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Accepted Manuscript
The Singapore Economic Review
Article Title: Time-Frequency Nexus Between Bitcoin and Developed Stock Markets in
the Asia-Pacific
Author(s): Ngo Thai Hung
DOI: 10.1142/S0217590820500691
Received: 05 November 2019
Accepted: 22 September 2020
To be cited as: Ngo Thai Hung, Time-Frequency Nexus Between Bitcoin and Developed
Stock Markets in the Asia-Pacific, The Singapore Economic Review, doi:
10.1142/S0217590820500691
Link to final version: https://doi.org/10.1142/S0217590820500691
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1
TIME-FREQUENCY NEXUS BETWEEN BITCOIN AND
DEVELOPED STOCK MARKETS IN THE ASIA-PACIFIC
Ngo Thai Hung
Faculty of Economics and Law
University of Finance-Marketing,
Ho Chi Minh City, Vietnam
Email: hung.nt@ufm.edu.vn
Phone: +840898524206
Fax: +84 028 3772 0403
https://orcid.org/0000-0002-6976-1583
Abstract
This study investigates the connectedness between Bitcoin pricesand major stock indices in
the Asia-Pacific region from February 2012 to August 2019. Based on the wavelet transform
framework, we find evidence of significant unidirectional association from Bitcoin to the
selected markets in the short, medium, and long-run in the Asia-Pacific region. Overall, Asia-
Pacific equity markets and Bitcoin cryptocurrency are weakly correlated at higher
frequencies throughout the sample period, but the dependence of Bitcoin on the equity
markets steadily increases at lower frequencies. Further, we construct the wavelet-based
Granger causality test at different time scales to provide additional support to our
connectedness results. Our findings provide important implications for policymakers,
portfolio managers, and investors who are invited to take into account the dynamic linkages
between Bitcoin and equity markets.
JEL classification: G15; F30; C22; C40.
Keywords: Bitcoin; Asia-Pacific financial markets; Waveletcoherence; Cross-wavelet;
Causality.
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1.Introduction
In recent years, blockchain technologies and cryptocurrencies have attracted much attention
from academics, practitioners, and become a valuable source of controversy among investors,
economists, regulators alike (Koutmos, 2019). The relationship between cryptocurrency and
financial equity markets is a much-debated issue in the empirical literature. In reality,
cryptocurrencies substantially provide some merits as a novel and efficient payment
instrument that assists in enlarging into an alternative international monetary system (Tiwari,
Raheem & Kang,2019). According to Dwyer (2015), Bitcoin uses peer-to-peer networks and
open-source software to stop spending and generate the finality of transactions. Bitcoin,
therefore, has been synthetic commodity money, and it is sharing a non-persistence of
intrinsic value with fiat money.
Furthermore, Bitcoin’s hedging ability is known as a medium of exchange or digital gold,
which is also a property of gold and the US dollar (Su, Qin, Tao & Zhang, 2020). According
to Bouoiyour,SelmiandWohar(2019), gold and Bitcoin are likely to be harmonious to each
other instead of in competition because there is a positive correlation between gold and
Bitcoin prices. GuesmiSaadi, Abid andFtiti (2019) point out a short position in the Bitcoin
markets allows hedging the risk investment for a wide range of various financial assets.
Namely, the portfolio’s risk of gold, oil, and equities with Bitcoin is fewer than an investment
strategy without it. Nevertheless, Bitcoin is unable to substitute gold owning to the
limitations on anti-money laundering and counterterrorism financing regulations (Su, Qin,
Tao & Zhang, 2020; Damianov&Elsayed, 2020; Shahzad,Bouri, Roubaud, Kristoufek&
Lucey, 2019; Klein,Thu & Walther, 2018).
Recently, literature has demonstrated an increasing interest in terms of measuring the impact
of the geopolitical risks on financial markets and macroeconomic indicators. Aysan,Demir,
Gozgorand Lau (2019) significantly contribute to the literature by investigating the effects
of the geopolitical risks on the Bitcoin market, and document that the changes in the global
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geopolitical risk index have predictive power on price volatility and returns of Bitcoin
market.To put it another way, Bitcoin may be seen as a significant tool to hedge the portfolio
against geopolitical risks.
Numerous studies in the literature focus on the associations between Bitcoin and several
macroeconomic indicators and financial assets (Corbet,Larkin, Lucey, Meegan &Yarovaya,
2020). Past studies incorporate stock prices and Bitcoin (Shahzad,Bouri,
Roubaud&Kristoufek,2019; MatkovskyyJalan & Dowling,2020), Bitcoin and exchange rate
(Dwyer, 2015; Li & Wang, 2017; Urquhart & Zhang, 2019), other commodity prices and
Bitcoin (Rehman &Apergis, 2019; Bouri,Das, Gupta &Roubaud, 2018; White,Marinakis,
Islam & Walsh,2020; Mensi, Sensoy, Aslan & Kang, 2019).More importantly, the
connectedness between cryptocurrencies and stock markets has offered two main strands of
the literature. The first strand puts forward the significant nexus between the cryptocurrencies
and stock markets (Baur& Lucey, 2010; Köchling,Müller &Posch, 2019; Bouri,Das, Gupta
&Roubaud, 2018). The second approach posits that there is a slightly weak connectedness
between them (Corbet et al., 2018a; Matkovskyy& Jalan, 2019;Matkovskyy,Jalan &
Dowling, 2020;Gil-Alana,Abakah&Rojo, 2020). In addition, the existing literature focuses on
information transmissions among cryptocurrencies (Wei, 2018; Brauneis&Mestel, 2018;
Antonakakis,Chatziantoniou&Gabauer,2019; Omane-Adjepong,Alagidedeand&Akosah,
2019), cryptocurrency behaviors (BouriLau, Lucey &Roubaud, 2019; Zharova&Lloyd, 2018)
as well as its association with conventional assets.
Besides the above highlighted issues, there are two primary reasons to implement this paper.
First, this research study is motivated by the convergence of some papers toward the
conclusion that Bitcoin is weakly connected and decoupled from traditional financial markets
(Rehman &Apergis, 2019; Bouri, Das, Gupta &Roubaud, 2018). Multiple determinants have
been put forward to explain that the Bitcoin is isolated from other financial asset classes. It
tends to be less dependent on conventional economic and financial variables and more on
their own technological and market development aspects
(Charfeddine,Benlagha&Maouchi,2020). This generates different risk factors that may make
Bitcoin a useful diversification tool (Brauneis&Mestel, 2018). The developing consensus
across scholars in the finance literature on the diminishing benefits from diversification in
conventional markets is the second motivation. Investors may hunt for new chances provided
by rapid growth and rising development of information and communication technologies.
Hence, Bitcoin can be considered as a possible new asset which has gained great attention
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from the various profile of investors seeking for making extra portfolio diversification profits.
This possibility is subject to the connectedness of Bitcoin prices with the traditional financial
assets, particularly given the higher variations of their prices, and the potential information
inefficiencies of their markets in comparison with traditional financial markets. This study
will provide linkages and lead-lag relationships between Bitcoin and stock markets in the
Asia-Pacific, which might be useful for financial investors, policymakers and regulatory
bodies to fully benefit from a new type of digital financial assets.
In spite of developing research on the behaviour of Bitcoin vis-à-vis major stock markets,
bonds, oil, gold, and the other commodity index, the connectedness between Bitcoin and
stock markets in the Asia-Pacific has so far been ignored. To enrich the related empirical
literature, in this paper, we investigate the time-frequency linkages between Bitcoin markets
and Asia-Pacific financial markets using wavelet transform frameworks. The present study
chooses wavelet analysis because it is the powerful and robust methodology employed in
financial time series to examine their co-movements (Reboredo,Rivera-Castro &Ugolini,
2017; Khalfaoui,Boutahar&Boubaker, 2015; Boubaker& Raza, 2017). These techniques have
significant superiority over the traditional time-domain methods used in previous studies
(Bouri et al. 2020b). Wavelet analysis expands the fundamental time series into a time-
frequency space in which both time and frequency -varying information of the series can be
visualized in a highly intuitive way. The interconnectedness and causalities between Bitcoin
and stock markets vary across frequencies, and changes over time are further achieved in a
time-frequency window. As a result, the short term and long term connectedness between
Bitcoin and stock indices, and possible structural changes and time-fluctuations in such nexus
can be correctly observed (Hung, 2020; Baruník et al. 2016).
We use a diversity of wavelet transform frameworks to give straightforward insight into
varying correlations between Bitcoin prices and Asia-Pacific equity markets under
consideration at different investment horizons. Unlike traditional models, the wavelet
technique outperforms the standard OLS regression, cointegration, VAR, ARDL, VECM, and
GARCH-type models, which restricts to one or two holding periods (Yi,Xu & Wang, 2018;
Raza,Sharif, Wong & Karim,2017; Dahir,Mahat, Razak &Bany-Ariffin,2018; Hung, 2019).
Succinctly, this study contributes to the existing literature on cryptocurrency markets and its
role in investment finance decisions in the following ways. Firstly, this study takes a novel
perspective in exploring the interdependence between Bitcoin prices and Asia-Pacific equity
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markets, which has not been studied in the literature. The article also contributes to the
understanding of the co-movements between Bitcoin future prices and other assets under
consideration. Secondly, the association among variables is captured by using the newly
developed technique named the wavelet transform approach, which adequately overcomes
the drawbacks of the methodological issues that the existing literature suffers from. Thirdly,
we use the maximal overlap discrete wavelet transform to decompose data to different time
frequencies, which enables us to detect the multiscale nonlinear causality relationships
between Bitcoin returns and Asia-Pacific equity markets. Moreover, we present the results of
Granger causality across frequency ranges and time scales using wavelet-based Granger
causality. The findings provide evidence of the weak relationship between cryptocurrency
markets and financial market indices. Last but not least, this result also has practical
significance for policymakers, investors, and portfolio managers with further insights into
global portfolios and monetary and of the connections between Bitcoin and other
conventional asset returns.
The rest of the paper is organized as follows: Section 2 elaborates on the empirical literature
covered on the co-movement of cryptocurrencies with other markets. Section 3 reports the
framework model, while Section 4 documentsempirical results. Finally, Section 5 concludes
the study.
2.Literature review
Intercorrelation between equity classes is significant for international investors since the
portfolio’s performance and portfolio selection are in connection with the dependence
structure of its components. More importantly, it plays a prominent role for policymakers in
making a momentous decision because if accurate information is transmitted across assets, a
policy decision is able to have cross-market influence (Baumöhl, 2019). The current study
belongs to the small but developing literature that concentrates on the association between
Bitcoin prices and conventional financial asset classes. We review some of the relevant
papers in this section.
There exists vital literature that investigates the nexus between Bitcoin prices and traditional
financial markets. Corbet et al. (2018a) analyze the time-frequency relationship between
three common cryptocurrencies and a diversity of other financial assets and report evidence
of the relative isolation of the cryptocurrencies from the financial and economic indicators. In
a similar fashion, Corbet et al. (2018b) look in whether the introduction of futures trading in
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Bitcoin is able to address the problems that stopped Bitcoin from taking into account
currency and conclude that Bitcoin is speculative equity rather than a currency that is not
replaced by the introduction of futures trading. In addition, the introduction of futures on
Bitcoin facilitates the entrance of institutional investors to the markets and provides a
structured way to short the cryptocurrency (Köchling et al., 2019).
Bouri et al. (2018b) examine the connectedness between Bitcoin and conventional
investments using return and volatility spillovers between this largest cryptocurrency and
four asset classes in bear and bull market conditions based on a smooth transition VAR
GARCH model. The authors point out that Bitcoin markets are dramatically connected with
those of most of the other assets, and provide significance and sign of the spillovers in the
two market conditions with evidence that Bitcoin receives more volatility than it transmits.
Matkovskyy and Jalan (2019) analyze contagion effects between conventional financial
markets, including five equity indices and the EUR, USD, GBP, and JPY centralized Bitcoin
markets using a regime-switching skew-normal model. The results document significant
contagion effects from financial to Bitcoin markets. In a similar spirit, Matkovskyy et al.
(2020) study the impact of economic policy uncertainty on the connectedness between
conventional financial markets (NASDAQ100, S&P500, Euronext100, FTSE100, and
NIKKEI225) and Bitcoin prices using divergent models (EWMA models, Spearman’s rho,
the Diebold and Yilmaz spillover index, GAS models with conditional multivariate Student–t
distribution and time-varying scales and correlations, BVAR models). Authors suggest that
the volatility correlation between Bitcoin and other financial assets is higher than
intercorrelation in terms of returns, and this relationship varies over time and rises post-
launch of the Bitcoin future. Further, Gil-Alana et al. (2020) examine the association between
six major cryptocurrencies (Bitcoin, Ethereum, Ripple, Litecoin, Stellar and Tether) and six
stock markets (S&P 500 Composite, S&P GSCI Commodity Total Return,VIX, S&P Bond
Index, S&P GSCI Gold Total Return, and US Nominal Dollar Broad Index) using fractional
integration techniques. Their findings provide evidence of no relationship between
cryptocurrency markets and stock market indices and show that the cryptocurrency markets
are decoupled from the main financial and economic asset class. Zhang et al. (2018) have
considered the relationship of cryptocurrency with Dow Jones using Multifractal Detrended
Cross-correlation Analysis (MF-DCCA), but the concentration of their research is crypto
market efficiency rather than connectedness. They reveal that cryptocurrencies and Dow
Jones Industrial Average are persistently cross-correlated.
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The second type of study is one that takes into consideration the cause and effects correlation
among different cryptocurrencies. For example, Wei (2018) investigates the liquidity of 456
various cryptocurrencies, and provide evidence that return predictability reduces in
cryptocurrencies with high market liquidity. The findings also show that cryptocurrencies
present signs of autocorrelation and non-independence, while Bitcoin returns show signs of
efficiency. In a same vein, Brauneis and Mestel (2018) make an outstanding contribution to
present literature by exhibiting different tests on the effectiveness of several cryptocurrencies
and additionally link efficiency to measures of liquidity. The authors confirm that
cryptocurrencies become less predictable because of the increase in liquidity. Antonakakis et
al.’s (2019) findings are the complete dynamic interrelatedness across several
cryptocurrencies with high dynamic variability ranging from 25% to 75%. The authors
proposed a novel approach based on a TVP-FAVAR correlation to assess the transmission
mechanism in the cryptocurrency markets. Recently, Omane-Adjepong et al. (2019)
investigate the persistence of the eight largest cryptocurrency markets using the ARFIMA-
FIGARCH class of models. Results report that persistence is found to be concealed during
the sample period and a break regime in which three crypto markets illustrate characteristics
opposite to the Efficient Market Hypothesis. Moreover, Bouri et al. (2019) show that trading
volume Granger causes extreme negative and positive returns of all cryptocurrencies using a
copula-quantile. Zharova and Lloyd (2018) highlight the importance of Bitcoin, which will be
given to recent improvement within Russia. More specifically, employing the spillover index,
Yi et al. (2018) look into both static and dynamic volatility interconnectedness among eight
typical cryptocurrencies, report that the interrelatedness fluctuates cyclically and significant
increasing trend since 2016.
The second type of study considers the non-linear relationship between cryptocurrencies and
foreign exchange rates. Dwyer (2015) makes a significant explanation of how the
technologies and limitations of the quantity produced can create an equilibrium in which a
digital currency has a positive value. Li and Wang (2017) document that the Bitcoin
exchange rate adjusts to changes in economic indicators and market conditions in the short
run, while it is less sensitive to technological elements in the long run. Da Gama Silva et al.
(2019) show that co-movements between Bitcoin and other currencies can be identified in all
cases. Urquhart and Zhang (2019) evaluate the connection between Bitcoin and currencies at
the hourly frequency using the ADCC model. They report that Bitcoin is able to be an
intraday hedge for the CHF, EUR, and GBP, while Bitcoin acts as a diversifier for the AUD,
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CAD, and JPY.Baumöhl (2019) examines the nexus between forex and cryptocurrencies
using the quantile cross-spectral framework. Results explain that there are several significant
negative dependencies between forex and cryptocurrencies from both the short- and long-
term scenarios.
As a summary, very limited research has been implemented on the connectedness of
cryptocurrencies with traditional financial assets and particularly those operating in the Asia-
Pacific region. Furthermore, the most often used techniques for relationship analysis in
financial asset literature are ARDL, GARCH-type models, which do not imply the underlying
time-frequency changes in the correlation as well as lead-lag structures. Hence, the primary
objective of this paper is to shed light on the time-frequency correlation between Bitcoin
prices and traditional assets classes in the Asia-Pacific region by using the wavelet transform
framework, which enables us to detect financial market interactions that are difficult to test
out by employing other econometric time series models (Aloui&Hkiri, 2014). The results of
this paper would reveal whether or not the investors get diversification, which is benefited by
investing in Bitcoin and other financial assets simultaneously.
3.Methodology and Data
We employ wavelet methodology in terms of continuous wavelets, and cross-wavelet
transforms to capture how the local variance and covariance of two-time series make
progress, and wavelet coherence and phase analysis to estimate the co-movement correlation
between two variables in the time-frequency domain (Reboredo et al., 2017). In addition,
discrete wavelets can be applied to measure the connectedness between the Bitcoin market
and Asia-Pacificfinancial market prices.More precisely,maximal overlap discrete wavelet
transform is applied to decompose Bitcoin and stock indices' original data into different time
scales, which present the elements operating at different time horizons. The continuous
wavelet analysis used in this paper consists of the continuous wavelet transform,wavelet
coherency, and phase-difference. The continuous wavelet transform expands the time series
into a time-frequency plane by mapping the original series into a time and frequency
function. A product of the continuous wavelet transform of two time series is referred to as
the cross-wavelet transform. Next, we carry out the wavelet coherency and phase-difference.
The wavelet coherency can be defined as a localized correlation coefficient in the time-
frequency space. It depicts the correlation between t
x
and t
yin a three-dimensional way,
including the time and frequency elements, and the correlation strength. The phase-difference
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describes synchronizations and delays between t
x
and t
y. It is computed between positive
and negative correlations and lead-lag connection because the value of the wavelet coherency
is positive.In this section, we briefly note on wavelet approach.
3.1 Discrete wavelet transform
A series ()
y
t can be decomposed into various time scales as:
, , , , 1, 1, 1, 1,
() () () () ()
Jk Jk Jk Jk J k J k k k
kk k k
yt s t d t d t d t
(1)
where
and
are the father wavelet and mother wavelet functions, denoting the smooth
(low frequency) parts of a signal and the detail (high frequency) components. The functions
()
J
s
t and ()
J
dt
are the smooth signals and the detail signals, respectively.
Therefore, the time series ()yt can be rewritten as:
11
() () () () ()
jjJ
y
tStDtDt Dt
(2)
where the highest-level approximation ()
j
St
is the smooth signal, and 12
( ), ( ),..., ( )
j
D
tDt Dt
are associated with oscillations of lengths 2-4, 4-8, …, 22
j
ji
, respectively. In our
empirical study, we employ daily data and establish J = 8 for multi-resolution level J because
past studies have proved that a moderate filter is suitable for financial data (Fernández-
Macho, 2012; Reboredo et al., 2017).
3.2 The continuous wavelet
The continuous wavelet transform ()
x
Ws
allow us to investigate the joint behavior of time
series for both frequency and time. The wavelet us defined as:
*
1
() ()
xt
Ws xt
s
s
(3)
where * denotes the complex conjugate and where the scale parameter s identifies whether
the wavelet can detect higher or lower components of the series ()
x
t, possible when the
admissibility condition yields.
3.3 Wavelet coherence
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To specify the joint behavior of both time and frequency between two time series variables,
we employ three specific techniques of wavelet, including the wavelet power spectrum,
cross-wavelet power and cross-wavelet transform. While the wavelet power spectrum
explores contribution to the variance of the series at each time scale, cross-wavelet power
measures covariance contribution in the time-frequency space. The cross-wavelet of two
series ()
x
t and ()yt can be defined as:
*
(,) (,) (,)
XY X Y
nnn
WusWusWus (4)
where u denotes the position, s is the scale, and * denotes the complex conjugate.
Torrence and Webster (1999) develops the wavelet coherence which can measure the co-
movement between two selected time series. The squared wavelet coefficient is defined as:
12
2
1212
|(,))|
(,) |(,)| |(,)|
XY
n
n
XY
SsW us
Rus Ss W us Ss Wus
(5)
where S is a smoothing parameter for both time and frequency. R2(u,s) is in the range
2
0(,)1Rus
, which is similar to correlation coefficient. If its value is close to zero,
evidence of weak interdependence will be determined and vice versa.
3.4 Phase
We cannot shed light on the dichotomy between positive or negative dependency using the
wavelet coherence since the coherence wavelet is squared. Therefore, we use the phase
difference tool to examine the dependency and causality interconnections between time
series. The phase difference between ()
x
t and ()
y
t is defined as follows: (Reboredo et al.,
2017)
1
1
1
{( (,)}
tan {( (,)}
XY
XY XY
SsW us
SsW us
(6)
where and are the imaginary and real parts of the smooth power spectrum,
respectively. Phase interrelatedness between two variables are shown in the coherence phase
by means of arrows: (1) the correlation is positive (negative) when the arrows point to the
right (left); and the second (first) variable leads the first (second) variable by 900 when the
arrows point to down (up).
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3.5 Data
In this paper, we use the daily data from one of the top cryptocurrencies Bitcoin (BIT),
Bitcoin Futures (BITF),two major stock markets (S&P 500 and Euronext (ENX)), and stock
index prices of five developed stock marketsin the Asia-Pacific region: Australia (ASX),
Hong Kong (HSCI), Japan (NIKKIE), New Zealand (NZ),Singapore (STI).Our sample period
was from February 2012 to August 2019. We downloaded all data from the Bloomberg
database. The daily return series is measured by LN(Pt/Pt-1).
<Insert Table 1 here>
Table 1 reports some preliminary descriptive statistics and unit root tests of our baseline data
for all return series during the sample period 2012-2019. From these summary statistics,
several characteristics can be identified. The mean value of the Bitcoin returns was highest,
while Japan’s average stock return was lowest. All return series experienced positive returns
on average during the sample period. In addition, equity returns are characterized by higher
levels of volatility, given that standard deviations are remarkably higher than the mean.
Skewness coefficients illustrate that return distributions are negatively skewed for all selected
series. Moreover, high kurtosis values indicate that all selected returns distributions are
highly leptokurtic in connection with the normal distribution, which is also confirmed by the
Jarque-Berra test. Specifically, we perform the Augmented Dickey-Fuller unit root test and
see that all the return series are stationary at the 1% significance level. These results are thus
appropriate for further statistical analysis.
4.Results
We employ wavelet analysis to evaluate the co-movement between Bitcoin prices and Asia-
Pacific equity markets as well as S&P 500 and ENX stock prices. Additionally, the dynamic
links between Bitcoin future prices and the selected series are also taken into account in this
paper. The estimates would shed light on how the series are related to different frequency
bands and how such associations progress in connection with time and across various
timescales. Finally, the study provides useful implications for global asset pricing, portfolio
manager, investors and policymakers.
4.1 The interplay between Bitcoin and the selected series
In this study, we employ the continuous wavelet method to decompose the data into eight
levels spanning various holding periods. These levels are divided into four holding periods,
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such as short term (D1+D2), medium term (D3+D4), long term (D5+D6) and very long term
(D7+D8).
<Insert Figure 1 here>
Fig.1 displays the results of the continuous wavelet power spectrum for Bitcoin and selected
return series, with the horizontal axis showing time and the vertical axis indicating frequency.
The shaded contours designate the 5% significance level against yellow noise, knows as
Monte Carlo simulations applying phase randomized surrogate series. The cone of influences
specifies the region affected by edge effects and is shown outside of the black line. The color
code for power ranges from blue (low power) to yellow (high power), regions in yellow
indicate strong variation, and regions in blue show weak variation. The intensity levels
gradually rise from blue to yellows. Overall, the continuous wavelet estimations for stock and
Bitcoin returns reveal that high variance in all series except the case of Nikkei existed but in
different timeframes. For Bitcoin, the high variance can be observed in all small, medium,
and long-time period but before 2015 and after 2018. By contrast, for the stock price returns,
most powers are evident at high variance in small scales during the 4-8-day cycle in the time
zone. We move our examination further to perform the cross-wavelet transform. The results
of the cross wavelet transform for Bitcoin, and the selected return series are represented in
Fig. 2.
<Insert Figure 2 here>
The cross-wavelet transform reflects the local covariance between Bitcoin and Asia-Pacific
financial asset returns at different scales and periods. The yellow (blue) colors suggest high
(low) power, the yellow regions imply that the two series have high joint power, while the
blue regions imply that Bitcoin and the financial asset returns have lower power. It is
noticeable that the path of arrows at different frequency bands in the cross-wavelet transform
reflecting the local covariance between these series are not in the same direction. Also, most
of the small-scale patterns are obscure to observe the direction of arrows and indicating no
causality. This graph shows that covariance slightly increased with scale, meaning that the
interrelatedness between Bitcoin and Asia-Pacific financial markets was more impacted by
long-term than by shoe-lived shocks. More specifically, in the medium scale, between 8 to
16-day cycles during 2012-2014, the patter of high frequency between the two variables
could be seen with arrows moving right down. This reveals that the two variables of Bitcoin
and Asia-Pacific financial markets are in-phase with Bitcoin leading the causal effect. We can
also see that the extent of the impact of Bitcoin prices on the selected market indices decayed
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with time, and therefore, covariance dropped at all time scales for all series in the later years
of the sample (2017-2019). Further, information on the phases indicates that the
interconnection between two variables was not homogeneous across scales, as arrows point
up, right, and leftover short time scales. Briefly, the power dynamics of most of the regions in
the cross-wavelet power spectrum are somewhat high. We can confirm that there exists a
linkage between Bitcoin and selected financial markets under examination.
In this section, the co-movement and lead-lag connectedness between Bitcoin and the
selected financial market returns are examined using the pairwise plots of wavelet coherence.
The horizontal axis denotes the time component while the vertical axis presents the frequency
element, and a color code measures the degree of relationship between the pair of series. The
warmer (yellow color) areas show that two variables are highly dependent, whereas cooler
(blue color) areas reveal that two variables are less dependent. In addition, the wavelet
coherence approach illustrates zones over time and scales that every pair of indexes is
significantly dependent or otherwise, corresponding to the local correlation ranging from 0 to
1. Put differently, the local correlation of 0.1 shows the relationship between two indexes is
weak, and this association is strong when the coefficient reaches 1.
Furthermore, the wavelet phase difference identifies the dynamic linkages of series by
observing lead-lag connectedness through various investment horizons. Arrows pointing out
phase difference suggest the direction of intercorrelation and cause-effect relationship. Right,
and left arrows reveal that the paired indexes are in-phase and out-phase, respectively. An in-
phase wavelet phase shows that two variables move jointly in the same direction or a positive
relationship. In contrast, an out-phase wavelet phase shows that two variables move in
opposite directions over a specific time and frequency bands or a negative correlation. The
right up or left down arrows indicate that Bitcoin returns, as the dependent variable, are
leading, and the right down and left up arrows show that the selected series, as independent
variables, are leading.
<Insert Figure 3 here>
The results of wavelet coherence and phase difference for the Bitcoin and all concerned
indices are displayed in Figure 3. A visual inspection of the pictures shows unusual situations
that Bitcoin and all equity indices are weakly correlated at higher frequencies, and this
weakness existed throughout the sample period. However, the dependence of Bitcoin on
Asia-Pacific equity markets remarkably increased at lower frequencies, but especially after
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14
2015 (European stock market collapse), gradually reaching high levels of dependence
concentrated at higher frequencies (from 128 to 512 days) from 2015 to 2019. This is true for
the case of BIT-S&P 500 and BIT-ENX. For example, in the small-time period in between
the 8-16-day cycle during 2014, the arrows were right up in pairs of BIT-HSCI, BIT-NZ,
BIT-NIKKEI, BIT-ENZ, BIT-S&P 500 suggesting an in-phase nexus with stock returns
leading. Specifically, Figure 3 shows that Bitcoin had dramatically influenced on equity
prices (NZ, ASX, ENX) around the year 2012, while after that period, the dependence
interconnectedness was slightly weak. Additionally, during 2016-2017 in the small-time
period, the pairs of BIT-NZ, BIT-HSCI, BIT-STI, BIT-ASX, BIT-ENX, BIT- S&P 500 the
arrows were left up, indicating that the variables were out-phase and anti-cyclic impacts with
Bitcoin leading. The same findings were found in the period 2015 in the case of BIT-NIKKEI
and BIT-S&P 500. However, the arrows were both left up and left down during 2015-2017 in
pairs of BIT-NZ, BIT-HSCI, BIT-STI, BIT-ASX, BIT-ENX, BIT-S&P 500 and BIT-NIKKEI
suggesting that variable were out-phase with Bitcoin leading and lagging simultaneously. We
report the findings of the wavelet coherence on bases of four major periods, such as short
term (D1+D2), medium-term (D3+D4), long term (D5+D6), and very long term (D7+D8)
which are summarized in Table 2.
<Insert Table 2 here>
In general, Fig. 3 reports that dependence between Bitcoin and other asset indices
dynamically changed through time and frequencies, indicating strong dependence at low
frequencies and weak dependence at high frequencies. These findings shed light on the
positive influence of Bitcoin on conventional financial markets documented byZharova and
Lloyd (2018). Furthermore, phases are presented by arrows pointing out the right most of the
time and for most of the frequencies, showing that local intercorrelations were positive and
that stock indices were leading Bitcoin. Overall, for all pairs, we can observe that phases
point up and point down, indicating that Bitcoin prices were leading the equity markets,
which was consistent along the sample period.
<Insert Figure 4 here>
Fig. 4illustrates the wavelet multiple covariance and correlation obtained. It can be seen that
the numerous associations between Bitcoin and stock market returns are all relatively low and
fluctuant. In all cases, the plot depicts that the multiple wavelet covariance and correlation
climbs within the range of -0.05 to 0.06 throughout the sample period, and increasing as the
time scale increases. This indicates that the existence of an accurate linear correlation
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15
between Bitcoin and the selected equity markets cannot be ruled out when periods more
extended than the year are considered. We can conclude that there is a significant integration
between Bitcoin and Asia-Pacific equity markets. Put differently, the dissimilarities between
the two markets are not only small, but they get dissipated within time horizons lower than
the year. The findings are consistent with previous studies ofCorbet et al. (2018a) and
Baumöhl (2019).
<Insert Table 3 here>
The granger causality test is used by considering the time-scaled components of the raw
series based on the wavelet transformation. It provides us the opportunity to analyze that
either BIT causes the change on very high, high, medium, and low frequencies of the selected
equity series. Table 3 reports the empirical results of the linear Granger causality test for
different scale components of BIT and the concerned asset indices. In a similar fashion, there
is evidence of no causality between BIT and other asset returns lasting to a time scale of 4
and 8 days. More importantly, Table 3shows that the original time series of BIT has
unidirectional influence over raw series of stock markets in the Asia-Pacific.The findings also
indicate the unidirectional causal impact of the stock markets on Bitcoin in the short,
medium, and long run. Moreover, the evidence on bidirectional causality at the long scales is
the pairs of BIT-STI, BIT-NIKKEI, BIT-S&P 500, and BIT-ENZ. These results support the
findings of wavelet coherence and correlation transform.
4.2 The interplay between Bitcoin future and the selected stockmarkets
The outcome of wavelet coherence explaining the coherence plots between Bitcoin future and
ASX, HSCI, NIKKEI, NZ, STI, S&P 500, ENX represented in Figure 5, which is analogous
to the wavelet coherence plots in Figure 4. The interdependence is observed to be quite weak,
with very few numbers of small yellow colors significant regions determined across the
various horizons. Notably, the pairs of BITF-ASX, BITF-NIKKEI, BITF-NZ reveal that the
nexus between Bitcoin future prices and these stock returns is statistically significant at lower
and medium frequency bands, while the rest of the index pairs are statistically insignificant.
Overall, the significantly weak connectedness between BITF and ASX, HSCI, NIKKEI, NZ,
STI, S&P 500, ENX is found in the four periods (short, medium, long, and very long term).
Therefore, we can conclude that the increase in Bitcoin future prices may not upsurge the
stock markets and vice versa. The results of Granger causality tests on the wavelet-
decomposed data also confirm these intercorrelations.
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16
<Insert Figure 5 here>
<Insert Table 4 here>
According to Fassas et al. (2020), Bitcoin future trading allows conventional investors to get
economic exposure to the Bitcoin price without having to address actual Bitcoins and Bitcoin
futures facilitate the price discovery process. There exists a relatively low correlation, and
spillover effects from Bitcoin future to other traditional financial assets suggest lower
informational efficiency and hedge effectiveness. This result supports the conclusion of
Corbet et al. (2018b) that a hedge using Bitcoin futures does not effectively reduce the
portfolio return volatility, and Bitcoin should be seen as a speculative asset rather than a
currency. Furthermore, Shynkevich, A. (2020) provide evidence of no signals of
improvement of market efficiency following the start of trading in Bitcoin futures.
Our findings, in line with previous papers on dynamic linkages, highlights the weak
correlation between cryptocurrency markets and the conventional financial asset prices. For
example, Gil-Alana et al. (2020) report that no cointegration between the cryptocurrencies
and the stock market indices, which means that the cryptocurrencies are decoupled from the
mainstream financial and economic assets. Corbet et al. (2018a) find evidence of the relative
isolation of cryptocurrencies from the financial and economic assets.
4.3 Policy implications
Our empirical results, as shown above, are significant and potentially valuable to researchers,
practitioners, regulators and Bitcoin market participants not only for better understanding the
hedging quality of cryptocurrencies but also in making momentous risk-management
decisions in terms of portfolio optimization.
The weak relationship between the cryptocurrency market and the traditional financial asset
indices found in this paper might have important implications on investor’s selection of asset
class to invest in owing to price interrelatedness. From a portfolio perspective, as price
movements in the financial asset classes have a low level of bilateral linkages with the
cryptocurrency market, market participants are able to take capital and somehow invest in
cryptocurrencies because of its inevitability benefits Gil-Alana et al. (2020).Further, what
investors should take steps to cement the diversification benefits in connection with their
investments in cryptocurrencies is to call for policymakers and regulators to enact methods
that will deepen the dispersed structural relationships between cryptocurrency markets and
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17
other conventional asset classes to make sure investors benefits with the diversification
returns.
The findings have crucial managerial implications because it provides a comprehensive
picture of the connectedness between cryptocurrencies and Asia-Pacific equity markets that
they should take into account in the assessment of the Bitcoin market. Since the other
financial asset prices have an influence on the cryptocurrency market, making a good
instrument for hedging to be considered in portfolio management decisions. In addition, it
would be important to monitor exchange market activities in economic decision-making
because cryptocurrencies continue to gain economic significance (Li and Wang, 2017).
5. Conclusion
Examining interrelations between cryptocurrency and traditional financial assets is significant
to understand better the broad spectrum of implications that may impact monetary policy,
corporate governance, and risk management (Antonakakis et al.,2019). In this study, we
explore the connectedness between Bitcoin cryptocurrency and Asia-Pacific equity markets,
including Australia, Hong Kong, Japan, New Zealand, and Singapore, from February 2012 to
August 2019 using the wavelet transform framework. More importantly, the cryptocurrency
market and its potential impact on the conventional financial markets, in general, are still
very much under-researched.
Turning to pairwise interrelation results, we note that there is a unidirectional association
from Bitcoin to the selected assets in the short, medium, and long-run in the Asia-Pacific
region. Specifically, evidence on bidirectional causality at the long scales is the pairs of BIT-
STI and BIT-NIKKEI. Overall, Asia-Pacific equity markets and Bitcoin cryptocurrency are
weakly correlated at higher frequencies throughout the sample period, but the dependence of
Bitcoin on developed financial markets in the Asia-Pacific region significantly increased at
lower frequencies. Further, we construct the wavelet-based Granger causality test at different
time scales to provide additional support to our connectedness results.
This paper focuses on thetime-frequency connectednessbetween Bitcoin and Asia-
Pacificequity markets, which have essential implications in hedging, financial regulation, and
portfolio diversification. Bitcoin has signs of moderate integration with the Asia-Pacific
financial markets, so investors and fund managers should be cautious when combining
Bitcoin with other asset classes. By doing so, market participants should consider all possible
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18
contingencies of market conditions. Moreover, policymakers and regulators should be
interested in the impactof theBitcoin marketon otherfinancial markets.
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Table 1. Descriptive statistics for return series
Mean Max. Min. Std. Dev Skewness Kurtosis Jar
q
ue-Bera ADF Obs.
ASX 0.020174 3.586999 -4.365690 0.912780 -0.293913 4.834187 422.6060* -52.3085
*2734
BIT 0.270622 30.85640 -37.24253 4.544108 -0.553411 12.78379 11043.96* -52.2104
*2734
HSCI 0.011894 30.78997 -13.58202 1.584948 2.680536 62.15693 4019.033* -52.0105
*2734
NIKKEI -0.139837 13.23458 -421.2549 8.203794 -49.50069 25.35923 7350.521* -52.2205
*2734
NZ 0.050431 2.737088 -3.709852 0.592936 -0.522267 5.717747 965.6948* -49.2488
*2734
STI 0.008286 7.530528 -8.695982 1.027328 -0.215865 11.96706 9181.073* -50.3595
*2734
S&P 500 0.038804 4.840324 -7.90103 0.998092 -0.75837 9.640666 5285.618* -54.7457
*2734
ENX 0.015502 8.140345 -10.6953 1.130205 -0.67670 10.10017 5951.477* -48.8921
*2734
BITF 0.197309 18.19375 -79.95526 8.847713 10.97389 23.04135 1946.573* -32.6475
*895
Note: ADF test is the Augmented Dickey-Fuller unit-root-test. * denotes the rejection of the
null hypothesis at the 1% significant level.
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Table 2. Wavelet coherence findings summary
Frequencies Cross-wavelet coherence
BITCOIN-HSCI
Very high frequency BIT HSCI
High frequency BIT HSCI
BIT HSCI
Medium frequency BIT HSCI
Low frequency BIT HSCI
BITCOIN-NZ
Very high frequency BIT NZ
High frequency BIT NZ
Medium frequency BIT NZ
Low frequency BIT NZ
BITCOIN-ASX
Very high frequency BIT ASX
High frequency BIT ASX
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BIT ASX
Medium frequency BIT ASX
Low frequency BIT ASX
BITCOIN-STI
Very high frequency BIT STI
High frequency BIT STI
Medium frequency BIT STI
Low frequency BIT STI
BITCOIN-NIKKEI
Very high frequency BIT NIKKEI
High frequency BIT NIKKEI
Medium frequency BIT NIKKEI
Low frequency BIT NIKKEI
BITCOIN-S&P 500
Very high frequency &500BIT S P
High frequency &500BIT S P
Medium frequency &500BIT S P
Low frequency &500BIT S P
BITCOIN-ENX
Very high frequency BIT ENX
High frequency BIT ENX
Medium frequency BIT ENX
Low frequency BIT ENX
Notes: denotes an increase in, denotes a decrease in, denotes the variable on the left side of
arrow leads the variable on the right side of the arrow.
Table 3. Results of wavelet-based Granger causality test at different time scales for Bitcoin and stock
markets
Time Domain Result Null hypothesis
Bitcoin does not Cause Stoc
k
Stock does not Cause Bitcoin
F-test P-Value F-test P-Value
BIT-HSCI
D1 No causalit
y
0.12129 0.8858 0.87237 0.4181
D2 HSCI BIT 2.22534 0.1082 2.75271 0.0639
D3 HSCI BIT 3.76817 0.0232 9.75651 0.000
D4 No causality 0.13049 0.8777 1.62157 0.1978
D5 No causality 2.07750 0.1254 1.75620 0.1729
D6 No causality 0.50559 0.6032 1.49857 0.2236
D7 HSCI BIT 1.87936 0.1529 3.24453 0.0391
D8 HSCI BIT 0.48444 0.9011 2.22171 0.0143
BIT-NZ
D1 No causalit
y
0.04514 0.9559 1.34004 0.2620
D2 No causalit
y
0.98716 0.3728 1.67175 0.1881
D3 NZ BIT 0.49320 0.6107 6.11559 0.0022
D4 NZ BIT 1.46160 0.2320 2.91455 0.0544
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D5 No causality 0.13821 0.8709 0.39157 0.6760
D6 NZ BIT 1.66720 0.1890 2.89391 0.0555
D7 No causality 0.49484 0.6097 0.52101 0.5940
D8 NZ BIT 1.48389 0.1388 1.39229 0.0772
BIT-ASX
D1 No causality 0.21151 0.1261 0.21151 0.8094
D2
B
IT ASX 2.97464 0.0512 0.28250 0.7539
D3
A
SX BIT 1.83509 0.1598 2.82853 0.0593
D4 No causalit
y
1.23544 0.2909 0.84530 0.4295
D5 No causalit
y
1.71959 0.1793 1.82541 0.1613
D6 No causalit
y
0.27618 0.7587 0.01982 0.9804
D7 No causalit
y
0.63335 0.5309 1.33789 0.2626
D8
A
SX BIT 0.61931 0.7986 2.35031 0.0092
BIT-STI
D1 STI BIT 0.35452 0.7015 2.87569 0.0565
D2 No causality 0.79066 0.4536 0.61605 0.5401
D3 No causality 1.38205 0.2512 0.27338 0.7608
D4 No causality 1.03305 0.3561 0.22866 0.7956
D5 No causality 0.54989 0.5771 0.70325 0.4951
D6 No causality 0.41846 0.6581 0.10450 0.9008
D7 STI BIT 0.15362 0.8576 3.55081 0.0288
D8 No causality 1.04597 0.4029 1.01617 0.4378
BIT-NIKKEI
D1 NIKKEI BIT 2.07021 0.1264 3.77420 0.0231
D2 BIT NIKKEI 2.72172 0.0659 0.34563 0.7078
D3 NIKKEI BIT 0.17699 0.8378 4.46937 0.0115
D4 No causality 1.97706 0.1387 0.40505 0.6670
D5 No causalit
y
0.67260 0.5105 2.10895 0.1216
D6 No causalit
y
0.63914 0.5278 1.10435 0.3316
D7 No causalit
y
0.79161 0.4532 1.65826 0.1907
D8
B
IT NIKKEI 1.90489 0.0090 1.24300 0.0208
BIT-ENX
D1 No causality 0.14157 0.8680 1.11410 0.3284
D2 No causality 0.68979 0.5018 0.09524 0.9092
D3 ENX BIT 0.36336 0.6954 2.53166 0.0797
D4
B
IT ENX 2.54250 0.0789 0.19177 0.8255
D5
B
IT ENX 7.42805 0.0006 10.3222 0.000
D6
B
IT ENX 5.00565 0.0068 6.16160 0.0021
D7 No causality 0.98949 0.3719 0.27482 0.7597
D8 No causalit
y
0.49422 0.6101 1.26235 0.2832
BIT-S&P 500
D1 No causalit
y
0.16440 0.8484 0.89560 0.4085
D2 No causalit
y
1.04951 0.3503 1.46334 0.2316
D3 &500BIT S P2.80387 0.0607 1.74375 0.1751
D4 No causality 0.92143 0.3981 0.51499 0.5976
D5 &500BIT S P3.03113 0.0484 1.22730 0.2932
D6 No causality 0.10825 0.8974 0.00412 0.9959
D7 &500BIT S P5.90830 0.0028 1.10904 0.3300
D8 No causalit
y
0.28030 0.7556 0.59225 0.5531
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Table 4. Results of wavelet-based Granger causality test at different time scales for Bitcoin future and
the selected stock market returns
Time Domain Result Null h
y
pothesis
BITF does not Cause Stoc
k
Stock does not Cause BITF
F-test P-Value F-test P-Value
BITF-HSCI
D1 No causalit
y
1.40659 0.2452 0.75247 0.4713
D2 No causality 0.88409 0.88409 0.38289 0.6819
D3 No causality 0.03385 0.9667 0.52913 0.5892
D4 No causality 0.23043 0.7942 0.89288 0.4096
D5 No causality 1.38988 0.2493 0.10497 0.9004
D6 No causality 1.36658 0.2552 0.86589 0.4208
D7 No causality 0.69914 0.4971 0.67166 0.5109
D8 No causality 0.24950 0.7844 0.11039 0.8967
BITF-NZ
D1 No causality 2.29951 0.1005 2.25502 0.1051
D2 NZ BITF 2.23282 0.1074 2.37594 0.0931
D3 No causality 0.01679 0.9834 1.02020 0.3607
D4 No causality 0.23685 0.7891 0.33241 0.7172
D5 No causality 0.90461 0.4048 1.66874 0.1887
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D6 No causality 0.39458 0.6740 1.20589 0.2996
D7
B
ITF NZ 7.55007 0.0005 6.03222 0.0024
D8 No causality 0.31512 0.7384 0.03824 0.9627
BITF-ASX
D1
B
ITF ASX 5.24305 0.0053 0.59164 0.5535
D2
B
ITF ASX 8.62678 0.0002 3.53875 0.0292
D3 No causalit
y
1.24892 0.2870 0.57078 0.5651
D4 BITF ASX 2.55937 0.0775 0.30383 0.7380
D5
A
SX BITF 1.85144 0.1572 5.46566 0.0043
D6
B
ITF ASX 5.27555 0.0052 4.35663 0.0129
D7
B
ITF ASX 3.44063 0.0322 2.31163 0.0993
D8 No causalit
y
1.24198 0.4071 0.86096 0.5897
BITF-STI
D1 No causalit
y
0.61823 0.5390 1.33772 0.2626
D2 No causality 0.79048 0.4537 0.47077 0.6246
D3 No causality 0.78772 0.4550 0.37704 0.6859
D4 No causality 0.13488 0.8738 0.01876 0.9814
D5 No causality 1.09086 0.3361 0.28946 0.7487
D6 No causality 2.05135 0.1288 0.89232 0.4098
D7 STI BITF 0.15362 0.8576 3.55081 0.0288
D8 No causalit
y
1.46068 0.2316 0.28280 0.5969
BITF-NIKKEI
D1 No causality 0.10250 0.9026 0.43212 0.6492
D2 No causality 0.13379 0.8748 0.43291 0.6487
D3 No causality 0.60536 0.5460 0.11112 0.8948
D4 No causality 0.37536 0.6871 1.11812 0.3270
D5 NIKKEI BITF 1.81073 0.1637 8.06397 0.0003
D6
B
ITF NIKKEI 4.64360 0.0097 4.78997 0.0084
D7 No causalit
y
0.84725 0.3591 0.06051 0.8061
D8 No causalit
y
1.15193 0.3586 0.51604 0.6135
BITF-ENX
D1 No causalit
y
0.11790 0.8888 0.02821 0.9722
D2 No causalit
y
0.22053 0.8021 0.02893 0.9715
D3 No causalit
y
0.89807 0.4075 0.22278 0.8003
D4 No causalit
y
0.91816 0.3994 0.55856 0.5721
D5 No causalit
y
0.45504 0.6345 1.02920 0.3574
D6 No causalit
y
0.59850 0.5497 1.17936 0.3076
D7
B
ITF ENX 2.74229 0.0646 4.69020 0.0093
D8 No causalit
y
0.44476 0.6410 0.05197 0.9494
BITF-S&P 500
D1 No causalit
y
0.80886 0.4455 0.61558 0.5404
D2 No causalit
y
0.00462 0.9954 0.27526 0.7594
D3 No causalit
y
1.20913 0.2986 0.39318 0.6749
D4 No causalit
y
0.22950 0.7950 1.25318 0.2858
D5 No causalit
y
0.59473 0.5518 0.43463 0.6476
D6 &500SP BITF0.61316 0.5417 4.72757 0.0089
D7 No causality 0.13278 0.8757 0.69959 0.4969
D8 No causalit
y
0.64605 0.5242 0.08546 0.9181
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Fig.1. Continuous wavelet power spectra for Bitcoin and the selected return series
Notes:Time and frequency are presented on the horizontal (time period from January 2012 to
August 2019, with 500 = 2012-2014, 1000 = 2014-2015, 1500 = 2015-2016, 2000 = 2016-
2017, 2500=2017-2019) and the vertical axis, respectively. The warmer the color of a region,
the greater the coherence is between the pairs. The solid black line isolates the statistical
significance area at the level of 5 %.
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Fig.2. Cross-wavelet transforms for Bitcoin and the selected return series.
Notes:Time and frequency are presented on the horizontal (time period from January 2012 to
August 2019, with 500 = 2012-2014, 1000 = 2014-2015, 1500 = 2015-2016, 2000 = 2016-
2017, 2500=2017-2019) and the vertical axis, respectively. The warmer the color of a region,
the greater the coherence is between the pairs. The solid black line isolates the statistical
significance area at the level of 5 %.
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Fig. 3. Wavelet coherence for Bitcoin and the selected return series
Notes:Time and frequency are presented on the horizontal (time period from January 2012 to
August 2019, with 500 = 2012-2014, 1000 = 2014-2015, 1500 = 2015-2016, 2000 = 2016-
2017, 2500=2017-2019) and the vertical axis, respectively. The warmer the color of a region,
the greater the coherence is between the pairs. The solid black line isolates the statistical
significance area at the level of 5 %.
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Fig. 4. Wavelet covariance and correlation between Bitcoin and the selected returnseries
Note: The upper and lower bound are presented with U and L, respectively at the 95%
confident interval. The black dotted line illustrates the covariance and correlation between
Bitcoin and the selected financial markets.
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Fig. 5. Wavelet coherence for Bitcoin future and the selected return series
Notes:Time and frequency are presented on the horizontal (time period from January 2012 to
August 2019, with 500 = 2012-2014, 1000 = 2014-2015, 1500 = 2015-2016, 2000 = 2016-
2017, 2500=2017-2019) and the vertical axis, respectively. The warmer the color of a region,
the greater the coherence is between the pairs. The solid black line isolates the statistical
significance area at the level of 5 %.
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