Volume 42, Issue 2
Examining the Dynamic Asset Market Linkages under the COVID-19 Global
Pandemic
Akihiko Noda
School of Commerce, Meiji University

Abstract
This study examines dynamic asset market linkages during the global COVID-19 pandemic based on market efficiency
in the sense of Fama (1970). In particular, we estimate the joint degree of market efficiency by applying a generalized
least squares (GLS)-based time-varying autoregressive (TV-VAR) model of Ito et al. (2014, 2017). The results showthat (1) the joint degree of market efficiency changes widely over time, consistent with the adaptive market hypothesis
of Lo's (2004), (2) the global COVID-19 pandemic may have eliminated arbitrage and improved market efficiency
through enhanced linkages among asset markets, and (3) market efficiency has continued to decline due to the Bitcoin
bubble that emerged at the end of 2020.

The author would like to thank the editors, John Conley and Qi Zhang, an anonymous referee, Mikio Ito, Yoichi Tsuchiya, Tatsuma Wada, andthe seminar participants at Keio University and Meiji University for their helpful comments and suggestions. The author is also grateful for thefinancial assistance provided by the Japan Society for the Promotion of Science Grant in Aid for Scientific Research, under grant number
19K13747. All data and programs used are available upon request.
Citation: Akihiko Noda, (2022) ''Examining the Dynamic Asset Market Linkages under the COVID-19 Global Pandemic'', Economics
Bulletin, Volume 42, Issue 2, pages 653-661
Contact: Akihiko Noda - anoda@meiji.ac.jp.
Submitted: November 27, 2021. Published: June 30, 2022.

1

Introduction

Since the development of Bitcoin as a cryptocurrency by Nakamoto (2008), the Bitcoin
market has expanded its market capitalization while experiencing several price bubbles.
The price bubble that has continued since 2020 is serious, and the market capitalization of
Bitcoin reached approximately USD 1.2 trillion on April 14, 2021.1 This means that themarket capitalization of Bitcoin expanded more than ten times compared to before March
11, 2020, when the WHO declared the global COVID-19 pandemic. The changes in market
capitalization suggest that investors regard Bitcoin as an asset – but this does not necessarilymean they do not also regard it as, for example, a safe haven. Therefore, economists havebeen examining the Bitcoin market from two perspectives: (i) whether the Bitcoin market
is efficient in the sense of Fama (1970), and (ii) whether Bitcoin has the ability to hedge
against other assets in the sense of Baur and Lucey (2010).
The first context is that of Urquhart (2016), who examines whether the price of Bitcoin is
efficiently determined. Several studies have examined whether Lo’s (2004) adaptive market
hypothesis (AMH) holds in the Bitcoin market and have shown that market efficiency varies
over time.2 For example, Khuntia and Pattanayak (2018) and Chu et al. (2019) show that the
AMH holds in the Bitcoin market, using a conventional statistical test with a rolling-window
framework proposed by Domínguez and Lobato (2003). Noda (2021) measures directly the
degree of market efficiency using Ito et al.’s (2016; 2017) generalized least squares (GLS)based time-varying autoregressive (TV-AR) model. Accordingly, it was found that market
efficiency in the Bitcoin market changes with time.
The second context is whether Bitcoin serves as a safe haven against other assets in thesense of Baur and Lucey (2010), that is, whether Bitcoin has the ability to hedge investors’
portfolio diversification. Klein et al. (2018) argue that Bitcoin has no stable hedging capabilities and is not a new alternative to gold as a safe haven. However, there is controversy
regarding whether Bitcoin is a safe haven in more recent studies. Conlon and McGee (2020)
show that Bitcoin does not work as a safe-haven asset against the U.S. stock market index,
the S&P 500. This implies that there are dynamic correlations between Bitcoin and traditional markets as shown in Corbet et al. (2020). In contrast, Chan et al. (2019) use monthly
data to reveal that Bitcoin is a strong hedge for several stock market indices, and Pal and
Mitra (2019) find effective hedging abilities of gold against Bitcoin.
Thus, the efficiency of the Bitcoin market and its hedging abilities against other assets
have been examined in the literature. Now, recall the definition of “efficient market” by Fama
(1970). If prices are informationally efficient, then there are no arbitrage opportunities among
financial assets, and if there are no arbitrage opportunities, then asset market linkages should
be confirmed. This is because investors search for “safe havens” to protect the financial riskin periods of financial instability and restructure their portfolios. Indeed, many prior studies
have found the relationship between informational efficiency and linkages in the financial
markets such as Tsutsui and Hirayama (2004) and Ito et al. (2014). Then, we have tomeasure market efficiency that takes into account the financial market linkages to indirectly1

The historical data for total market capitalization are available from CoinMarketCap (https://coinmarketcap.com/charts/).
2
The AMH was proposed as an alternative to the efficient market hypothesis of Fama (1970), which
explains why market efficiency (or return predictability) changes over time.

examine hedging abilities against other assets in the Bitcoin market. We should also consider
the possibility that market efficiency and hedging abilities in the Bitcoin market vary withtime, as discussed in Akhtaruzzaman et al. (2021) and Noda (2021).
This paper is organized as follows. Section 2 presents our method of examining the variation in market efficiency over time based on a GLS-based time-varying vector autoregressive(TV-VAR) model of Ito et al. (2014, 2017). Section 3 describes the daily prices in three asset
markets (S&P500, Bitcoin, and gold) to calculate the returns, and presents preliminary unit
root test results. Section 4 presents our empirical results and discusses the time-varying
nature of the market linkages from the perspective of the AMH, which indicates that market
efficiency changes over time. Section 5 presents the conclusion.

2

Model

In this section, we introduce Ito et al.’s (2014; 2017) GLS-based TV-VAR model toinvestigate the dynamics of asset market linkages between three securities (S&P500, Bitcoin,and gold) from the perspective of informational efficiency. Suppose that pt is a price vectorof the three securities in t period. Our main focus is reduced to the following condition:
E [xt | It−1 ] = 0,(1)

where xt denotes a return vector of the securities in t period, namely, the i-th component
of xt is ln pi,t − ln pi,t−1 for i = S, B, G. That is, all expected returns in period t given theinformation set available in period t − 1 are zero.
When xt is stationary, the Wold decomposition allows us to consider the time-series
process of xt as
xt = µ + Φ0 ut + Φ1 ut−1 + Φ2 ut−2 + · · · ,where µ is a vector of the mean of xt and {ut } follows an independent and identically
distributed multivariate process with a mean of zero vector, and a covariance matrix of σ 2 I,∑∞′
i=0 ||Φi Φi || < ∞ with Φ0 = I. Note that the efficient market hypothesis (EMH) holds
if and only if Φi = 0 for all i > 0, which suggests that how the market deviates from theefficient market reflects the impulse response, a series of {ut }’s. In this study, we construct
an index based on the impulse response to investigate the dynamics of asset market linkagesin the sense of whether the EMH holds.
The easiest way to obtain the impulse response is to use a VAR model and algebraicallycompute its coefficient estimates. Under some conditions, the vector return process {xt } ofsecurities is invertible. We consider the following TV-VAR(q) modelxt = ν + A1 xt−1 + A2 xt−2 + · · · + Aq xt−q + εt ; t = 1, 2, . . . , T,(2)where ν is a vector of intercepts and εt is a vector of error terms with E [εt ] = 0, E [ε2t ] = σε2 I,
and E [εt εt−m ] = 0 for all m ̸= 0. We use the idea of Ito et al. (2014, 2017) when we measuremarket efficiency that varies over time.

Directly applying Equation (2) to the model, we obtain the degree computed through the
VAR estimates, A1 , · · · , Aq , as follows. First, we compute a cumulative sum of the coefficientmatrixes of the impulse response,Φ(1) = (I − A1 − A2 − · · · − Aq )−1 ,(3)Second, we define the joint degree of market efficiency,√
ζ = max [(Φ(1) − I)′ (Φ(1) − I)],(4)

to measure the deviation from the efficient market. Note that in the case of the efficient
market where A1 = A2 = · · · = Aq = 0, our degree ζ becomes zero; otherwise, ζ deviatesfrom zero. For this reason, we call ζ the joint degree of market efficiency. When we finda large deviation of ζ from 0 (both positive and negative), we can regard some deviationfrom one as evidence of market inefficiency. If there are no arbitrage opportunities among
the three markets, we consider that the degree improves because zeta should approach zero.
That is, the deterioration of the degree implies that the market linkages weaken over time.
Furthermore, we can construct this degree to vary over time when we obtain time-varying
estimates in Equation (2).
Adopting a method developed by Ito et al. (2014, 2017), we estimate VAR coefficientsin each period to obtain the degree defined in Equation (4) in each period. In practice,following the ideas of Ito et al. (2014, 2017), we use a model in which all VAR coefficients,
except for the one that corresponds to the vector of intercepts, ν, follow independent random
walk processes. That is, we assume
Al,t = Al,t−1 + Vl,t , (l = 1, 2, · · · , q),(5)where an error term matrix {Vl,t } (l = 1, 2, · · · , q and t = 1, 2, · · · , T ) satisfies E [Vl,t ] = O
for all t, E [vec(Vl,t )′ vec(Vl,t )] = σv2 I and E [vec(Vl,t )′ vec(Vl,t−m )] = O for all l and m ̸= 0.
The method of Ito et al. (2014, 2017) allows us to estimate the TV-VAR model:
xt = ν + A1,t xt−1 + A2,t xt−2 + · · · + Aq,t xt−q + εt ,(6)

together with Equation (5).
To conduct statistical inference on our time-varying degree of market efficiency, we apply
a residual bootstrap technique to the TV-VAR model above. In practice, we build a set ofbootstrap samples of the TV-VAR estimates under the hypothesis that all TV-VAR coefficients are zero. This procedure provides us with a (simulated) distribution of the TV-VAR
coefficients, assuming the securities return processes are generated under the EMH. Then,
we can compute the corresponding distribution of the impulse response and degree of market efficiency. Finally, by using confidence bands derived from such simulated distribution,
we conduct statistical inference on our estimates and detect periods when the asset market
linkages are weak from the perspective of market efficiency.

3

Data

We utilize the daily spot prices of Bitcoin, S&P500, and gold (London bullion market)
obtained from Yahoo!Finance (https://finance.yahoo.com/). The start and end dates
for all datasets are the same: September 14, 2014 to August 31, 2021. We take the log firstdifference of the time series of prices to obtain the returns of each asset.
Table 1: Descriptive Statistics and Unit Root Tests

RS
RB
RG

Mean
SD
Min
Max
0.0005 0.0115 -0.1277 0.0897
0.0027 0.0472 -0.4647 0.2251
0.0002 0.0091 -0.0526 0.0513

ADF–GLS-10.5354-4.1933-4.4568Lags
φ̂
8-0.1472100.378011
0.3102

N
1685
1685
1685

Notes:(1) “RS ,” “RB ,” and “RG ” denote the returns of S&P 500, Bitcoin, and gold, respectively.
(2) “ADF–GLS” denotes the augmented Dickey–Fuller GLS test statistics, and “Lag” denotes
the lag order selected by the Bayesian information criterion.
(3) In computing the ADF–GLS test, a model with a time trend and constant is assumed. The
critical value at the 1% significance level for the ADF–GLS test is −3.96(4) “N ” denotes the number of observations.
(5) R version 4.1.3 was used to compute the statistics.

Table 1 shows the descriptive analysis for the returns. We confirm that the mean andstandard deviation of returns on Bitcoin are higher than those of other assets. This indicatesthat Bitcoin is a risky asset and is not an alternative to gold, which is a representative riskfree asset. For estimations, all variables that appear in the moment conditions should bestationary; we confirm whether all our variables satisfy this condition using Elliott et al.’s(1996) augmented Dickey–Fuller GLS (ADF–GLS) test. The ADF–GLS test rejects the null
hypothesis that all returns contain a unit root at the 1% significance level.

4

Empirical Results

We assume a standard VAR model with constants and select the optimal lag order for themodel using Schwarz’s (1978) Bayesian information criterion (BIC). Accordingly, we choose
the first-order standard VAR model, hereafter called the standard VAR(1) model.

The preliminary results for the above model are shown in Table 2.

Table 2: Preliminary Estimation

Constant
RS,t−1RB,t−1RG,t−1
R̄2
GrangerLC

RS,t
0.0006[0.0003]−0.1910[0.0820]−0.0057[0.0119]−0.0410[0.0451]
0.03892.2812∗RB,tRG,t0.00280.0003[0.0012] [0.0002]−0.0026 −0.0417[0.1160] [0.0322]−0.0011 0.0021[0.0306] [0.0042]−0.1729 0.0004[0.1342] [0.0229]−0.0006 0.0009
0.58781.5944163.5671∗∗∗

Notes:(1) “Rt−p ,” “ R̄2 ,” “Granger,” and “LC ” denote the VAR(p) estimates, the adjusted R2 ,the F statistics for Granger’s (1969) causality test, and Hansen’s (1992) joint L statistic with variance, respectively.
(2) “***” and “*” indicate that the null hypothesis of each test is rejected at the 1% and
10% significance levels, respectively.
(3) Newey and West’s (1987) robust standard errors are within parentheses.
(4) R version 4.1.3 was used to compute the statistics.

The estimates of autoregressive terms are not statistically significant at conventional
levels, except for the S&P500. Furthermore, the null hypothesis of Granger’s (1969) causality
test for the S&P 500 is rejected at the 10% significance level, suggesting that the S&P 500 is
causal in the sense that it allows prediction of the other variables. Then, we employ Hansen’s(1992) parameter constancy test to examine whether the parameters of the standard VAR(1)model were time stable. As shown in Table 2, we rejected the null hypothesis of constantparameters against the parameter variation as a random walk at the 1% significance level.
Therefore, we estimated the time-varying joint degree of market efficiency using a GLS-based
TV-VAR model Ito et al.’s (2014; 2017) to explore dynamic asset market linkages during the
global COVID-19 pandemic.

1.5
1.0
0.5
0.0

Joint Degree of Market Efficiency

2.0

Figure 1: Time-Varying Joint Degree of Market Efficiency

14.09.19

15.12.04

17.02.28

18.05.21

19.08.08

20.10.28

Time

Notes:(1) The dashed red lines represent the 95% confidence intervals of the efficient market degrees.
(2) The dotted blue line represents the time period when the World Health Organization
declared the COVID-19 a “global pandemic” on March 11, 2020.
(3) We ran bootstrap sampling 10,000 times to calculate the confidence intervals.
(4) R version 4.1.3 was used to compute the estimates.

Figure 1 shows the variation of the joint degree of market efficiency among the three
assets. We first find that market efficiency changes widely over time, as described in the
AMH of Lo (2004), while the price formation function works well for the entire period. Thisis also consistent with Ito et al. (2016) and Noda (2016, 2021), who investigated the timevarying nature of market efficiency in the stock and cryptocurrency markets. We observe
some periods for improving and declining market efficiency as follows: (1) the end of 2015,(2) mid-2019, and (3) early 2020.
The price of Bitcoin rose by more than 50% at the end of 2015, and increased pricevolatility reduced market efficiency. After that, the price of Bitcoin experienced a temporary
increase until late 2017 and early 2018, but the price remained stable from mid-2018 to mid2019. As a result, we believe that market efficiency improved significantly until mid-2019.
These results are consistent with those of Noda (2021) who examines the weak-form market
efficiency for the Bitcoin market. Moreover, market efficiency improved from March 11,
2020, when the WHO declared COVID-19 a global pandemic. Thus, the pandemic may haveeliminated arbitrage and improved market efficiency through enhanced linkages among theasset markets. In fact, Caferra and Vidal-Tomás (2021) find a financial contagion in March
2020 since both cryptocurrency and stock prices fell steeply.

Subsequently, market efficiency has continued to decline due to the Bitcoin bubble thatemerged at the end of 2020. Note that we measure the joint degree of market efficiency
among the financial markets except for Bitcoin and find that market efficiency temporarily
declines right after the declaration of COVID-19 as a global pandemic by WHO, and thenmarket efficiency rapidly improves. This implies that S&P 500 and gold hardly contributeto decline in market efficiency. In particular, it is also known that prices are not formed as
efficiently as those of other typical financial assets, such as gold, stocks, and foreign exchange,
as shown in Al-Yahyaee et al. (2018). This suggests that during the bubble, price formationin the Bitcoin market was extremely speculative, which weakened the market linkage througha significant decrease in market efficiency.

5Concluding Remarks

In this study, we examine dynamic asset market linkages during the global COVID-19
pandemic from the perspective of market efficiency in the sense of Fama (1970). If market
efficiency changes over time, as suggested in Lo (2004), then the existence of arbitrage opportunities should also change over time. Moreover, when arbitrage opportunities between
markets do not exist (or exist), the linkages between markets are expected to be stronger(weaker). In particular, we estimate the joint degree of market efficiency based on a GLSbased TV-VAR model of Ito et al. (2014, 2017). The empirical results show that (1) the
joint degree of market efficiency changes widely over time, as shown in Lo (2004), (2) market
efficiency improved immediately after the WHO’s declaration of the global COVID-19 pandemic on March 11, 2020, and (3) market efficiency continued to decline due to the Bitcoin
bubble that emerged at the end of 2020. Therefore, we conclude that the empirical results
support the AMH, and the pandemic may have eliminated arbitrage and improved market
efficiency through enhanced linkages among asset markets.

References
Akhtaruzzaman, M., Boubaker, S., Lucey, B., and Sensoy, A. (2021), “Is Gold a Hedge or a
Safe-haven Asset in the COVID-19 Crisis?” Economic Modelling, 102, 105588.
Al-Yahyaee, K. H., Mensi, W., and Yoon, S. M. (2018), “Efficiency, Multifractality, andthe Long-Memory Property of the Bitcoin Market: A Comparative Analysis with Stock,
Currency, and Gold Markets,” Finance Research Letters, 27, 228–234.
Baur, D. and Lucey, B. (2010), “Is Gold a Hedge or a Safe Haven? An Analysis of Stocks,
Bonds and Gold,” Financial Review, 45, 217–229.
Caferra, R. and Vidal-Tomás, D. (2021), “Who Raised from the Abyss? A Comparison
between Cryptocurrency and Stock Market Dynamics during the COVID-19 Pandemic,”
Finance Research Letters, 101954.

Chan, W. H., Le, M., and Wu, Y. W. (2019), “Holding Bitcoin Longer: The Dynamic Hedging
Abilities of Bitcoin,” Quarterly Review of Economics and Finance, 71, 107–113.
Chu, J., Zhang, Y., and Chan, S. (2019), “The Adaptive Market Hypothesis in the HighFrequency Cryptocurrency Market,” International Review of Financial Analysis, 64, 221–
231.
Conlon, T. and McGee, R. (2020), “Safe Haven or Risky Hazard? Bitcoin during the Covid-19
Bear Market,” Finance Research Letters, 35, 101607.
Corbet, S., Larkin, C., and Lucey, B. (2020), “The Contagion Effects of the COVID-19
Pandemic: Evidence from Gold and Cryptocurrencies,” Finance Research Letters, 35,
101554.
Domínguez, M. A. and Lobato, I. N. (2003), “Testing the Martingale Difference Hypothesis,”Econometric Reviews, 22, 351–377.
Elliott, G., Rothenberg, T. J., and Stock, J. H. (1996), “Efficient Tests for an Autoregressive
Unit Root,” Econometrica, 64, 813–836.
Fama, E. F. (1970), “Efficient Capital Markets: A Review of Theory and Empirical Work,”
Journal of Finance, 25, 383–417.
Granger, C. W. J. (1969), “Investigating Causal Relations by Econometric Models and CrossSpectral Methods,” Econometrica, 37, 424–438.
Hansen, B. E. (1992), “Testing for Parameter Instability in Linear Models,” Journal of Policy
Modeling, 14, 517–533.
Ito, M., Noda, A., and Wada, T. (2014), “International Stock Market Efficiency: A NonBayesian Time-Varying Model Approach,” Applied Economics, 46, 2744–2754.
— (2016), “The Evolution of Stock Market Efficiency in the US: A Non-Bayesian TimeVarying Model Approach,” Applied Economics, 48, 621–635.
— (2017), “An Alternative Estimation Method for Time-Varying Parameter Models,” [arXiv:
1707.06837], Available at https://arxiv.org/pdf/1707.06837.pdf.
Khuntia, S. and Pattanayak, J. (2018), “Adaptive Market Hypothesis and Evolving Predictability of Bitcoin,” Economics Letters, 167, 26–28.
Klein, T., Thu, H. P., and Walther, T. (2018), “Bitcoin is not the New Gold – A Comparisonof Volatility, Correlation, and Portfolio Performance,” International Review of Financial
Analysis, 59, 105–116.
Lo, A. W. (2004), “The Adaptive Markets Hypothesis: Market Efficiency from an Evolutionary Perspective,” Journal of Portfolio Management, 30, 15–29.
Nakamoto, S. (2008), “Bitcoin: A Peer-to-Peer Electronic Cash System,” Online Available
at https://bitcoin.org/bitcoin.pdf.

Newey, W. K. and West, K. D. (1987), “A Simple, Positive Semi-Definite, Heteroskedasticity
and Autocorrelation Consistent Covariance Matrix,” Econometrica, 55, 703–708.
Noda, A. (2016), “A Test of the Adaptive Market Hypothesis using a Time-Varying AR
Model in Japan,” Finance Research Letters, 17, 66–71.
— (2021), “On the Evolution of Cryptocurrency Market Efficiency,” Applied Economics Letters, 28, 433–439.
Pal, D. and Mitra, S. (2019), “Hedging Bitcoin with Other Financial Assets,” Finance Research Letters, 30, 30–36.
Schwarz, G. (1978), “Estimating the Dimension of a Model,” Annals of Statistics, 6, 461–464.
Tsutsui, Y. and Hirayama, K. (2004), “Appropriate Lag Specification for Daily Responses ofInternational Stock Markets,” Applied Financial Economics, 14, 1017–1025.
Urquhart, A. (2016), “The Inefficiency of Bitcoin,” Economics Letters, 148, 80–82.