Connexion Between Cryptocurrencies Liquid and Futures Markets: Discernment from Static,Dynamic and Wavelet Approach

Abstract

The knowledge of the interconnectedness between liquid and futures markets of cryptocurrencies amidst dynamic contemporary environment can be enriched through the full characterization of the direction, persistence and intensity of information flows between these markets. So, the present study attempts to investigate the static and dynamic connexions between liquid and futures markets of Bitcoin, Ethereum, Litecoin, Ripple XRP and Bitcoin Cash from June 2018 to June 2022. The connexion between their liquid and futures markets is first investigated using unconditional correlation, Johansen’s cointegration, vector error correction and Wald’s block exogeneity. Their estimates discern connexions encompassing significant long-run relationships between their liquid and futures markets; momentous unidirectional long-run causality from their futures market to liquid market; and momentous bidirectional short-run causality from their liquid market to futures market and from their futures market to liquid market. The present treatise encompasses methodological advancement in the investigation of interconnectedness between these markets by employing a dynamic conditional correlation model and a wavelet transform framework. Their discerned estimates indicate that the markets of Bitcoin, Litecoin, Ethereum and Bitcoin Cash have only momentous long-run perseverance, lingering and spillover effects of shocks’ sway on conditional correlations. However, there is momentous short- and long-run perseverance, lingering and spillover effects in the case of Ripple XRP. The wavelet coherence analysis also confirms these results by indicating a bidirectional short-run causal relation and a long-run positive comovement between liquid returns and futures returns of these cryptocurrencies. These discernments may help investors, portfolio managers and policymakers to enhance hedging effectiveness through optimal portfolio allocation and monitor financial contagion to attain and sustain financial stability in economies.

Keywords

Cryptocurrency Markets Interconnectedness Cointegration Causality Dynamic Conditional Correlation Model Spillover Effect Wavelet Coherence

Introduction

The interconnectedness of markets among various financial assets and economies is a vital factor for determining hedging opportunities for investors and for monitoring financial contagion for financial regulators. The analysis of this factor encompasses the exploration of a broad set of relationships and interactions among financial market participants (Kara et al., 2015) through correlation, cointegration, causality, spillover effect and coherence. The knowledge of these facets amidst dynamic environment is crucial for comprehending the exact nature of interconnectedness among financial market participants, which may help investors, portfolio-managers and policymakers in taking decisions for enhancing hedging effectiveness through optimal portfolio allocation and to monitor financial contagion to attain and sustain financial stability in economies. There is diverse literature on interconnectedness among various economies and financial assets, specifically focusing on empirical measures that stipulate a framework for the comprehension of financial interconnectedness and exploring long-term relationship theory in finance. Many researchers like Eun et al. (1989), Hamao and Masulis (1990), Lin et al. (1994), Booth et al. (1997), Janakiramanan and Lamba (1998), Kanas (2000), Johnson and Soenen (2002), Kaur (2004), Choi (2009), Beirne et al. (2013), Louzis (2013), Natarajan et al. (2014), Zhang and Jaffry (2015), Singh and Singh (2016), Dangi (2016), Yarovaya et al. (2016), Al Rahahleh and Bhatti (2017), Yin et al. (2017), Hung (2019), BenSaïda (2019) and Behera and Rath (2021) have studied interconnectedness among various economies based on main indices of their national stock exchanges. These studies have confirmed the interlinkages of economies through various static and dynamic econometric models. Researchers have also studied the interconnectedness in the form of integration, causality and innovation response among various financial assets to explore their diversification prospects by employing dynamic econometric models. Like Tsai (2015), evaluated dynamic information transfer between US housing and stock market and revealed substantial short-term causal relations. The US housing market transferred information to the stock market in ordinary periods. However, the stock market exhibited net information spillover during financial crisis. Shchepeleva (2017) analysed stock market interconnectedness using forecast error variance decomposition in equity, government bond and real estate markets in 10 countries. It was found that the USA, France and Germany are the major transmitters of shocks to other countries. The results pointed to more spillover effects in stock markets, while bond markets were more sensitive to internal instability. Geraci and Gnabo (2018) applied time-varying vector autoregression (VAR) to investigate dynamic financial spillover drifts in S&P 500 and interdependencies at sectoral and institutional echelons. They found a gradual decrease in interconnectedness after the capital management and financial crisis. They further confirmed more stable interconnectedness at institutional echelon. Mansour et al. (2020) studied volatility spillover between oil prices and Islamic stock markets employing the bivariate VARMA-BEKK-GARCH models. They found the distinctiveness of Islamic marketplaces in reducing volatility, transmission and perseverance. Yip et al. (2020) employed the GFI-VAR model to capture dynamic volatility spillover effects and the Markov’s SAR model to discern crude-oil regimes. They found that the reduction in spillover impact from crude oil to agricultural commodities had shrunken during the low-volatility regime of crude oil and vice versa. Yousuf and Zhai (2021) investigated the dynamic connectedness and spillover effects between Gulf Cooperation Council countries, crude oil prices and equity markets in Europe, the USA and China by applying the DCC-GARCH model and Diebold and Yilmaz (2014) methodology, respectively. They found European and US markets were global contributors of shocks, while Chinese markets were gradually gaining momentum. Many researchers have also studied the interconnectedness between derivative markets and liquid markets to investigate price efficiency based on spot futures parity theory or the cost of carry model of Cornell and French (1983). They have provided empirical evidence for theoretical relationship between spot prices, futures prices and other variables encompassing risk-free rate, dividend yield and time to maturity. The investigation of this relationship has provided insights for market players to identify arbitrage opportunities that arise when there is a violation of spot futures parity. Kawaller et al. (1987), Stoll and Whaley (1990), Chan et al. (1991), Wahab and Lashgari (1993), Pizzi et al. (1998), Thomas and Karande (2001), Roope and Zurbruegg (2002), Zapata et al. (2005), Gupta and Singh (2006), Bose (2007), Wagner and Marliese (2009), Zhang (2010), Srinivasan (2012) and Dangi (2014) have studied the interconnectedness among liquid and derivative markets using static econometric models for exploring price efficiency, arbitrage opportunities and hedging prospects. Later, Ewing and Malik (2013), using GARCH models, studied the volatility dynamics of gold and oil futures, encompassing structural discontinuities. They found significant volatility transmission between gold and oil returns while accounting for structural discontinuities in variance. Kang et al. (2017) examined spillover impacts among futures markets of silver, gold, crude oil, rice, corn and wheat by employing the DECO-GARCH model. They found bidirectional spillovers across these markets. There was empirical evidence that silver and gold were information transmitters to other markets. Huo (2018) investigated market interdependency among stock markets and derivative markets in China using different multivariate VAR and GARCH models. This study found a bidirectional causal relationship as futures market significantly led spot market; however, there was a weaker lead to futures market from spot market in terms of lasting time and scale. Katusiime (2019) applied GVAR, MGARCH, DCC, CCC and VCC models to study the effects of commodity prices’ volatility spillovers on financial sector’s constancy and found low volatility spillovers and market interdependencies. However, spillovers and interdependencies had markedly increased in crisis periods. Wang et al. (2020) examined return interconnectedness among futures markets of gold, wheat, WTI crude oil and copper on interval as well as frequency domains and found copper was an information transmitter to other commodity futures under financial stress. Further, they confirmed that this connectedness has increased sharply during crises. Researchers have also extended the static and dynamic methodologies to explore the interconnectedness among cryptocurrencies. Like Yi et al. (2018), discerned volatility interconnectedness among cryptocurrencies using spillover-index approach. They found tight interconnection with cyclical fluctuation. Bação et al. (2018) investigated the information transmission between Bitcoin, Bitcoin Cash, Ripple, Litecoin and Ethereum employing VAR model and computed Geweke-feedback estimates and generalized impulse response functions (GIRFs). They found that most information-transmissions were contemporaneous. However, there were some lagged effects on Bitcoin from other cryptocurrencies. The GIRFs confirmed that there was a strong contemporaneous correlation, indicating that there was not much evidence of lagged effects. Zięba et al. (2019) examined interdependencies between log returns of cryptocurrencies using minimum spanning tree method and VAR model. They found hierarchical clusters in cryptocurrencies indicating topological properties. They further concluded that the changes in Bitcoin’s price did not affect and were not affected by changes in the prices of other cryptocurrencies. Dahir et al. (2020) discerned the dynamic connexion between Bitcoin and equity market information using the TVP-VAR model of Antonakakis and Gabauer (2017). They found weak volatility transmission of Bitcoin returns to market returns in BRICS economies. Yousaf and Ali (2020) examined spillover effects between Litecoin, Bitcoin and Ethereum using VAR-AGARCH model during pre-COVID and COVID period. They found variation in return spillovers across these phases for Litecoin–Bitcoin, Ethereum–Bitcoin and Litecoin–Ethereum pairs. However, volatility spillovers varied for Litecoin–Bitcoin and Ethereum–Bitcoin pairs. Qureshi et al. (2020) investigated the dynamics of multiscale interdependencies among Bitcoin, Ethereum, Ripple, Litecoin and Bitcoin Cash. The empirical results confirmed the short-run and long-run market integration among some cryptocurrencies with switch in the lead and lag relations. They also found significantly more stable coherence at lower frequencies than at higher frequencies. Bouri et al. (2021) investigated connectedness among seven leading cryptocurrencies during extreme events with variance decomposition of a quantile VAR model and found strengthening of return connectedness with shock size. They also found more intense propagation in the return shocks during extreme events than in calm periods. Shahzad et al. (2021) studied connexions among 18 cryptocurrencies using Markov regime-switching VAR model. They found evidence of much higher spillovers in high- volatility regimes during the COVID-19 outbreak, indicating infectivity during wrenched periods. Kumar et al. (2022) investigated interconnectedness in the 10 most capitalized cryptocurrencies to understand their relationship structure with a special focus on differences in investment horizons. They found a structural change in connectedness in 2020 due to unprecedented monetary injections to counter the COVID-19-induced economic standstill. Assaf et al. (2022) quantified information flows between Bitcoin, Ripple and Ethereum using Rényi’s transfer entropy. They found bidirectional transmission between Ripple and Bitcoin, whereas there was unidirectional transmission from Ripple to Ethereum. They further confirmed the absence of nonlinear transmission. Shahzad et al. (2022) examined the interdependence of median and tail-based returns among cryptocurrencies in normal as well as extreme market conditions using the LASSO technique with quantile regression. They found that the volatilities of market, momentum and size drove return connectedness and clustering coefficients in normal as well as extreme market conditions. In a nutshell, there is a plethora of research on the static and dynamic connexions among economies, financial instruments and markets. These treatises by Yi et al. (2018), Bação et al. (2018), Zięba et al. (2019); Dahir et al. (2020), Yousaf and Ali (2020), Qureshi et al. (2020), Bouri et al. (2021), Shahzad et al. (2021), Kumar et al. (2022) Assaf et al. (2022), Shahzad et al. (2022) had explored the connectedness across cryptocurrencies. But neither of these studies explored the static and dynamic connexions among liquid and futures markets of cryptocurrencies that can benefit market participants in discovering their prices for hedging and better asset allocation. So, there is a lack of exploration of the connexions among liquid and futures markets of cryptocurrencies in terms of full characterization of the direction, persistence and intensity of information flows between these markets. The present study attempts to fill this lacuna by discerning the static and dynamic connexions between cryptocurrencies’ liquid market and futures market using a static, dynamic and wavelet approach that will provide full characterization of direction, persistence and intensity of information flows between these markets. Hence, this treatise makes methodological progression by applying wavelet coherence analysis in addition to static and dynamic models. The discernment of connexions between liquid and futures markets of cryptocurrencies using a static, dynamic and wavelet approach will contribute to the comprehensive body of knowledge for investors and portfolio managers for identifying arbitrage and hedge prospects and will also provide signals to financial regulators to monitor financial contagion and take appropriate policy decisions.

Objectives

The focal objective is to examine the static and dynamic connexions between cryptocurrencies liquid and future markets. This focal objective is further delineated into the following points:

To examine unconditional and dynamic-conditional correlation between cryptocurrencies liquid and futures markets.

To investigate cointegration in between cryptocurrencies liquid and futures markets.

To study short-run and long-run causality among cryptocurrencies liquid and futures markets.

To investigate spillover effects among cryptocurrencies liquid and futures markets.

To study wavelet coherence between cryptocurrencies liquid and futures markets.

Database

The daily closing liquid prices and futures prices of Bitcoin, Ethereum, Litecoin, Ripple XRP and Bitcoin Cash from June 2018 to June 2022 are taken from the online databases of CoinMarketCap and Binance.

Econometric Methodology

The data of liquid and futures prices of Bitcoin, Ethereum, Litecoin, Ripple XRP and Bitcoin Cash is rigorously studied through Phillips–Perron test (PPt) and augmented Dickey–Fuller test (ADFt) for stationarity. The connexion between their liquid and futures markets is studied with Johansen’s test of cointegration, vector error correction approach, Wald’s block exogeneity test, dynamic conditional correlation and wavelet coherence analysis. The Johansen cointegration test is exercised on their price series to discern cointegration between two markets; the VECM is exercised on their return series to test long-term causality between two markets; Wald’s block exogeneity test is exercised on their return series to discern any short-term causality between two markets; and Engle’s dynamic conditional correlation model (Engle, 2002) is applied to apprehend the intensity of volatility-correlation variations between markets, that is, spillover effect. The constant correlation model connects conditional covariance to variance (Bollerslev, 1990). However, Bera and Kim (2002) and Tse and Albert (2002) found empirical implausibility in assuming constant correlation over time. So, Engle (2002) proposed a dynamic conditional correlation model encompassing correlations varying over time. Its variance-covariance matrix is

{\dot{V C v}}_{' t'} = {\dot{C S D}}_{' t'} {\dot{C C r}}_{' t'} {\dot{C S D}}_{' t'}

(1)

Here, ${\dot{C S D}}_{' t'}$ is conditional standard deviations diagonal matrix, $C C r_{' t'}$ is conditional correlation matrix. The exponential smoothing approach of this formulation is defined as

Q_{' t'} = ç' * (ε' - A - B) + A * (ε_{' t' - I}) (ε'_{' t' - I}) + B * (Q_{' t' - I}),

(2)

where $ç'$ = unconditional correlation matrix of standardized residuals’ vector and $Q_{' t' - I}$ = symmetric positive variance-covariance matrix.

Engle had taken $Q_{' t'}$ dynamically with the conditional correlation matrix and defined $C \dot{C} r_{' t'}$ as

C \dot{C} r_{' t'} = diag {({\dot{Q}}_{' T'})}^{- 1} {\dot{Q}}_{' t'} diag {({\dot{Q}}_{' T'})}^{- 1}

(3)

Here, ${\dot{Q}}_{' T'}$ is matrix of square roots of each element in Q and diagis $({\dot{Q}}_{' T'})$ a matrix encompassing diagonal elements of ${\dot{Q}}_{' T'}$ .

Further, the wavelet transform framework is applied to investigate wavelet coherence to provide a full characterization of the direction, persistence and intensity of information flows between the liquid and future markets of these cryptocurrencies. The wavelet coherence discerns connexions encompassing time and scale as

W C = \frac{{| \dot{S} (C_{w t (L)} (x, y) C_{w t (F)} (x, y) |}^{2}}{\dot{S} {| C_{w t (L)} (x, y) |}^{2} . \dot{S} {| C_{w t (F)} (x, y) |}^{2}}

(4)

Here, $C_{w t (L)} (x, y)$ and $C_{w t (F)} (x, y)$ are continuous wavelet transforms of liquid and futures returns at scales $x$ and positions $y;$ $\dot{S}$ is a smoothing factor in time and scale.

Basic Description Coupled with Decomposition Discernment of Cryptocurrencies’ Series

The liquid and futures price series of Bitcoin, Litecoin, Ethereum, Ripple XRP and Bitcoin Cash from June 2018 to June 2022 have been taken for discerning their description through descriptive estimates and decomposition analysis. The descriptive estimates of these cryptocurrencies in Table 1 reveal that all liquid and futures price series of Bitcoin, Ethereum, Litecoin, Ripple XRP and Bitcoin Cash have similar values of average, spread and skewness. The skewness is positive for all series, indicating the right tendency of their distribution. The kurtosis value is greater than three for Litecoin, Ripple XRP and Bitcoin Cash. And it is less than three for Bitcoin and Ethereum, indicating different peaks in their price series. The value of probability of Jarque and Bera’s test (1980) is zero in all price series, indicating the rejection of normal distribution. The probability values of PP and ADF tests are greater than 0.05, indicating that these price series are non-stationary at level. The graphical exhibition and decomposition analysis of these price series in Figures 1 and 2 clearly discern lateral impulsive soaring movement trailed by random movement. The seasonal element in all price series has been changing sluggishly, which indicates similar seasonal patterns from June 2018 to June 2022 in liquid as well as futures price series of Bitcoin, Ethereum, Litecoin, Ripple XRP and Bitcoin Cash. Note that the estimation from non-stationary time series has an excessive likelihood of discerning spurious outcomes (Malliurus & Urrutia, 1991). Therefore, the price series are commuted into return series with the following equations:

Table 1.

Basic Description of Liquid and Futures Price Series of Cryptocurrencies.

Descriptive Statistics	Liquid Príce Seríes					Futures Príce Seríes
Descriptive Statistics	Bítcoín	Ethereum	Lítecoín	Ripple XRP	Bítcoín Cash	Bítcoín	Ethereum	Lítecoín	Ripple XRP	Bítcoín Cash
Mean	21,479.01	1,153.55	97.37	0.49	389.40	21,506.81	1,154.36	97.27	0.49	389.61
Standard deviation	18,423.61	1,316.02	61.00	0.31	213.10	18,417.06	1,315.14	61.07	0.31	212.50
Skewness	0.82	1.06	1.34	1.41	1.48	0.82	1.06	1.34	1.42	1.48
Kurtosis	2.16	2.71	4.76	4.52	6.29	2.16	2.71	4.76	4.53	6.30
Jarque–Bera	210.45	286.71	639.02	641.00	1,215.81	210.50	285.77	638.10	645.02	1,220.87
P_JB	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
PP	–5.2109	–6.4528	–14.412	–17.171	–20.098	–5.102	–6.3221	–14.317	–17.45	–20.05
P_PP	0.8191	0.7498	0.3058	0.1519	0.0707	0.8251	0.7571	0.3112	0.1364	0.0714
ADF	–1.5301	–1.6703	–2.5805	–2.6460	–3.4517	–1.4962	–1.6253	–2.5471	–2.7166	–3.2879
P_ADF	0.7772	0.7179	0.3326	0.3048	0.0469	0.7916	0.7369	0.3467	0.2750	0.0728
Observations	1,491	1,491	1,491	1,491	1,491	1,491	1,491	1,491	1,491	1,491

Notes: P_JB, probability value of Jarque–Bera test; P_PP, probability value of Phillips–Perron test; P_ADF, probability value of augmented Dickey–Fuller test.

Figure 1.

Liquid and Futures Price Series of Cryptocurrencies.

Figure 2.

Decomposition Analysis of Cryptocurrencies’ Liquid and Futures Price Series.

R_{spot} = (I n S_{' t'} - I n S_{' t' - 1}) \times 100

(5)

R_{futures} = (I n F_{' t'} - I n F_{' t' - 1}) \times 100

(6)

where $R_{spot}$ and $R_{f u t u r e s}$ are liquid and futures returns for day t, respectively; $S_{' t'} and F_{' t'}$ are closing liquid and futures prices for day t, respectively; $S_{' t' - 1}$ and $F_{' t' - 1}$ are closing liquid and closing futures prices of previous trading day, respectively. The descriptive statistics of the estimated return series of cryptocurrencies in Table 2 displays positive mean returns for Bitcoin and Ethereum, indicating increasing trend in their returns during the sample period. However, the liquid and futures returns series of Litecoin, Ripple XRP and Bitcoin Cash display negative mean returns, indicating decreasing trend in their returns during the sample period. It is empirically apparent from these measurements that Bitcoin liquid and futures offer the highest returns with low risk. The liquid and futures series of Litecoin, Ripple XRP and Bitcoin Cash have negative mean returns with high volatility. An eccentric observation is that the standard deviation is larger than the mean for each return series. The negative skewness in the case of all cryptocurrencies except Ripple XRP clearly determines the predisposition in Bitcoin, Litecoin, Ethereum and Bitcoin Cash to receive negative returns and the predisposition in Ripple XRP to receive positive returns. These estimated returns series for liquid and futures markets have similar facets of average, standard deviation, skewness and peakiness. These return series are asymmetric, having fat tails and high volatility. Further, the probability values of PP and ADF tests for all these series are zero, depicting that all return series are stationary series. The pictorial portrayal of these return series in Figure 3 also exhibits their transformation from non-stationarity to stationarity.

Table 2.

Basic Description of Liquid and Futures Returns Series of Cryptocurrencies.

Descriptive Statistics	Liquid Returns Series					Futures Returns Series
Descriptive Statistics	Bítcoín	Ethereum	Lítecoín	Ripple XRP	Bítcoín Cash	Bítcoín	Ethereum	Lítecoín	Ripple XRP	Bítcoín Cash
Mean	0.066	0.043	–0.053	–0.041	–0.151	0.065	0.041	–0.054	–0.042	–0.153
Standard deviation	3.962	5.205	5.499	5.479	6.179	3.843	5.027	5.292	5.876	6.036
Skewness	–1.296	–1.199	–0.808	0.250	–0.322	–1.210	–1.179	–0.802	0.050	–0.390
Kurtosis	20.55	15.93	11.66	13.38	16.38	19.35	15.21	11.52	17.73	16.55
Jarque–Bera	19,547.82	10,737.57	4,818.38	6,705.73	11,136.01	16,964.69	9,602.23	4,670.44	13,469.84	11,433.01
P_JB	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
PP	–1,756.7	–1,794.5	–1,704.4	–1,427.1	–1,750.3	–1704.6	–1,732.5	–1,648.7	–1,582.8	–1,690.9
P_PP	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
ADF	–10.773	–10.657	–11.438	–11.101	–11.059	–10.75	–10.672	–11.503	–11.235	–10.888
P_ADF	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
Observations	1,490	1,490	1,490	1,490	1,490	1,490	1,490	1,490	1,490	1,490

Notes: P_JB, probability value of Jarque–Bera test; P_PP, probability value of Phillips–Perron test; P_ADF, probability value of augmented Dickey–Fuller test.

Figure 3.

Liquid Returns and Futures Returns Series of Cryptocurrencies.

Static and Dynamic Connexion Between Liquid and Futures Markets of Cryptocurrencies

The investigation of static interconnectedness of liquid and futures markets of cryptocurrencies is initiated with the estimation of unconditional correlation. Table 3 portrays the estimates of unconditional correlation between liquid returns and futures returns series. It is empirically evident from these estimates that the relationships between liquid returns and futures returns of Bitcoin, Ethereum and Litecoin are negative and statistically significant. However, Bitcoin Cash’s liquid returns and futures returns demonstrate a negative but insignificant relationship. An eccentric observation is that the relationship between liquid returns and futures returns of Ripple XRP is positive and statistically significant. The next phase of investigation of connexion between liquid and futures markets of cryptocurrencies is the estimation of the cointegration of these markets. As all series are non-stationary at level and stationary at first difference, these series may be cointegrated as I(1) series. So, Johansen’s test is used to detect cointegration between liquid and futures price series. The results of its eigenvalue and trace statistic in Table 4 discern the existence of cointegration between liquid and futures price series, as the null hypothesis of no cointegration cannot be accepted. So, the long-run relation between liquid and futures markets of these cryptocurrencies is empirically evident. But note that there are chances of being misled by the ordinary least squares equation in the presence of dynamic variance, so the liquid and futures return series are further examined for autocorrelation and heteroskedasticity through Breusch–Godfrey’s LM test of serial correlation and Engle’s test of autoregressive conditional heteroskedasticity, respectively. Their estimates in Table 5 clearly determine the presence of autoregressive conditional heteroskedasticity in all series of Bitcoin, Litecoin, Ethereum, Ripple XRP and Bitcoin Cash. So, the connexion between their liquid and futures markets is further examined with the dynamic conditional correlation model of Engle (2002), which determines the integration between these markets through volatility correlation transformations between these markets, that is, volatility spillover. The estimates from this dynamic model for dcca and dccb parameters are demonstrated in Table 6. The dcca parameters are statistically insignificant in all cryptocurrencies except Ripple XRP, which discerns insignificant short-run persistence, lingering and spillover effects of shocks’ sway on conditional correlations in the markets of all cryptocurrencies except Ripple XRP. However, the dccb parameters are statistically significant for all cryptocurrencies, depicting a significant long-run persistence, lingering and spillover effect of shocks’ sway on conditional correlations in the markets of all cryptocurrencies. So, the optimal parameters of this model confirm momentous short-run and long-run perseverance, lingering and spillover effects of shocks’ sway on conditional correlations in markets for Ripple XRP. However, the markets for Bitcoin, Litecoin, Ethereum and Bitcoin Cash have only long-run persistence, lingering and spillover effect of shocks’ sway on conditional correlations. The graphical presentation of conditional correlation dynamics between liquid returns series and futures returns series in Figure 4 depicts deviations in the highest and lowest dynamic conditional correlation of these cryptocurrencies. The vector error correction methodology proposed by Engle and Granger (1987) is further employed on liquid and futures returns of these cryptocurrencies to examine long-term causal relationship between liquid and futures markets. The lag length for this model is chosen using the vector autoregressive lag order information criterion developed by Schwarz. Note that one is deducted from the selected lag length to apply it to the vector error correction model. The significant negative coefficients discern the presence of long-run causality from exogenous to endogenous variables. However, positive coefficients regardless of their significance indicate the dearth of long-term causal relation from exogenous to endogenous variable. The results in Table 7 provide empirical evidence of long-run causal connexion from futures market to liquid market of all these cryptocurrencies, as the coefficients are significantly negative. However, there is absence of long-run causal connexion from liquid market to futures market for all these cryptocurrencies, as their coefficients are positive. So, it can be comprehended that there is a unidirectional long-run causal connexion from futures market to liquid market of Bitcoin, Ethereum, Litecoin, Ripple XRP and Bitcoin Cash. The Wald’s block exogeneity test is further applied to test the short-run causal connexion between their liquid and future markets. The significant estimates in Table 8 clearly indicate the presence of bidirectional short-run causality from liquid market to futures market and from futures market to liquid market of these cryptocurrencies. The same results are affirmed by the wavelet coherence analysis in Figure 5. Note that the wavelet transform framework analyses facets of cryptocurrencies’ time series without dropping information using the biwavelet package of Gouhier et al. (2013). The left-pointing arrows downwards up to scale 4 and the right-pointing arrows downwards between scale 4 and scale 16 designate bidirectional short-run causality from futures market to liquid market and from liquid market to futures market of Bitcoin, Litecoin, Ethereum and Bitcoin Cash. The pictorial presentation of this analysis illustrates the direction of comovements between liquid returns and future returns of Bitcoin, Litecoin, Ethereum, Ripple XRP and Bitcoin Cash. It can be clearly seen in Figure 5 that there is an elongated positive comovement between liquid returns and futures returns of these cryptocurrencies. The degree of interdependence in the figure is epitomized through red and blue colours. The red colour depicts the facets of major interactions in liquid and futures markets of these cryptocurrencies, whereas the blue colour depicts the facets of lower interactions in their liquid and futures markets. Note that the results outside the boundaries of the cone of influence are not significant.

Table 3.

Unconditional Correlation Between Liquid and Futures Returns Series.

Cryptocurrencies	Unconditional Correlation	t-statistic	df	Prob.
Bitcoin liquid and Bitcoin futures	–0.061845	–2.3902	1,488	0.0169
Ethereum liquid and Ethereum futures	–0.069654	–2.6934	1,488	0.0071
Litecoin liquid and Litecoin futures	–0.058810	–2.2725	1,488	0.0232
Ripple XRP liquid and Ripple XRP futures	0.752436	44.066	1,488	0.0000
Bitcoin Cash liquid and Bitcoin Cash futures	–0.036180	0.1628	1,488	0.1628

Table 4.

Estimates of Johansen’s Test of Cointegration.

Cryptocurrencies	Hypothesized Number of Cointegrated Equation/s: None*
Cryptocurrencies	Eigenvalue	Trace Statistic	Critical Value at 0.05	Probability
Bitcoin liquid and Bitcoin futures	0.1492	241.82	15.495	0.000
Ethereum lquid and Ethereum futures	0.1802	296.77	15.495	0.000
Litecoin liquid and Litecoin futures	0.1083	175.81	15.495	0.000
Ripple XRP liquid and Ripple XRP futures	0.1390	228.82	15.495	0.000
Bitcoin Cash liquid and Bitcoin Cash futures	0.0998	172.04	15.495	0.000

Table 5.

Estimates of Breusch–Godfrey’s LM Test of Serial Correlation and Engle’s Test of ARCH.

Cryptocurrencies	Statistic	Breusch–Godfrey’s LM Test of Serial Correlation	Engle’s Test of ARCH	Probability	Breusch–Godfrey’s LM Test of Serial Correlation	Engle’s Test of ARCH
Bitcoin	F-statistic	3.024441	7.705638	F	0.0489	0.0056
Bitcoin	Obs*R-squared	6.040576	7.676224	Chi-Square	0.0488	0.0056
Ethereum	F-statistic	4.975613	18.26059	F	0.0070	0.0000
Ethereum	Obs*R-squared	9.911638	16.06333	Chi-Square	0.0070	0.0000
Litecoin	F-statistic	2.622201	18.94702	F	0.0730	0.0000
Litecoin	Obs*R-squared	5.240026	18.73381	Chi-Square	0.0728	0.0000
Ripple XRP	F-statistic	139.5131	377.1136	F	0.0000	0.0000
Ripple XRP	Obs*R-squared	235.5483	301.2274	Chi-Square	0.0000	0.0000
Bitcoin Cash	F-statistic	5.336414	18.28796	F	0.0049	0.0000
Bitcoin Cash	Obs*R-squared	10.62524	18.09007	Chi-Square	0.0049	0.0000

Table 6.

Estimates from Dynamic Conditional Correlation Model.

Cryptocurrencies	Optimal Parameters	Estimate	Standard Error	t Value	Probability
Bitcoin liquid and Bitcoin futures	dcca	0.000000	0.000066	0.000077	0.999938
Bitcoin liquid and Bitcoin futures	dccb	0.926060	0.310416	2.983289	0.002852
Ethereum fiquid and Ethereum futures	dcca	0.000000	0.000045	0.000893	0.999288
Ethereum fiquid and Ethereum futures	dccb	0.911779	0.150783	6.046967	0.000000
Litecoin liquid and Litecoin futures	dcca	0.000000	0.000071	0.000039	0.999969
Litecoin liquid and Litecoin futures	dccb	0.927776	0.247771	3.744485	0.000181
Ripple XRP liquid and Ripple XRP futures	dcca	0.072690	0.014986	4.850600	0.000001
Ripple XRP liquid and Ripple XRP futures	dccb	0.925630	0.014950	61.91600	0.000000
Bitcoin Cash liquid and Bitcoin Cash futures	dcca	0.004472	0.004607	0.970660	0.331720
Bitcoin Cash liquid and Bitcoin Cash futures	dccb	0.979206	0.029210	33.52331	0.000000

Figure 4.

Dynamic Conditional Correlation Between Cryptocurrencies Liquid and Futures Returns Series.

Table 7.

Estimates of VEC Model.

Endogenous Variable	Lags	Coefficient	SE	t-Statistic	Probability
D(Bitcoin liquid)	2	–1.727751	0.04450	–38.8270	0.00000
D(Bitcoin futures)	2	2.028167	0.47437	4.27553	0.00001
D(Ethereum liquid)	4	–2.681152	0.08780	–30.5383	0.00000
D(Ethereum futures)	4	1.690078	1.06146	1.59223	0.11155
D(Litecoin liquid)	5	–3.261299	0.11580	–28.1640	0.00000
D(Litecoin futures)	5	1.567007	0.84630	1.85160	0.06428
D(Ripple XRP liquid)	4	–2.642932	0.19394	–13.6274	0.00000
D(Ripple XRP futures)	4	0.409460	0.23285	1.75848	0.07889
D(Bitcoin Cash liquid)	6	–2.208223	0.09883	–22.3426	0.00000
D(Bitcoin Cash futures)	6	3.118725	0.69426	4.49215	0.00000

Table 8.

Estimates of Wald’s Block Exogeneity Test.

Endogenous Variable	Excluded	Chi-Square	df	Probability
D(Bitcoin liquid)	D(Bitcoin futures)	400.0490	2	0.0000
D(Bitcoin futures)	D(Bitcoin liquid)	131.3203	2	0.0000
D(Ethereum liquid)	D(Ethereum futures)	711.3733	4	0.0000
D(Ethereum futures)	D(Ethereum liquid)	54.88650	4	0.0000
D(Litecoin liquid)	D(Litecoin futures)	878.5085	5	0.0000
D(Litecoin futures)	D(Litecoin liquid)	21.84412	5	0.0006
D(Ripple XRP liquid)	D(Ripple XRP futures)	142.2067	4	0.0000
D(Ripple XRP futures)	D(Ripple XRP liquid)	19.78137	4	0.0006
D(Bitcoin Cash liquid)	D(Bitcoin Cash futures)	406.1388	6	0.0000
D(Bitcoin Cash futures)	D(Bitcoin Cash liquid)	50.94186	6	0.0000

Figure 5.

Notes: Where, BSR is Bitcoin liquid returns; BFR is Bitcoin future returns; ETHSR is Ethereum liquid returns; ETHFR is Ethereum future returns; LSR is Litecoin liquid returns; LFR is Litecoin future returns; XSR is Ripple XRP liquid returns; XFR is Ripple XRP future returns; BTCSR is Bitcoin Cash liquid returns; BTCFR is Bitcoin Cash future returns.

Discussion

The present treatise discerns the time series of Bitcoin, Ethereum, Litecoin, Ripple XRP and Bitcoin Cash through descriptive estimates and decomposition analysis. The pragmatic evidence of high volatility, asymmetry and not-normal distribution encompassing fat tails is found in these series. These comprehensions are similar to the features of most financial series. A plethora of studies exists that have investigated the interconnectedness of economies, financial assets and markets using static and dynamic econometric methodologies. However, there is a lack of exploration of connexions among liquid and futures markets of cryptocurrencies. So, the present treatise contributes to the literature by examining the static and dynamic connexions between cryptocurrencies’ liquid and futures markets. This treatise makes methodological progression by applying wavelet coherence analysis. The outcomes of this treatise affirm the results of the aforementioned studies of Stoll and Whaley (1990), Chan et al. (1991), Wahab and Lashgari (1993), Pizzi et al. (1998), Thomas and Karande (2001), Roope and Zurbruegg (2002), Zapata, Fortenbery and Armstrong (2005), Gupta and Singh (2006), Bose (2007), Wagner and Marliese (2009), Zhang (2010), Srinivasan (2012) and Dangi (2014) in terms of significant long-run relationship facet of interconnectedness between liquid and derivative markets as per spot futures parity theory or cost of carry model of Cornell and French (1983) using static econometric models. The present study also affirms the results of earlier studies of Ewing and Malik (2013), Kang et al. (2017), Huo (2018), Yi et al. (2018), Wang et al. (2020), Yousaf and Ali (2020) and Assaf et al. (2022) in terms of the presence of significant dynamic interconnectedness between liquid and derivative markets as per spot futures parity theory using dynamic econometric models. However, the findings of Katusiime (2019) are contrary to the results of the present study, as this study found an insignificant long-run relationship between liquid market and derivative market, arousing arbitrage prospects, whereas the present treatise discerns significant long-run relationship between the cryptocurrencies’ liquid and futures markets, arousing hedge prospects. The outcomes of this treatise affirm the results of Chan et al. (1991), Gupta and Singh (2006), Bose (2007), Kang et al. (2017) and Huo (2018) in terms of bidirectional dependence in short run only between liquid market and derivative market of the cryptocurrencies. However, the studies of Wahab and Lashgari (1993), Roope and Zurbruegg (2002), Zapata et al. (2005), Wagner and Marliese (2009) and Dangi (2014) discerned unidirectional causality in terms of a stronger lead effect in derivative market, and the results of the present treatise also affirm a stronger lead effect in the cryptocurrencies’ derivative market in long run.

Conclusion

The interconnectedness of cryptocurrencies’ liquid and futures markets amidst dynamic contemporary environment can play a prominent role in hedging price risk through price discovery. The present treatise encompasses methodological advancements in the investigation of interconnectedness between these markets by employing dynamic econometric models and wavelet transform framework. This investigation provides the full characterization of the direction, persistence and intensity of information flows between liquid market and future market of these cryptocurrencies (namely Bitcoin, Ethereum, Litecoin, Ripple XRP and Bitcoin Cash). The decomposition analysis reveals the lateral impulsive rising movement followed by random movement in the liquid and future price series of these cryptocurrencies. The seasonal component in all price series has been changing slowly, indicating similar seasonal patterns from June 2018 to June 2022 in the liquid as well as futures price series of Bitcoin, Ethereum, Litecoin, Ripple XRP and Bitcoin Cash. The results of eigenvalue and trace statistic of Johansen’s test of cointegration discern cointegration between liquid and futures price series of these cryptocurrencies. The estimates of the dynamic conditional correlation model discern momentous long-run persistence, lingering and spillover effects of shocks’ sway on conditional correlations in markets for Bitcoin, Litecoin, Ethereum and Bitcoin Cash. However, the estimates discern momentous short-run and long-run perseverance, lingering and spillover effects in markets for Ripple XRP. The coefficients of VEC model discern unidirectional long-run causal connexion from futures market to liquid market of these cryptocurrencies. However, the significant estimates from the block exogeneity test discern momentous bidirectional short-run causality from liquid market to futures market and from futures’ market to liquid market of these cryptocurrencies. The same results are affirmed by the wavelet coherence analysis, which highlights the full characterization of the direction, persistence and intensity of information flows between these markets. The bidirectional causality in the short run indicates the contribution of both future and liquid returns of these cryptocurrencies to their price discovery mechanism. So, investors in these cryptocurrencies can effectively hedge their price risk by analysing the information of futures market for current and future prices. However, the unidirectional causality in the long run indicates the contribution of future returns of these cryptocurrencies to their price discovery mechanism. So, investors in these cryptocurrencies can effectively hedge their price risk by analysing the information of futures market for future prices only in the long run. This empirical evidence in the present treatise highlights the virtuous performance of futures market in price discovery of these cryptocurrencies, as it is convenient to take leverage positions in these markets due to low transaction costs and the availability of ample futures contracts. The discernment using static, dynamic and wavelet approaches also contributes to the comprehensive body of knowledge encompassing holistic approach covering all facets of interconnectedness theory. Prudent investors and portfolio managers are virtuously inclined to investigate these facets of interconnectedness to enhance their returns through arbitrage dealings and safeguard themselves from adverse effects of temporal price volatility using hedge dealings in derivatives market. The results of the present treatise may benefit these market players in analysing futures market dealings in cryptocurrencies for exploring arbitrage and hedging opportunities. The present exploration of these markets not only aids investors and portfolio managers in enhancing their hedge effectiveness through optimal portfolio allocation, but it also provides signals to financial regulators in monitoring financial contagion and take appropriate policy decisions. So, this knowledge of static and dynamic interconnectedness may enrich the holistic vision of investors, portfolio managers and financial regulators.

Footnotes

Declaration of Conflicting Interests

The author declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding

The author received no financial support for the research, authorship and/or publication of this article.

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