied to analyze the data. We used parametric tests such as the conventional
regression model with dummy variables and ANOVA. Non-parametric tests like the
Mood median test were also employed to address potential biases. Additionally,
the Ordinary Least Squares (OLS) regression model with dummy variables and the
GARCH (1,1) model were utilized.
The study commenced by applying descriptive statistics to characterize the returns
distribution of the various days of the week for Bitcoin and Ethereum. We then used
the Jacque-Bera (JB) test statistics and the Anderson-Darling (AD) test statistics to
check for normality. Once the normality was conducted, we calculated returns by
taking the log dierence of consecutive daily closing prices of the cryptocurrencies,
as described by Akyildirim et al. (2021). This process is expressed by the following
equation:
Rn = (In CPn – In CP(n–1)) × 100 (1)
where Rn denotes returns on an nth day in percentage; CPn denotes closing price
on an nth day; CP(n–1) denotes closing price on the previous trading day; and In is a
natural log.
Log returns for Bitcoin and Ethereum were then assessed using the Augmented
Dickey-Fuller (ADF), Philips-Perron test and Kwiatkowski-Phillips-Schmidt-Shin (KPSS),
to conrm the stationarity of the series. These unit root tests have been utilized
in various studies to analyze the stationarity of economic variables, environmental
factors, and market indicators. The application of these tests provides insights
into the behavior of time series data and aids in identifying trends, patterns, and
potential relationships within the data (Ali et al., 2019; Haruna et al., 2022; Dao &
Staszewski, 2021).
Following the assessment of stationarity, the study employed a dummy regression
model that assumed constant return variance for cryptocurrencies. The equation for
the Ordinary Least Squares (OLS) regression model is as follows:
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Returnt = β1MONDAYt + β2TUESDAYt + β3WEDNESDAYt + β4THURSDAYt + β5FRIDAYt+
β6SATURDAYt + β7SUNDAYt + εt (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 coecients; and εt is error term.
To prevent perfect multicollinearity, the intercept term was excluded, and dummy
variables for all seven days of the week were included. The coecients of these
seven dummy variables represent the returns for each day of the week.
Following the least square regression analysis, the residuals were examined for
autoregressive conditional heteroscedasticity using the ARCH test. If the residuals
demonstrated an ARCH eect, indicating volatility clustering, the GARCH (1,1) model
was employed. GARCH (1,1) serves as a mathematical framework utilized for both
modelling and forecasting volatility in time series data, notably in cryptocurrencies
(Kyriazis, 2019). This model is adept at capturing the inherent volatility clustering
often observed in nancial data, as it enables the modelling of both the mean and
the variance of a time series (Kargar, 2021).
Research conducted by Micu and Dumitrescu (2022) further supports the
eectiveness of the GARCH (1,1) model, highlighting its superior t in modelling
volatility across major cryptocurrencies. In the GARCH (1,1) model, the variance
equation is given by:
(3)
Where
α is the coecient of the lagged squared error term, representing the impact of past
volatility shocks on current volatility.
β is the coecient of the lagged conditional variance term, representing the
persistence of volatility.
ω is the constant term representing the long-term average variance.
= is the previous period ARCH term
= is the previous period GARCH term
Sonal Sahu
Market Eciency and Calendar Anomalies Post-COVID: Insights from Bitcoin and Ethereum
Eciencia del mercado y anomalías de calendario pos-COVID: perspectivas de bitcoin y ethereum
21
In the study, seven dummy variables were incorporated into the GARCH (1,1) model
to investigate the day-of-week eect on cryptocurrency market volatility. These
dummy variables allowed for assessing how the variance of asset returns changes
across dierent days of the week. By including these dummy variables, any structural
changes or anomalies in volatility associated with specic days were captured,
providing deeper insights into market dynamics and investor behavior.
4. Analysis and discussion
Analyzing the daily prices of Bitcoin and Ethereum revealed insights into the day-
of-the-week eect. Converting the prices of Bitcoin and Ethereum into return series
provided data for further examination. Table 1 displays the basic statistics derived
from these return series (see Table 1). Ethereum, in particular, stands out with its
highest average returns, suggesting greater potential for protability. The negative
skewness observed in both cryptocurrencies indicates left-skewed distributions,
implying a likelihood of small prots and minimal potential for signicant losses.
Ethereum’s lower variability in returns compared to Bitcoin is evident from its
low coecient of variation (C.V). Additionally, the Jarque-Bera normality test,
consistent with previous research, rejects the null hypothesis of normality for both
cryptocurrencies. Interestingly, maximum returns for Bitcoin and Ethereum occur
on Tuesdays.
Investigating variations across days of the week, one-way ANOVA and Mood’s median
tests were conducted. Additionally, the Anderson-Darling test for normality was
performed. The p-values for both coins were less than 0.05, indicating rejection of the
null hypothesis and non-normality of the data (see Table 2). Scrutinizing the one-way
ANOVA results at a 95% condence level revealed no signicant dierences in mean
returns among days of the week. The Mood’s-median test, a robust nonparametric
test, was employed to examine median equality for log returns across seven days,
as shown in Table 2. No coins yielded signicant p-values, indicating no observed
day-of-week eects, consistent with Kaiser’s (2019) ndings.
22
Table 1. Daily descriptive statistics for Bitcoin and Ethereum Post-COVID period
Bitcoin Returns
Descriptive
statistics
Monday
Returns
Tuesday
Returns
Wednesday
Returns
Thursday
Returns
Friday
Returns
Saturday
Returns
Sunday
Returns
Overall
Returns
Mean -0.098 0.368 0.102 0.539 -0.244 -0.071 0.103 0.100
Maximum 9.314 17.603 8.179 11.966 13.774 11.622 9.148 17.603
Minimum -10.170 -17.252 -11.533 -14.466 -43.371 -10.886 -8.989 -43.371
Standard
Deviation
2.854 4.673 3.383 3.962 5.323 3.751 2.384 3.874
Coecient of
Variation
-29.056 12.682 33.152 7.355 -21.811 -52.933 23.224 38.813
Skewness -0.311 0.023 -0.550 -0.159 -3.615 0.008 -0.200 -1.429
Kurtosis 4.856 5.242 4.166 4.868 31.138 4.217 6.076 19.683
Jarque-Bera 23.467 30.798 15.748 21.998 5169.707 9.066 58.927 12282.830
23
Ethereum Returns
Descriptive
statistics
Monday
Returns
Tuesday
Returns
Wednesday
Returns
Thursday
Returns
Friday
Returns
Saturday
Returns
Sunday
Returns
Overall
Returns
Mean 0.196 0.511 0.108 0.707 -0.345 0.003 0.471 0.236
Median 0.338 0.558 0.144 0.996 0.071 -0.176 0.647 0.348
Maximum 21.786 21.941 14.499 12.889 15.046 18.123 11.441 21.941
Minimum -17.727 -18.782 -13.644 -30.520 -56.308 -16.209 -14.822 -56.308
Standard
Deviation
4.331 5.943 4.235 5.428 6.827 5.181 3.919 5.209
Coecient of
Variation
22.100 11.626 39.296 7.682 -19.801 1775.665 8.323 22.092
Skewness 0.429 0.075 -0.024 -1.286 -3.911 -0.156 -0.172 -1.464
Kurtosis 8.430 4.886 4.196 9.280 32.559 4.079 5.171 18.420
Jarque-Bera 185.125 21.928 8.771 282.078 5726.383 7.726 29.599 10561.600
Source: Data elaborated by the author based on information gathered from coinmarketcap.com
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Table 2. Results of the Parametric and Nonparametric Tests on Bitcoin and Ethereum
The table summarizes results from tests for Normality (Anderson-Darling — a parametric test),
Central tendency (Mood’s median test — a non-parametric test, One-way ANOVA — a parametric
test), and Variance (Levene’s and Bartlett’s tests).
Normality
Test
Central tendency
Test
Variance
test
Anderson
Darling test
P-values
Mood’s
median test
P-values
One Way
Anova
P-values
Bartlett’s test
P-values
Bartlett’s test
P-values
Bitcoin <0.050 0.733 0.676 0.000 0.000
Ethereum <0.050 0.674 0.675 0.000 0.001
Source: Elaborated by the author
Equal variances between days of the week were tested to assess variability and
potential day-of-week eects. Bitcoin and Ethereum reject the null hypothesis at 95%
condence, indicating signicant dierences in variances among days. Both coins,
with p-values below 0.05, are further analyzed to explore variance distribution. Table
3 reveals that the maximum variation for Bitcoin and Ethereum occurs on Tuesdays
(see Table 3). It is noteworthy that the minimum variation is observed on Sundays.
This observation aligns with the ndings of Balcilar et al. (2017) and Doreitner and
Lung (2018), suggesting that many traders abstain from weekend trading, possibly
due to leisure activities or other commitments.
Utilizing both parametric and non-parametric tests can detect day-of-the-week
eects, but integrating dummy variables into GARCH models presents a more
rened approach. This method enables modelling of time-varying volatility patterns,
resulting in improved forecasts and deeper insights into the inuence of particular
days on nancial returns and volatility.
We checked the stationarity of the time series data by conducting unit root tests,
utilizing the Augmented Dickey-Fuller, and Phillips-Perron tests, which are standard
tools in time series analysis (Liao et al., 2021). The results, presented in Table 4 for
the ADF test and PP test, consistently showed p-values below 0.05 (see Table 4). The
time series data’s stationarity was conrmed, and the null hypothesis was rejected
at a 95% condence level due to strong evidence.
25
Table 3. Results of Levene’s test for Variance
Monday Tuesday Wednesday Thursday Friday Saturday Sunday
Bitcoin
Lower Limit 0.747 1.022 0.865 0.934 0.970 0.895 0.644
Upper Limit 1.026 1.403 1.187 1.281 1.330 1.228 0.883
Standard Deviation 0.867 1.185 1.003 1.082 1.124 1.038 0.746
Ethereum
Lower Limit 0.775 1.000 0.806 0.937 0.945 0.931 0.735
Upper Limit 1.063 1.372 1.106 1.285 1.296 1.277 1.008
Standard Deviation 0.898 1.159 0.934 1.086 1.095 1.079 0.852
Source: Derived and expanded upon by the author.
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Table 4. Augmented Dickey-Fuller Test and Phillips-Perron Test results
Augmented Dickey-Fuller
Test Statistics
Phillips-Perron
Test statistic
Bitcoin Ethereum Bitcoin Ethereum
t-Statistic -33.829 -34.677 -33.784 -29.931
P-value 0.000 0.000 0.000 0.000
Source: Derived and expanded upon by the author.
After conducting the ADF and PP tests to assess the stationarity of the time series
data for both Bitcoin and Ethereum, the KPSS test was also conducted. The KPSS test
serves as a complementary tool to the ADF and PP tests, oering additional insights
into the stationarity properties of the data.
The KPSS test is particularly useful because it complements the ADF and PP tests by
focusing on dierent aspects of stationarity. While the ADF and PP tests primarily
detect trends in the data, the KPSS test is sensitive to detecting other forms of non-
stationarity, such as level shifts, changes in variance, or sudden shocks. By running
the KPSS test alongside the ADF and PP tests, a more comprehensive assessment of
the stationarity of the time series data is ensured.
The results of the KPSS test, as shown in Table 5, indicate that the test LM statistics
are less than the critical values at 99%, 95%, and 90% signicance levels for both
Bitcoin and Ethereum (see Table 5). This suggests that the null hypothesis of
stationarity cannot be rejected, providing evidence that the time series data for both
cryptocurrencies is stationary. Therefore, it can be concluded that the data does not
exhibit signicant non-stationarity, further validating the analysis and conclusions.
Table 5. Kwiatkowski-Phillips-Schmidt-Shin Test results
Bitcoin Ethereum
KPSS LM-Statistics 0.090 KPSS LM-Statistics 0.070
Critical value at 1% 0.216 Critical value at 1% 0.439
Critical value at 5% 0.146 Critical value at 5% 0.463
Critical value at 10% 0.119 Critical value at 10% 0.347
Source: Derived and expanded upon by the author.
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Market Eciency and Calendar Anomalies Post-COVID: Insights from Bitcoin and Ethereum
Eciencia del mercado y anomalías de calendario pos-COVID: perspectivas de bitcoin y ethereum
27
Following the unit root tests, proceeded with Ordinary Least Squares (OLS) regression,
incorporating dummy variables into the analysis. Subsequently, we scrutinized the
OLS residuals for evidence of volatility clustering, employing Engle’s ARCH test. Table
6 shows the results consistently yielded p-values below 0.05, compellingly rejecting
the null hypothesis and accepting the existence of ARCH eects (see Table 6). After
this GARCH(1,1) was applied and checked for robustness to predict the day-of-week-
eect and volatility.
Table 6. Test results for Engle’s Arch test
Bitcoin
F-statistics 0.142 F Probability 0.047
Obs*R-squared 0.284 Probability Chi-Square 0.047
Ethereum
F-statistics 3.724 F Probability 0.025
Obs*R-squared 7.416 Probability Chi-Square 0.025
Source: Derived and expanded upon by the author.
The signicant p-values of both the ARCH and GARCH terms, as shown in Table 7,
indicate their importance in both Bitcoin and Ethereum. This signicance implies
that the returns on these cryptocurrencies exhibit continuous and time-varying
volatility (see Table 7). Moreover, it suggests that the volatility of cryptocurrencies is
heavily inuenced by both recent historical data and projected future values.
For Bitcoin, the ARCH + GARCH terms being less than 1 indicate decaying volatility,
suggesting a persistence of volatility over time. The daily returns show negativity for
Friday and Saturday and positivity for other days, aligning with ndings of previous
studies (Lopez-Martin, 2022; Naz et al., 2023). Additionally, there are no signicant
p-values for any day-of-week eect. Prior to the COVID period, Bitcoin did not show
a day-of-the-week eect, and it has grown increasingly eective with time. These
ndings of Bitcoin are consistent with the research of various authors (Tiwari et al.,
2019; Aggarwal, 2019; Lade & Yi, 2020; Baur et al., 2019; Kinateder & Papavassiliou,
2021; Dumrongwong, 2021) but do not support the ndings of others (Aharon &
Qadan, 2019; Lopez-Martin, 2022; Naz et al., 2023).
Similarly, for Ethereum, the ARCH + GARCH terms being less than 1 also signify
decaying volatility, indicating a persistence of volatility. The daily returns for all
days are positive. Additionally, the signicant p-value for Thursday’s daily returns is
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28
noteworthy, which is in line with previous research (Lopez-Martin, 2022; Karaömer
& Kakilli, 2023).
Table 7. GARCH (1,1) model estimation for return of Bitcoin and Ethereum
Dependent Variable: Bitcoin returns
GARCH = C(8) + C(9)*RESID(-1)^2 + C(10)*GARCH(-1)
Variable Coecient Std. Errors z-Statistics Probability
MONDAY 0.108 0.243 0.444 0.657
TUESDAY 0.405 0.211 1.915 0.546
WEDNESDAY 0.132 0.213 0.620 0.535
THURSDAY 0.353 0.222 1.594 0.111
FRIDAY -0.022 0.223 -0.097 0.923
SATURDAY -0.072 0.237 -0.303 0.762
SUNDAY 0.191 0.272 0.703 0.482
Variance Equation
Constant 0.312 0.170 1.833 0.067
ARCH Term 0.068 0.022 3.078 0.002
GARCH Term 0.924 0.020 45.430 0.000
Dependent Variable: Ethereum returns
GARCH = C(8) + C(9)*RESID(-1)^2 + C(10)*GARCH(-1)
Variable Coecient Std. Errors z-Statistics Probability
MONDAY 0.173 0.365 0.475 0.635
TUESDAY 0.580 0.314 1.843 0.065
Sonal Sahu
Market Eciency and Calendar Anomalies Post-COVID: Insights from Bitcoin and Ethereum
Eciencia del mercado y anomalías de calendario pos-COVID: perspectivas de bitcoin y ethereum
29
Dependent Variable: Ethereum returns
GARCH = C(8) + C(9)*RESID(-1)^2 + C(10)*GARCH(-1)
Variable Coecient Std. Errors z-Statistics Probability
WEDNESDAY 0.016 0.333 0.047 0.963
THURSDAY 0.887 0.314 2.827 0.005
FRIDAY 0.089 0.321 0.279 0.780
SATURDAY 0.196 0.322 0.610 0.542
SUNDAY 0.526 0.399 1.320 0.187
Variance Equation
Constant 1.943 0.766 2.537 0.011
ARCH Term 0.086 0.028 3.095 0.002
GARCH Term 0.842 0.044 18.990 0.000
Source: Derived and expanded upon by the author.
To assess the robustness of the GARCH (1,1) model for the study’s time series, two
diagnostic tests were applied. Firstly, the Nyblom stability test examined structural
changes within the time series by testing whether the higher-order autocorrelations
of the squared residuals are zero. This test, robust to heavy-tailed distributions
and outliers, accepted the null hypothesis at a 95% condence level, indicating
stable behavior of the variables in the GARCH (1,1) model. Secondly, the Engle &
Ng sign bias test detected misspecications in conditional volatility models, such
as nonlinearity or asymmetry in the conditional variance. Robust to heavy-tailed
distributions and outliers, this test ensures the dependability of the GARCH model’s
results for forecasting and risk management purposes.
The study period being post-COVID reveals a day-of-week eect in Ethereum,
the high-return cryptocurrency, while Bitcoin shows no calendar anomalies. This
suggests that the most traded cryptocurrency, Bitcoin, is becoming ecient over
time. Inconsistencies in cryptocurrency calendar anomalies stem from various
The Anáhuac Journal, Vol. 24, núm. 1, 2024.
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30
factors, including the relatively new and less mature nature of the cryptocurrency
market, methodological disparities among scholars, the speculative environment
of the market, and its susceptibility to external factors such as news, rumors,
socioeconomic trends, and political movements.
Furthermore, the decentralized and global nature of the cryptocurrency market
presents challenges in identifying and quantifying market-wide eects. The interplay
between market sentiment and the adoption of cryptocurrencies for commercial
activities, coupled with shifts in government policies and regulations, further
underscores the adaptive market hypothesis.
5. Conclusion
The study aimed to explore the presence of day-of-the-week eects in the virtual
currency market post-COVID-19, focusing specically on Bitcoin and Ethereum.
Through a comprehensive analysis employing both parametric and non-parametric
tests, alongside sophisticated econometric models like the GARCH (1,1) model, we
uncovered valuable insights into the dynamics of these cryptocurrencies.
Our ndings reveal that Bitcoin shows no evidence of calendar anomalies, while
Ethereum exhibits a notable day-of-the-week eect, characterized by uctuations
in returns across dierent days. This suggests a trend towards eciency in Bitcoin,
the most traded cryptocurrency, over time. However, the susceptibility of Ethereum
to day-of-the-week eects underscores the ongoing challenges and complexities
within the cryptocurrency market.
The disparities in calendar anomalies across cryptocurrencies can be attributed
to various factors, including the nascent and evolving nature of the market,
methodological disparities among researchers, and the speculative environment
intrinsic to cryptocurrency trading. Furthermore, the decentralized and global
nature of the cryptocurrency market poses challenges in accurately identifying and
quantifying market-wide eects.
By providing empirical evidence of day-of-the-week eects in the cryptocurrency
market and shedding light on changing market dynamics, our work contributes
signicantly to the existing literature. This identication of day-of-the-week
eects holds signicant implications for investors’ risk management strategies.
By understanding and leveraging these eects, investors can enhance their risk
Sonal Sahu
Market Eciency and Calendar Anomalies Post-COVID: Insights from Bitcoin and Ethereum
Eciencia del mercado y anomalías de calendario pos-COVID: perspectivas de bitcoin y ethereum
31
management approaches, particularly in timing their trades and allocating resources
more eectively. Incorporating day-of-the-week eects into risk management
frameworks can aid in optimizing portfolio diversication strategies, ultimately
assisting investors in achieving a more balanced risk-return prole. Hence, our
study underscores the practical utility of considering day-of-the-week eects in
cryptocurrency investment decision-making, providing investors with valuable tools
for navigating the complexities of the market.
Moving forward, additional research is essential to explore other elements that may
inuence market dynamics and delve deeper into the fundamental mechanisms
driving day-to-day eects in cryptocurrencies. Additionally, continuous monitoring
of regulatory developments and technological advancements will be pivotal
in understanding the evolving landscape of the cryptocurrency market and its
implications for investors.
This work is under international License Creative Commons Attribution-
NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0).
The Anáhuac Journal, Vol. 24, núm. 1, 2024.
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32
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About the author
Sonal Sahu is a seasoned professor at Tecnológico de Monterrey, Guadalajara,
Mexico, with a decade-long tenure in the Department of Finance and Accounting.
With over 11 years of work experience at Tecnológico de Monterrey, Sonal has
demonstrated her expertise in nance and accounting education. Prior to her tenure
at Tecnológico de Monterrey, Sonal held signicant roles in the nancial sector,
accumulating over 10 years of experience working with prestigious institutions such
as JP Morgan Chase, Deutsche Bank, ICICI Bank, and the Allianz Group. Currently
pursuing a Ph.D. in Finance at EGADE Business School, her research focuses
on cryptocurrencies and international investments, reecting her dedication to
understanding evolving nancial landscapes. Sonal has showcased her scholarly
prowess through publications in esteemed journals like the Risks Journal and
presentations at conferences such as the European Conference on Games-Based
Learning. Her contributions in academia and research underscore her commitment
to advancing knowledge in nance and shaping future nancial practices.
sonal.sahu@tec.mx
https://orcid.org/0000-0002-2755-0980
