Pattern and determinants of tail-risk transmission between cryptocurrency markets: new evidence from recent crisis episodes

Abstract

The main objective of this study is to investigate tail risk connectedness among six major cryptocurrency markets and determine the extent to which investor sentiment, economic conditions, and economic uncertainty can predict tail risk interconnectedness. Combining the Conditional Autoregressive Value-at-Risk (CAViaR) model with the time-varying parameter vector autoregressive (TVP-VAR) approach shows that the transmission of tail risks among cryptocurrencies changes dynamically over time. During crises and significant events, transmission bursts and tail risks change. Based on both in- and out-of-sample forecasts, we find that the information contained in investor sentiment, economic conditions, and uncertainty includes significant predictive content about the tail risk connectedness of cryptocurrencies.

Introduction

Understanding the nature and extent of the linkages among different financial markets is important for portfolio managers, investors, and policymakers. From a theoretical standpoint, (Engle et al. 1990) established heat waves and meteor shower hypotheses, wherein the heat wave refers to the notion that shocks are market-specific. Conversely, the meteor shower hypothesis suggests that shocks generated in one market are transmitted to others. Over the past few decades, the globalization of financial markets has led to higher levels of financial integration (Beine et al. 2010). Consequently, interdependence among international stock markets has grown substantially (e.g., Kim et al. 2005; Morana and Beltratti 2008). This is detrimental to international diversification and increases the transmission of shocks among financial markets (Karolyi and Stulz 1996).

Recognizing this, renewed interest in alternative asset classes such as cryptocurrencies has emerged. Indeed, cryptos are enjoying rising popularity, global reliance, and increasing trading volume. Cryptocurrencies emerged after the subprime crisis of 2008, when credit in the global financial system collapsed (Maghyereh and Abdoh 2022a; Maghyereh and Al-Shboul 2023). Constituting an attractive asset class, cryptocurrencies are often considered “safe haven” assets against other asset classes (Urquhart and Zhang 2019). First released by Nakamoto (2008), Bitcoin has received considerable attention from the media and investors. Starting humbly at 0.0001 USD in 2008, cryptocurrencies grew significantly, reaching a market capitalization of $916.070 billion in October 2022 (see Table 1). Karim et al. (2022) maintain that the growth in cryptos over the last two decades can be attributed to nonfungible tokens, decentralized financial instruments, and metaverses.

Table 1 The sample cryptocurrencies by market capitalization

Tail risk transmission among cryptocurrencies can occur through various channels, such as market sentiment, direct investments in multiple cryptocurrencies, or spillovers from economic conditions. Several studies show a high degree of correlation among the returns of various cryptocurrencies, suggesting that tail risk transmission may be a significant issue in the cryptocurrency market. Accordingly, this study examines tail dependence between major cryptocurrencies and disentangles the underlying causes of tail dependence. The analysis incorporates Bitcoin, Ethereum, Tether, Binance, XRP, and Cardano, which constitute the six major cryptocurrencies in the market today and jointly account for approximately 71% of the overall market capitalization of cryptocurrencies.

A related subject to the financial spillover literature¹ is the hypothesis of financial contagion; the fundamental view of contagion explains the propagation of shocks across countries via real channels such as bilateral trade, trade of similar goods with a common market, monetary policy coordination, and macroeconomic similarities (see Corsetti et al. 2005). Alternatively, Forbes and Rigobon (2002) defined financial contagion as a significant increase in correlations after a shock to a single market. In other words, contagion exists if markets show a significant increase in co-movement during a crisis compared to periods of stability. This phenomenon can be explained by banking sector inefficiencies or investor herding. The 2008 subprime crisis revealed how the interaction between financial institutions could pose a systemic risk to the entire financial system and threaten the functioning of the financial market. Consequently, financial contagions and extreme-risk spillovers have received widespread academic attention. Consequently, multiple frameworks have been proposed to examine the risk propagation mechanisms. For example, (Diebold and Yilmaz 2009, 2012, 2014) devised the connectedness index and network topologies. Another approach involves quantile regression and CAViaR (Koenker and Hallock 2001; Engle and Manganelli 2004a; White et al. 2015), which describe the dependence structure in the median along the tail of the conditional distribution.

As financial assets, cryptocurrencies are secluded from conventional financial systems that use blockchain² technology (Yermack 2017). While many different variants of cryptocurrencies are available, Bitcoin was the first, created in 2009 using a scheme proposed by Nakamoto (2008), enjoying considerable market capitalization and trading volume. Using a platform similar to that adopted by Bitcoin, Litecoin is a peer-to-peer cryptocurrency introduced in 2011. Using the blockchain generated by Ethereum, Ether is a cryptocurrency that dates back to 2013. Ripple is based on the Ripple Platform, a settlement scheme introduced in 2012 (Borri 2019).

Within the literature³ examining interrelationships among cryptocurrencies, Corbet et al. (2018) argue that Bitcoin, Litecoin, and Ripple are highly interconnected with parallel trends in returns and volatility. From a methodological standpoint, Bouri et al. (2017b), Canh et al. (2019), Katsiampa et al. (2019), and Bouri et al. (2021a, b) studied the risks of volatility connectedness among cryptocurrencies using GARCH-type models. Katsiampa (2017) compares the performance of different GARCH models in examining the links among cryptocurrencies and finds that AR-CGARCH best fits the data. While a few studies employ the wavelet coherency approach (see Omane-Adjepong and Alagidede 2019; Kumar and Anandarao 2019), a major strand of the literature exploits variants of the spillover index and network topology of variance decompositions proposed by Diebold and Yilmaz (2009, 2012, 2014) to analyze the risk spillovers among cryptocurrencies. Prominent examples include the works of Koutmos (2018), Yi et al. (2018), Ji et al. (2019), and Gillaizeau et al. (2019). Yi et al. (2018) examine multiple cryptocurrencies and find that Bitcoin is a net transmitter of volatility spillovers to other cryptocurrencies. Similarly, Ji et al. (2019) maintain that popular cryptocurrencies, such as Bitcoin, Ethereum, and Litcoin, are net transmitters of volatility. These results contradict those of Katsiampa et al. (2019), who use GARCH models to report that Bitcoin is not a dominant cryptocurrency despite enjoying the highest capitalization.

The novelty of the literature is that some studies examine the impact of exogenous variables on the connectedness of cryptos. For example, Ji et al. (2019) explored connectivity via return and volatility spillovers across six cryptocurrencies using the connectedness method of Diebold and Yilmaz (2012), Diebold and Yılmaz (2014). Their findings indicate that Litecoin and Bitcoin are at the core of an interconnected network of returns and volatility. Furthermore, their analyses reveal that trading volume, the investment substitution effect, and global financial uncertainty are the factors that determine net directional spillovers among cryptocurrencies. Sohag and Ullah (2022) used the cross-quantilogram technique to examine the impact of Twitter-based economic uncertainty on Bitcoin returns and volatility. Their findings indicated that Twitter-based economic uncertainty significantly influences volatility, whereas Bitcoin returns are net recipients. Parallel to this, Bouri et al. (2021c) expand spillover research to examine the interactions in the second moment and reveal that the entire conditional distribution of volatility connectedness is positively linked to traders’ happiness at its lower quantiles of sentiment, despite the contrary being detected at the higher quantiles of investor happiness. Similarly, Al-Shboul et al. (2022) use the Quantile-VAR method to demonstrate that market uncertainty significantly impacts the interconnectedness of cryptocurrencies.

While the abovementioned studies attempt to investigate the time-varying return and volatility spillovers among cryptocurrencies, the inherent joint dynamics between extreme (tail) risks have not been directly investigated. Dynamic tail risk spillovers indicate a tail risk contagion pattern within a network of variables (Chatziantoniou et al. 2022). In this sense, analyzing tail risk connectivity is critical for examining the contagious effects among cryptocurrencies. Furthermore, previous studies used GARCH models to measure risk; however, these methods may have underestimated the structure of extreme market events (Han et al. 2016). In addition, the conditional variance characterized by GARCH models is a symmetric risk measure,⁴ which makes it insufficient to examine the tail risk of a skewed distribution (Xu et al. 2021). Therefore, volatility does not accurately measure tail risk spillovers among financial assets. Additionally, the spillover index generally focuses on mean linkages and fails to account for tail dependence. Cryptocurrency returns have significantly heavier tails than traditional financial assets (Bouri et al. 2017b, a). Additionally, existing studies lack in-depth analyses of the in-sample and out-of-sample predictive power of dynamic tail risk connectedness concerning the cryptocurrency market’s investor sentiment and macroeconomic and uncertainty indicators. Furthermore, some existing studies have examined the risk interconnectedness among cryptocurrencies during the COVID-19 outbreak but have not used the most updated sample period that covers the COVID-19 vaccination and Russian-Ukrainian (R-U) war.

For methodological design, we apply the conditional autoregressive Value at Risk (CAViaR) framework developed by Engle and Manganelli (2004a) to measure the tail risks for each selected cryptocurrency. The CAViaR framework uses a semiparametric approach based on autoregression to model the dynamic quantile, which, unlike the unconditional Value-at-Risk (VaR), makes no assumptions about the financial series distribution and instead explores the behavior characteristics of the distribution's tail (Engle and Manganelli 2004a). Hence, our approach is distribution-free, ideal for financial series that do not follow a normal distribution (Patton et al. 2019), and capable of capturing the volatility asymmetry and leverage effect. Subsequently, we exploit the results of the CAViaR model to explore the transmission mechanism between the tail risks of different cryptocurrencies. In detail, we use the TVP-VAR connectedness approach of Antonakakis et al. (2020) to construct the time-varying spillover among tail risks. This approach is advantageous as it provides information on the directions and magnitudes of connectedness in tail risks under different market conditions (i.e., during normal and crisis periods). Essentially, this method ameliorates the traditional connectedness method of Diebold and Yilmaz (2012), Diebold and Yılmaz (2014) via the following: (1) It precisely monitors parameter variations; (2) It avoids lost observations; (3) It is more robust to the existence of outliers; and (4) It does not require the selection of arbitrary window size. While several studies have investigated the tail risk of crypto-asset markets, only a few have focused on their tail-risk interconnectedness. Furthermore, to our knowledge, no study investigated the common factors that forecast the dynamic tail-risk connectedness among different crypto-asset markets. Thus, in addition to examining the extreme risk transmission between the crypto-asset markets, this study aims to investigate factors (investor sentiment, economic conditions, and economic uncertainty) that can help predict the dynamic connectedness. This is important for academics interested in joining the debate on the dynamics of contagion among cryptocurrencies. Moreover, investigating the channels behind financial contagion is important for policymakers, as they can design policies and macroeconomic strategies to mitigate contagion and preserve financial stability. Finally, the study period encompasses multiple events, including the COVID-19 pandemic and the Russian-Ukrainian conflict.

The results indicate a higher level of total tail connectedness during turbulent periods such as the COVID-19 era and the Russian-Ukrainian war. A similar trajectory of tail risk connectedness was observed at 1% and 5% risk levels. Furthermore, embedding information from the Aruoba-Diebold-Scotti Business Condition Index, Fear & Greed Crypto Index, Geopolitical Risk Index, Economic Policy Uncertainty Index, and Twitter-based Economic Uncertainty Index ameliorates the predictability of the total tail connectedness of cryptocurrencies in the system. From the perspective of pairwise connectedness, Bitcoin and Ethereum display the strongest links. Finally, despite having less capitalization than Bitcoin, Ethereum is the most influential cryptocurrency, despite the increasing dynamism of Binance, XRP, and Cardano in 2022.

The rest of the paper proceeds as follows: Section two discusses the econometric framework, while Section three details the data. Section four presents the empirical results, and section five concludes.

Methodology

Measuring tail risks

This study applies the conditional autoregressive Value at Risk $(CAViaR)$ framework developed by Engle and Manganelli (2004a) to measure tail risks for each of the selected cryptocurrencies. To show tail risk explicitly, the $CAViaR$ framework uses a semiparametric approach based on autoregression to model dynamic quantiles. Compared with the unconditional Value-at-Risk (VaR) method of Danielsson and Vries (2000) and $CoVaR$ method of Adrian and Brunnermeier (2016), this framework makes no assumptions about financial series distribution. Instead, it explores the behavioral characteristics of the distribution's tail (Engle and Manganelli 2004). Hence, it is distribution-free and ideal for financial series that do not follow a normal distribution (Wang et al. 2018; Patton et al. 2019; Maghyereh and Yamani 2022). It can capture volatility asymmetry and the well-known leverage effect. Following Engle and Manganelli (2004), the general $CAViaR$ specifications are as follows.

(1)

where ${x}_{t}$ is the returns of cryptocurrency at time $t$, ${f}_{t}\left(\beta \right)\equiv {f}_{t}\left({x}_{t-1},{\beta }_{\theta }\right)$ is the time $t \theta -$ quantile of the distribution of cryptocurrency returns at time $t-1$, $p=q+r+1$ is the dimension of $\beta$ and is a function of a finite number of lagged values of observables (${x}_{t-j}).$ Notice that the subscript $\theta$ is omitted from ${\beta }_{\theta }$ in Eq. (1) for simplicity. Because of the autoregressive terms $\sum_{i=1}^{q}{\beta }_{i}{f}_{t-i}\left(\beta \right),$ the quantile is guaranteed to vary "smoothly" over time. The purpose of the term is to link ${f}_{t}\left(\beta \right)$ to observable variables inside the information set.

As shown by Eq. (1), VaR is affected equally by both positive and negative returns. To allow for asymmetric effects, we adopt the asymmetric slope (AS) quantile specification as follows:

$${f}_{t}\left(\beta \right)={\beta }_{1}+{\beta }_{2}{f}_{t-1}\left(\beta \right)+{\beta }_{3}\left|{y}_{t-1}\right|I\left({y}_{t-1}>0\right)+{\beta }_{4}\left|{y}_{t-1}\right|I\left({y}_{t-1}<0\right)$$

(2)

where ${y}_{t-1}$ is the observed cryptocurrency returns at $t-1$, the coefficient ${\beta }_{1}$ is the model constant, ${\beta }_{2}$ is the coefficient on the lagged $VaR$, and the two coefficients, ${\beta }_{3}$ and ${\beta }_{4}$ capture the asymmetric (i.e., the response of $VaR$ to positive and negative returns). Our analysis estimated the $AS-CAViaR$ and provided tail risks for 1% and 5% VaR levels. We used the Dynamic Quantile (DQ) test introduced by Engle and Manganelli () to ensure that the model best fits the data.

Dynamic connectedness method

In the subsequent stage, we use the results retrieved from the CAViaR model to explore the transmission mechanism between the tail risks of cryptocurrencies. This study uses the Time-Varying Parameter Vector Autoregressive (TVP-VAR) connectedness approach of Antonakakis et al. (2020) and Chatziantoniou et al. (2022) to construct a time-varying spillover among the tail risks. This approach offers a rich source of information on the directions and magnitudes of connectedness between tail risks under different market conditions (i.e., during normal and crisis periods).

Following Antonakakis et al. (2020), Chatziantoniou et al. (2022), Sohag et al. (2023a), and Cui and Maghyereh (2023a, b), we use a TVP-VAR (p) model in the following form⁵:

$${y}_{t}={\Phi }_{t}{y}_{t-1}+{\epsilon }_{t} {\epsilon }_{t}\sim N\left(0,{S}_{t}\right)$$

(3)

$$vec\left({\Phi }_{t}\right)=vec\left({\Phi }_{t-1}\right)+{\xi }_{t} {\xi }_{t}\sim N\left(0,{{\beth }}_{t}\right)$$

(4)

where ${{\text{y}}}_{{\text{t}}}$ is a $N\times 1$ vector of time series variables of interest (i.e., tail risk series), ${\epsilon }_{t}$ and ${\xi }_{t}$ are an N × 1 vector, ${\Phi }_{t}, {S}_{t} {\text{and}} {\beth }_{t}$ are $N\times N$ matrices. The vector autoregression with time-varying parameters, TVP-VAR(1), is then expressed by ${{\varvec{y}}}_{t}=\sum_{i=1}^{p}\Phi {{\varvec{y}}}_{t-i}+{\varepsilon }_{t}$, where $\Phi$ is a parameter matrix that summarizes all of the dynamic interactions among the tail risk series,⁶$\varepsilon$ is a white noise that follows a normal distribution and $\sum$ covariance matrix. Typically, the formula for the moving average can be written as ${{\varvec{y}}}_{t}=\sum_{i=0}^{\infty }A{\varepsilon }_{t-i}$.

Generalized connectedness may be determined using generalized forecast error variance decompositions (GFEVD) after the time-varying coefficients and variance–covariance matrices are computed using TVP-VAR(1).⁷ Following this framework, the H-step-ahead forecast error variance decomposition is defined as

$${\theta }_{ij,t}^{g}\left(H\right)=\frac{{S}_{jj,t}^{-1}\sum_{h=0}^{H-1}{\left({e}_{i}^{^{{\prime}}}{A}_{t}{S}_{t}{e}_{j}\right)}^{2}}{\sum_{j=1}^{k}{\sum }_{t=1}^{H-1}\left({e}_{i}{A}_{t}{S}_{t}{A}_{t}^{^{{\prime}}}{e}_{i}\right)}, i,j,1,\dots ,N$$

(5)

where ∑ is the variance matrix of the vector of errors ε, and ${{\text{S}}}_{jj}$ is the standard deviation of the error term of the ${j}{th}$ variable. Finally, ${e}_{i}$ is a selection vector with one for the ${i}{th}$ element and zero otherwise. This yields an $N\times N$ matrix $\Phi \left(H\right)={\left[{\Phi }_{ij}(H)\right]}_{ji}$, where each entry gives the contribution of variable $j$ to the forecast error variance of variable $i$.

Equation (5) can be used to determine the total directional connectedness To others (i.e., shock variable $i$ transmits its shock to all other variables $j$) as follows:

$${S}_{i\to j,t}^{g}\left(H\right)=\frac{\sum_{\begin{array}{c}i,j=1\\ i\ne j\end{array}}^{N}{\widetilde{\theta }}_{ji,t}^{g}\left(H\right)}{\sum_{i,j-1}^{N}{\widetilde{\theta }}_{ji,t}^{g}\left(H\right)}\times 100$$

(6)

Then, the total directional connectedness From others (shocks received by variable $i$ from variable $j$) is calculated as

$${S}_{i\leftarrow j,t}^{g}\left(H\right)=\frac{\sum_{\begin{array}{c}j=1\\ i\ne j\end{array}}^{N}{\widetilde{\theta }}_{ij,t}^{g}\left(H\right)}{\sum_{j=1}^{N}{\widetilde{\theta }}_{ij,t}^{g}\left(H\right)}\times 100$$

(7)

NET total directional connectedness (i.e., the net of the influencing variable $i$ to the other variables $i$) can be computed by offsetting (6) and (7) as follows:

$${S}_{i,t}^{g}\left(H\right)={S}_{i\to j,t}^{g}\left(H\right)-{S}_{i\leftarrow j,t}^{g}\left(H\right)$$

(8)

A positive NET total directional connectedness indicates that $i$ variable is a net giver of shocks to another variable, whereas a negative value indicates that variable $i$ is a net receiver.

Finally, the total connectivity index (TCI), which is an overall measure of how all variables are connected, can be defined as

$${S}_{i}^{g}\left(H\right)=\frac{\sum_{\begin{array}{c}i,j=1\\ i\ne j\end{array}}^{N}{\widetilde{\theta }}_{ij,t}^{g}\left(H\right)}{N} \times 100$$

(9)

Data

To explore the analysis, we choose Bitcoin (BTC), Ethereum (ETC), Tether (USD), Binance (BNB), XRP, and Cardano (ADA)—the six major cryptocurrencies on the market today (which together account for around 71% of the overall market capitalization of cryptocurrencies) (see Table 1).⁸ The dataset contains 1786 observations of daily closing prices from September 11, 2017, to September 30, 2022.⁹ The data cover the most recent crises, such as the COVID-19 pandemicpandemic and the Russian-Ukrainian conflict. The data were sourced from Thomson Reuters DataStream. For each cryptocurrency, daily continuous returns are computed as follows: ${r}_{it}=ln\left({p}_{it}\right)-ln\left({p}_{it-1}\right)$, where ${r}_{it}$ denotes the daily returns, and ${p}_{it}$ represents the i-th daily price.

Figure 1 depicts the daily dynamic movements of cryptocurrency prices. The graph indicates that all cryptocurrencies have similar evolutionary patterns.¹⁰ Prices rose abruptly in December 2018 and then fluctuated at lower levels in 2019 and 2020 before rising swiftly and reaching an all-time high in April 2021. Prices declined significantly until they began to rise again in July 2021, peaking in November 2021, and then decreasing again in March 2021.

Fig. 1

Daily cryptocurrencies prices

Table 2 summarizes the descriptive statistics for the daily returns of cryptocurrencies. Binance had the greatest mean positive value, followed by Ethereum, Bitcoin, Cardano, and XRP, while Tether had a negative mean value. The tether had the lowest standard deviation, whereas the cardano had the highest volatility. All series had excess kurtosis and a heavy right tail, suggesting they were leptokurtic. The results of the Jarque–Bera test indicate that all return series are nonnormal. The ADF unit root test results reveal that all the return series are stationary.

Table 2 Summary statistics of daily returns

Figure 2 shows the correlation heatmap of the six cryptocurrencies analyzed. The greater the degree of correlation, the more intense is the color (red). The graph demonstrates a strong correlation between the returns on all six cryptocurrencies. This finding is in line with those of prior studies (e.g., Hu et al. 2019; Ferreira et al. 2020; Al-Shboul et al. 2022; Cui and Maghyereh 2022; among others), which reveal that most cryptocurrency returns are positively correlated.

Fig. 2

Correlation heatmap matrix over the entire sample period

Empirical results

In this section, firstly, we use the model to estimate the tail risk of each cryptocurrency at the 1% and 5% levels. Second, using the TVP-VAR connectedness approach, we study the dynamic tail risk connectedness between the six cryptocurrencies, focusing on the impact of the current crises (i.e., the COVID-19 pandemic and the Russian–Ukraine conflict) on this connectivity. Finally, we perform in-sample and out-of-sample analyses to explore the role of investor sentiment and economic conditions in predicting the total connectedness of the tail risks of cryptocurrencies.

Tail risks results

Using the CAViaR model, we calculate the risk losses at 5% and 1% levels. Table 3 presents the DQ test statistics and p-values based on the adaptive specification (AS) of CAViaR for six popular cryptocurrencies. The p-values of the DQ test show that AS fits the tail risks of all cryptocurrencies. Table 4 presents the summary statistics of daily tail risk at 1% and 5% levels and shows that the risk is higher in XRP and ADA, with higher CAViaR at 1% and 5%, respectively. Figure 3 provides evidence of the substantial risks posed by XRP and ADA, especially in 2018.

Table 3 DQ test for CAViaR specification

Table 4 Summary statistics of daily tail risk

Fig. 3

Daily returns and tail risks (CAViaR) of the cryptocurrencies. Notes: The figure illustrates the returns and estimated 1%/5% CAViaRs of return on the six cryptocurrencies using the asymmetric slope model. The red line represents the daily returns. The blue and black lines represent VaR at 1% and 5% respectively

Tail risks connectedness

Average connectedness

Table 5 presents the static tail risk spillovers between cryptocurrencies at 1% (Panel A) and 5% (Panel B) levels. The rows in Table 5 indicate the contribution of each cryptocurrency to the forecast error variance of a specific crypto in the system. In contrast, columns represent the effect that a specific crypto has on all other cryptos independently. In other words, the main diagonal of the matrix recaps the contribution of shocks in the market i to its own forecast error variance. The off-diagonal column sums (“To others”) along with row sums (“From others”) display the directional connectedness to all variables in the system from i and from all others to j, correspondingly. The row "Net connectedness" represents the total sum of net-pairwise directional spillover expressed as a negative (positive) value for the net recipient (net transmitter). Finally, the TCI stands for the total connectedness index of a whole system.

Table 5 Averaged connectedness among tail risks over the entire sample period

Table 5 depicts the connectedness among tail risks at 1% and 5% levels. At first glance, we observed a general similarity in the results at both levels. The TCI records 65.19% at 5% and 66.17% at 1%. These observations indicate that external rather than intrinsic innovations can explain more than half of the movement forecasts. Furthermore, this result echoes the high connectedness in the tails among cryptocurrencies, which is consistent with Al-Shboul et al. (2022) findings. Indeed, at 1% and 5%, ETC, XRP, and ADA constituted net transmitters to the system, and their net pairwise directional connectedness (NPT) rankings were 1, 2, and 3, respectively. Such outcomes reflect their dominance in the network and the net pairwise setup. On the other hand, BTC, USD, and BNC are net importers of information. This result indicates that BTC lost its status as an important influencer on the movements of other cryptocurrencies, corroborating the findings of Katsiampa et al. (2019).

With readings in their 30 s for self-explained innovations, BTC and ETC are the most integrated cryptos in the system, as approximately 70% of their variances are explained by external factors in the system. Parallel to that, BTC and ETC are strongly connected to each other at 1% and 5% risk levels, with around 17% of BTC variance explained by innovations from ETC and around 21% vice versa. This is in sharp contrast to USD and XRP to a lesser extent. Within the USD, approximately 66% of its forecasted innovations are self-explanatory, and external impact hovers around 33% at both 1% and 5%. These figures designate the USD as the least integrated currency in the system. Interestingly, readings such as − 11.38 at 1% and − 9.85% at 5% net connectedness values for USD make it the least influential crypto in the system.

From a directional tail risk transmission standpoint, the node size in Fig. 4 reflects the magnitude of the net sender/receiver of spillovers, which depicts the strength of the spillovers. The blue color of a node indicates that the market is a net giver of spillovers, whereas the yellow color labels it a net receiver of spillovers. Figure 4 provides information on the spillover trends regarding direction and intensity. While the results at 1% and 5% remain broadly similar, Fig. 4 presents the following discrepancies; First, at the 1% tail risk level, BNB imports information from ETC, ADA, and XRP, whereas XRP is the sole exporter of information to BNB at 5%. Second, BTC’s vulnerability to innovation from ADA, XRP, and BNB evaporated at the 1% level. Such discrepancies highlight important information about the extreme spillovers and financial contagion among cryptos. Conversely, and consistent with Table 5, USD is on the receiving end of other cryptos, regardless of the risk quantile. Similarly, corroborating the findings of Xu et al. (2021), the ETC and XRP originate from important flows of tail risk innovations for other cryptos.

Fig. 4

Tail risk directional connectedness network over the entire sample period. Note: The connectedness is calculated using a TVP-VAR model with a length of order 1 chosen by the BIC. The generalized forecast error variance decomposition is based on a 20-step-ahead. Each node represents a cryptocurrency, the size of the node indicates its information contribution to the system, the width of the line denotes the magnitude of the information spillover, and the arrow symbolizes its direction

Time-varying connectedness

Figure 5 depicts the time-varying connectedness at 5% and 1% risk levels. Like the static model results, the tail risk connectedness follows a similar trajectory at 1% and 5% risk levels. In 2018, the connectedness index became relatively high and set around 80% before increasing sharply in March 2020, reaching more than 95%. These results echo the high level of tail risk connectedness among cryptocurrencies, as Borri (2019) argues. Following Kumar et al. (2022) and Cui and Maghyereh (2022), the COVID-19 impact persisted in 2020, resulting in a soaring connectedness index throughout the year only to fall sharply in 2021; the latter can be associated with the lifting of COVID-19 precautions and “return to normal” policies. Between 2021 and 2022, the level of connectedness rebounded to a new average that hovered around 50%. However, in 2022, the TCI returned to its pre-COVID-19 average of 70% due to the geopolitical stress accompanying the Russian-Ukrainian war. The extraordinary circumstances that persisted amid the COVID-19 era and the geopolitical stress in Ukraine triggered important shifts in investor behavior, wherein higher interest in non-conventional asset classes (such as cryptos) emerged. This can be explained as follows. First, lockdowns triggered uncertainties around conventional businesses amid the COVID-19 pandemic. Second, cryptocurrencies can be an alternative means of sending transfers circumventing Western sanctions against Russia. Finally, cheap energy prices in Russia might prompt higher crypto-mining activities, especially during geopolitical turbulence and uncertain business environments.

Fig. 5

Dynamic total connectedness. Notes: The results are based on a TVP-VAR model with a length of order 1 chosen by the BIC. The generalized forecast error variance decomposition is based on a 20-step-ahead

These results corroborate the findings of Gillaizeau et al. (2019), who argue that bitcoin prices display strong volatility spillovers from conventional currencies during periods of high uncertainty. Simultaneously, our results display conventional cyclical movements in risk spillovers, which contradict the increasing trend in risk connectedness proposed by Xu et al. (2021). Extreme connectedness amid turbulent circumstances may signal herding behavior among cryptocurrency traders, as (Kumar and Anandarao 2019) argued. Lastly, the total risk connectedness during the COVID-19 phase was more intense than during the Russian-Ukrainian War because of the larger scope of the former.

Figure 6 illustrates the transmission of shocks from a specific cryptocurrency to others, and Fig. 7 illustrates the transmission from other cryptocurrencies to a specific currency. Intuitively, the individual charts in Fig. 5 present the total dynamic connectedness of the system. Within this, we can see that the overall connectedness (Fig. 5) mimics the ETC chart, further reflecting ETC's large footprint in the system. This is consistent with the findings of Ji et al. (2019). While this is visible from 2018 to 2022, the increasing dynamism of BNB, XRP, and ADA can explain the higher overall connectedness in 2022. Notably, a sudden interest in specific cryptos can be linked to the “fear of missing out” of individual investors and may yield to financial bubbles (see Geuder et al. 2019). Essentially, our results align with those of Luu Duc Huynh (2019), who exploited Granger causality methods alongside copulas and reported that BTC tends to be influenced by ETC and XRP. However, contrary to our results, Luu Duc Huynh (2019) finds that the ETC trajectory is independent of other cryptos.

Fig. 6

Transmits shock of tail risk from asset i to all other assets. Notes: The results are based on a TVP-VAR model with a length of order 1 chosen by the BIC. The generalized forecast error variance decomposition is based on a 20-step-ahead

Fig. 7

The directional connectedness of one asset receives from other assets. Notes: The results are based on a TVP-VAR model with a length of order 1 chosen by the BIC. The generalized forecast error variance decomposition is based on a 20-step-ahead

Subtracting the values presented in Fig. 7 from those in Fig. 6 produces Fig. 8, which illustrates net total directional connectedness. Mirroring the findings in Table 5, the results do not vary much at the 1% and 5% levels. ETC is the system's most dominant crypto and net contributor throughout most of the sample period. However, while being a consistent net contributor of information before 2020, BTC lost its status and became a net receiver of shocks from 2021 until the end of the sample. This outcome contradicts the results of Omane-Adjepong and Alagidede (2019) and Koutmos (2018), who argue that BTC played a dominant role in influencing other cryptos. The difference in results can be attributed to the newer sample in our study, the different econometric approach, and the high dynamism in cryptocurrency markets. The USD is the polar opposite of the ETC and has been a net receiver of shocks throughout most of the sample period. Likewise, the BNB acted as a net importer of shocks from 2018 to 2020 and subsequently switched to a net exporter. Finally, although both XRP and ADA fluctuate between net contributors and receivers of information, the former is generally more influential in the system.

Fig. 8

Net total directional connectedness. Notes: The results are based on a TVP-VAR model with a length of order 1 chosen by the BIC. The generalized forecast error variance decomposition is based on a 20-step-ahead

Figure 9 shows net directional connectedness. Viewing both Panels A (depicting the tail risk at 1%) and Panel B (depicting the tail risk at 5%), we can see clear evidence of BTC losing its influence on other currencies as time passes. This can be observed in the BTC-ETC and BTC-BNB pairs. USD, whereas generally on the receiving end, received strong spills in early 2022 from the BNB, XRP, and ADA. Our results conform with those of Xu et al. (2021), who examine tail risk spillovers and report an active role for ETC and a passive role for BTC.

Fig. 9

Net pairwise directional connectedness. Notes: The results are based on a TVP-VAR model with a length of order 1 chosen by the BIC. The generalized forecast error variance decomposition is based on a 20-step-ahead

Figure 10 illustrates the dynamic pairwise connectedness of the sampled cryptocurrencies in an amalgamated manner. Notably, the connectedness between BTC and ETC is consistently higher than that of the other pairs, regardless of the tail risk specification and period. Both well-established and highly capitalized currencies can explain such links (see Table 1). The USD and BTC pairwise connectedness with other currencies experienced a jump between 2020 and 2021, whereas a slump in 2021 occurred in the XRP and BNB connectedness with other cryptos.

Fig. 10

Dynamic pairwise connectedness. Notes: The results are based on a TVP-VAR model with a length of order 1 chosen by the BIC. The generalized forecast error variance decomposition is based on a 20-step-ahead.

The impact of investor sentiment and economic conditions on tail risks connectedness

The empirical evidence in the previous section shows that the transmission of the total tail risk among cryptocurrencies changes dynamically over time. Transmission bursts and tail risks change during crises and other significant events. Hence, we hypothesize that investor mood and economic conditions can explain tail risk transmission. We hypothesize that the transmission of tail risks may increase when fear-induced emotions increase and economic circumstances deteriorate. Therefore, this section examines the extent to which investor mood, economic conditions, and economic uncertainty can predict the connectedness among cryptocurrency tail risks.

To proxy for investor emotions and sentiment, we use the Fear & Greed Crypto Index (FGCI). This index gauges investors’ behavior and emotions in the cryptocurrency market. Using a needle that moves from left to right and ranges between 0 and 100, FGCI indicates whether investors are now feeling bold or afraid. The lower value represents "more fearful investors," whereas the higher value represents "more greedy investors.” The value of the index is based on several factors, including the level of volatility in the cryptocurrency market, the volume of trade, social media momentum, and the dominance of Bitcoin. The FGCI data were derived from https://alternative.me/crypto/.

To proxy for economic conditions, we use the Aruoba-Diebold-Scotti Business Condition Index (ADS Index), which tracks real business conditions at a high frequency and is based on economic indicators collected at varying frequencies. An index is constructed such that its average value is zero. Progressive positive values of the index indicate progressive improvement in business conditions and a better-than-average business environment. The ADS index data were downloaded from the official website of the Federal Reserve Bank of Philadelphia at https://www.philadelphiafed.org/surveys-and-data/real-time-data-research/ads.

As uncertainty proxies, we use the Geopolitical Risk Index (the GPR index hereinafter) by Caldara and Iacoviello (2022), the Economic Policy Uncertainty Index (the EPU index hereinafter) by Baker et al. (2016), and the Twitter-based Economic Uncertainty Index (the TEU index hereinafter). Based on ten newspapers, the GPR index assesses the proportion of total news stories addressing geopolitical tensions. GPR index data were obtained from https://www.matteoiacoviello.com/gpr.htm. The EPU index measures economic policy uncertainty, and its value depends on the number of EPU articles published, the number of federal tax codes set to expire, and the number of disagreements among forecasters about future economic conditions. The TEU index is constructed based on all messages transmitted over the Twitter social media network containing keywords related to “uncertainty” and “economy.” Data on the EPU and TEU indices were downloaded from the Economic Policy Uncertainty website at https://www.policyuncertainty.com/index.html.

Table 6 presents the summary statistics for the variables used in the prediction models, and Fig. 11 depicts the daily time series of these variables. The figure shows that the ADS, while generally hovering around zero, sharply decreased around the onset of the COVID-19 pandemic. This observation mirrors the lockdown and associated business closures. On the other hand, GPR experienced more fluctuations that culminated in a peak during the Russian-Ukrainian war. TEU and EPU display similar trajectories, wherein a break was noticed between the pre- and post-COVID-19 eras in 2020. Finally, the FGCI appeared to follow a distinctive pattern away from geopolitical and biological hazards.

Table 6 Summary statistics for variables used in prediction regressions

Fig. 11

Time-series plots of the variables used in the prediction model. Notes: TCI: total connectedness index:FGCI: Fear & Greed Crypto Index; ADS: Aruoba-Diebold-Scotti Business Condition Index; GPR: Geopolitical Risk index; EPU: Economic Policy Uncertainty; index; TEU: Twitter-based economic uncertainty index

Causality test

Before discussing the prediction models, we check the causality between each investor mood, economic condition, economic uncertainty variable, and the connectedness of the cryptocurrencies' tail risks. For this purpose, we utilized the novel time-varying Granger causality test proposed by Shi et al. (2020). Compared with traditional Granger causality test statistics, this test is robust to heteroskedasticity, deterministic trends, and nonlinearity. Furthermore, the test is not sensitive to outliers, skewness, or time window selection (Maghyereha et al. 2022).

Table 7 reports the Wald test statistics for the Granger causality test using recursive evolving heteroskedasticity algorithms. We find evidence of Granger causality from all predictable variables to the connectedness of the cryptocurrencies' tail risks over the entire sample period. Figure 12 depicts the recursively evolving Granger causality test statistic (Wald statistic sequence) and their bootstrapped 10% and 5% critical values (lower- and upper-horizontal lines). The minimum window size is set at 60 days (two months). BIC selects the lag length for the whole sample period with a maximum lag order of 12. In graphs, if the Wald statistic sequence surpasses its corresponding critical value during a period, then a significant causality is evident. Confirming the results in Table 7, causality is evident at the 1% and 5% risk levels. Yet, a time-varying element is detected; within this, the causality running from EPU, GPR, and FGCI is short-lived, whereas ADS and TEU display a consistent causal footprint on the TCI of cryptos starting from 2020 until the end of the sample.

Table 7 Wald test statistics for time-varying Granger causality

Fig. 12

Time-varying Granger causality tests. Notes: The time-varying causality is obtained from a lag-augmented VAR (LA-VAR) model with d = 1. The ag orders are determined by BIC. Wald test statistics computed using recursive evolving-heteroskedasticity algorithms. Like Shi et al. (2020), the 10% and 5% bootstrapped critical values (lower- and upper-horizontal lines) are based on 199 replications

In-sample regression

Our analysis in this subsection is based on the following predictive model (Westerlund and Narayan 2012, 2015; Salisu et al. 2022, 2023):

$${{\text{TCI}}}_{t}={\beta }_{0}+\sum_{i=1}^{7}{\beta }_{i}{X}_{jt-i}+\gamma \left({X}_{jt}-\varphi {X}_{jt-1}\right)+{\varepsilon }_{t}$$

(10)

where ${{\text{TCI}}}_{t}$ is the total connectivity index between the tail risks of cryptocurrency at time $t$, $X$ is one of the investor sentiment, economic conditions, and economic uncertainty indicators (i.e., FGCI, ADS, GPR, EPU, and TEU). We add the lags of the indicators to control for persistence. ${\beta }_{0}$ is the intercept, ${\beta }_{i}$ is the coefficient of the effect of the indicator, and the error term ε is assumed to be independent and identically distributed with mean 0 and constant variance. Following Westerlund and Narayan (2012, 2015) and Salisu et al. (2022, 2023), we added the term $\gamma \left({X}_{jt}-\varphi {X}_{jt-1}\right)$ to the model to eliminate the potential endogeneity bias (that would be present due to model misspecification and/or omitted variables and structural break) as well as any potential persistence effect. Based on the aforementioned model's in-sample estimate, we examine the null hypothesis of no predictability by testing the restriction $\sum_{i=1}^{7}{\beta }_{i}=0$ using the Wald joint test.¹¹ The rejection of the null hypothesis implies the predictability of the variable of interest for the cryptocurrencies' tail risk connectedness.

Table 8 presents the results of the in-sample predictability. This table reports the Wald test statistic and the corresponding p-value for the null hypothesis, which states that the slope coefficient in the predictive regression is zero. Our findings indicate that all five variables have a strong predictive ability for cryptocurrencies' tail risk connectedness because the null hypothesis of a zero-slope coefficient can be rejected at conventional significance levels in all five univariate regressions. These results confirm the relative importance of investor sentiment and economic conditions in the connectedness of cryptocurrency tail risks.

Table 8 In-sample prediction

Out-of-sample prediction

Our last stage of the analysis consists of the out-of-sample forecast performance of the predictors in Eq. (10) compared with a random-walk-with-drift benchmark model, $AR(1)$: ${{\text{TCI}}}_{t}={\beta }_{0}+{\mathrm{\delta TCI}}_{t-1}+{\varepsilon }_{t-1}.$ To conduct out-of-sample forecasting, we followed Clark and West (2007) and divided our full sample into an in-sample period spanning from September 11, 2017, to May 30, 2021, and an out-of-sample period from June 1, 2021, to September 30, 2022. Our out-of-sample period, therefore, covers roughly 25% of the entire sample period. We investigate out-of-sample forecasting performance over the forecasting horizons $h \in \{10, 20, 30\}$ days ahead using a recursive window technique. The forecasting performance was evaluated using the mean square forecast error (MSFE)-adjusted statistics from Clark and West (2007). The null hypothesis of the MSFE-adjusted statistics is that the model has no predictability and that the model containing information on investor sentiment/economic conditions does not improve the connectedness of the cryptocurrencies' tail risks.

The results of the MSFE-adjusted statistics in Table 9 confirm the improved predictability of the model containing information on FGCI, ADS, GPR, and TEU conditions at 10, 20, and 30-day horizons with a p-value of 1%. Information on EPU improves the model's forecasting ability at the 5% risk level for all time horizons, whereas, at the 1% risk level, the model’s forecasting ability improves at 10 and 20 days. Hence, both the in-sample and out-of-sample findings lead us to conclude that the information contained in investor sentiment and economics includes predictive content about the connectedness of cryptocurrencies in a constant manner. The positive sign of the predictors indicates that higher uncertainty (risk) is linked to trading behavior expected to push cryptos in the same direction and is consistent with financial contagion effects.

Table 9 Out-of-sample prediction (MSFE-adj.)

Additional results

The empirical findings of the Granger causality test and the in-sample and out-of-sample forecasts indicate that the information contained in investor sentiment, economic conditions, and uncertainty includes significant predictive content about the tail risk connectedness of cryptocurrencies. While the abovementioned methods capture the response of one variable to another instantaneously (i.e., at a given point in time), they are silent on the time–horizon relationship, and hence, our results may be subject to some limitations.¹² To validate our results across different time horizons, we employed two novel methods: the cross-quantilogram (CQ) method of Han et al. (2016) and the quantile cross-spectral dependence (QS) approach of Baruník and Kley (2019). The CQ allows us to test the spillover effect between variables across different quantiles. Unlike other methods that focus solely on the direction of the relationship, the CQ method allows for a simultaneous assessment of the link between two variables in terms of their duration and direction by considering long lags (Sohag et al. 2022,2023a, b; Husain et al. 2022). QS is valuable because it captures the interdependence between variables at different time frequencies and quantiles. The following section provides a brief overview of the proposed method.¹³

Cross-quantilogram (CQ) method

As in Han et al. (2016), let there be a set of ${{\varvec{X}}}_{t}=\left({x}_{t,j1},{x}_{t,j2}\right)$ that are two strictly stationary series, cross-quantilogram is defined as the cross-correlation of the quantile-exceedance processes $\left\{{x}_{1t-k}\le {q}_{1t-k}\left({\tau }_{1}\right)\right\}$ and $\left\{{x}_{2t-k}\le {q}_{2t-k}\left({\tau }_{2}\right)\right\}$ where ${q}_{it-k}\left({\tau }_{i}\right)$ is the conditional ${\tau }_{i}-{\text{quantile}}$ of ${x}_{it}$ for ${\tau }_{i} \in (0, 1)$, for $i = 1, 2$, and $k=0,\mp 1,\mp 2,\dots$ represents the lag length that is able to capture the cross-quantile dependence between the variables across various time horizons, thereby quantifying the strength and duration of dependency. The cross-correlation of the various quantile-hit processes is then described as

$${\rho }_{\tau }\left(k\right)=\frac{E\left[{\psi }_{\tau 1}\left({x}_{1t}-{q}_{1t}\left({\tau }_{1}\right)\right){\psi }_{\tau 2}\left({x}_{2t-k}-{q}_{2t-k}\left({\tau }_{2}\right)\right)\right]}{\sqrt{E\left[{\psi }_{\tau 1}^{2}\left({x}_{1t}-{q}_{1t}\left({\tau }_{1}\right)\right)\right]}\sqrt{{\psi }_{\tau 2}^{2}\left({x}_{2t-k}-{q}_{2t}\left({\tau }_{2}\right)\right)}}$$

(11)

where ${\psi }_{\tau }\left({x}_{1t}\right)\equiv 1\left[{y}_{1t}\le {q}_{1t}\left({\tau }_{i}\right)\right]$-${\tau }_{i}$ represents the quantile-hit process.$\widehat{{\rho }_{\tau }}\left(k\right)\in \left[-\mathrm{1,1}\right]$ with $\widehat{{\rho }_{\tau }}\left(k\right)=0$ indicates the absence of any cross-dependence between the variables.

Han et al. (2016) recommend using a quantile version of the Box-Ljung statistics to test for directional predictability from one time series to another over a set of quantiles ${\widehat{Q}}_{\tau }$(K), as follows

$${\widehat{Q}}_{\tau }\left(K\right)\equiv \frac{T\left(T+2\right)\sum_{k=1}^{p}{\widehat{\sigma }}_{\tau }^{2}}{T-k}$$

(12)

The cross-quantilograms between the tail risk connectedness at 5% and each predictor are displayed in Fig. 13.¹⁴ We report the cross-quantilograms of lag k = 1, 2, …, 60 over the lower (α = 0.05), middle (α = 0.5), and extreme upper (α = 0.95) quantiles.

Fig. 13

Cross-quantilograms correlation. Note: The figure plots the directional predictability from each predictor variable to total tail risk connectedness index estimated at 5% CAViaRs. The graph depicts the directional predictability at lag k = 1, 2, …, 60 over the lower quantile (α = 0.05), middle (α = 0.5), and extreme upper (α = 0.95) quantiles.  The 95% bootstrap confidence intervals are indicated by the red dotted lines

The results generally show that the predictor variables at the lower quantile (α = 0.05) are positively and statistically significantly correlated with cryptocurrencies' tail risk connectedness at most lags, except for ADS, where dependence is mostly negative. In the middle quantile (α = 0.50), we again observed that the CQs were mostly positive and significant in both the short and long runs, suggesting that the predictability from FGCI, GPR, and TEU to the connectedness of cryptocurrencies is positive during normal states. For ADS, the CQs were negative and statistically significant from 20 days to 50. Furthermore, we found substantial positive directional prediction at the longest lags when the predictor variables were at the extreme upper quantiles (α = 0.95). The Box-Ljung (portmanteau) statistics displayed in Fig. 14 provide additional confirmation of the significant cross-quantilogram correlation.

Fig. 14

Box–Ljung test statistic.  Note:  The figure plots Box–Ljung test statistic between each predictor variable to total tail risk connectedness index estimated at 5% CAViaRs The 95% bootstrap confidence intervals are indicated by the red dotted lines

Quantile cross-spectral method

Similar to the CQ approach, let ${\varvec{X}}t$ to be two stationary time-series, with components ${{\varvec{X}}}_{t}=\left({x}_{t,j1},{x}_{t,j2}\right)$, the quantile coherency between these two processes ${(\mathfrak{R}}^{{j}_{1},{j}_{2}})$ can be written as

$${\Re }^{{j_{1} ,j_{2} }} \left( {\omega ;\tau_{1} ,\tau_{2} } \right):= \frac{{f^{{j_{1,} j_{2} }} \left( {\omega ;\tau_{1} ,\tau_{2} } \right)}}{{\left( {f^{{j_{1,} j_{1} }} \left( {\omega ;\tau_{1} ,\tau_{1} } \right)f^{{j_{2,} j_{2} }} \left( {\omega;\tau_{2} ,\tau_{2} } \right)} \right)^{1/2} }}$$

(13)

where${f}^{{j}_{1,}{j}_{2}}$, ${f}^{{j}_{1,}{j}_{1}} {\text{and}} {f}^{{j}_{2,}{j}_{2}}$ are the quantile cross-spectral density and the quantile spectral densities of variables, $-\pi <\omega <\pi$ and${(\tau }_{1},{\tau }_{2})\in \left[\mathrm{0,1}\right]$, obtained from the Fourier transform of the matrix of quantile cross-covariance kernels $\Gamma \left({\tau }_{1},{\tau }_{2}\right):$=${\left(f\left(\omega ;{\tau }_{1},{\tau }_{2}\right)\right)}_{{j}_{1,}{j}_{2}}$, where

$${\gamma }_{k}^{{j}_{1},{j}_{2}}:=Cov\left(I\left\{{X}_{t+k,{j}_{1,}}\le {q}_{{j}_{1}\left({\tau }_{1}\right)}\right\},I\left\{{X}_{t+k,{j}_{2,}}\le {q}_{{j}_{2}\left({\tau }_{2}\right)}\right\}\right)$$

(14)

for ${j}_{1},{j}_{2}\in \left\{1,\dots ,d\right\}$, $k\in {\mathbb{z}}$,${\tau }_{1},{\tau }_{2}\in \left[\mathrm{0,1}\right]$, and I{A} is the indicator function of event A. The frequency domain matrix of quantile cross-spectral density kernels is $f\left({\omega ;\tau }_{1},{\tau }_{2}\right):$=${\left(f\left(\omega ;{\tau }_{1},{\tau }_{2}\right)\right)}_{{j}_{1,}{j}_{2}}$. According to Barunik and Kley (2019), quantile coherency is estimated as follows

$${\widehat{\mathfrak{R}}}_{n,R}^{{j}_{1},{j}_{2}}\left(\omega ;{\tau }_{1},{\tau }_{2}\right):=\frac{{\widehat{G}}_{n,R}^{{j}_{1},{j}_{2}}\left(\omega;{\tau }_{1},{\tau }_{2}\right)}{{\left({\widehat{G}}_{n,R}^{{j}_{1},{j}_{1}}\left(\omega ;{\tau }_{1},{\tau }_{1}\right){\widehat{G}}_{n,R}^{{j}_{2},{j}_{2}}\left(\omega;{\tau }_{2},{\tau }_{2}\right)\right)}^\frac{1}{2}}$$

(15)

where ${\widehat{G}}_{n,R}^{{j}_{1},{j}_{2}}$ are the smoothed quantile cross-periodograms, ${I}_{n,R}^{{j}_{1},{j}_{2}}$ is the rank-based copula cross-periodogram matrices (CCR-periodograms), and ${W}_{n}$ is a sequence of weight functions.

The coherence between the tail risk connectedness at 5% and each predictor indicated is reported in Fig. 15.¹⁵ The plots show the real (left) and imaginary (right) parts of the quantile coherency for the lower $\left.(0.05\right|0.05)$, middle $\left.(0.5\right|0.5)$, and higher quantiles $(\left.0.95\right|0.95)$. The daily cycles over the intervals are shown on the horizontal axis, whereas the vertical axis measures the magnitude of the co-dependence between the two variables. The upper label (W, M, Y) of the horizontal axis shows the time frequencies corresponding to the weekly (short run), monthly (medium run), and yearly (long run) periods. These time frequencies translate to $\omega \in 2\pi \left\{1/7, 1/30,1/365\right\}$.

Fig. 15

Quantile coherency. Notes: Plot of the real (left) and imaginary (right) parts of the quantile coherency at 0.05, 0.5, and 0.95 quantiles with 95% confidence intervals. W, M, and Y denotes weekly, monthly, and yearly periods

Figures reveal a positive coherency between the tail risk connectedness of cryptocurrencies and the FGCI, ADS, GPR, EPU, and TEU conditions across all quantile ranges between − 0.1 and 0.2 in the short-run dynamics (i.e., at weekly cycles). However, this quantile coherency became stronger during lower quantiles (i.e., 0.05|0.05 quantiles) and extreme conditions (i.e., 0.95|0.95 quantiles) for (i.e., at monthly and yearly cycles). In other words, these results reveal significant upper quantiles and long-run dependence, whereas the real coherency is between − 0.2 and 0.6 during the middle quantiles of the joint distribution and between − 0.2 and 0.2 during the upper quantiles of the joint distribution quantiles. Overall, the findings indicate the predictive abilities of the FGCI, ADS, GPR, EPU, and TEU conditions across all time horizons.

Conclusion

Motivated by cryptocurrencies’ increasing importance and popularity in the financial arena, this study examines tail connectedness among cryptocurrencies and their underlying factors. The main results indicate an increasing level of tail connectedness during turbulent periods. ETC is the main influencer among cryptocurrencies despite having lower capitalization than BTC. Simultaneously, an increase in the dynamics of BNB, XRP, and ADA is expected in 2022. Finally, the highest pairwise connectedness is between ETC and BTC.

Our analysis is important to both investors and portfolio managers. In essence, a cryptocurrency portfolio comprising the most popular cryptocurrencies involves a high level of dependency, which means investors should exercise extreme caution when positioning highly interconnected cryptocurrencies such as BTC and ETC. In a possible collapse, these cryptocurrencies would represent a substantial portion of total cryptocurrency capitalization. This is particularly important given that cryptocurrencies present heavier tail distributions, implying unusually high levels of tail risk.

Policymakers and regulators should also be particularly cautious during extraordinary periods, as cryptocurrency selloffs due to herding behavior and panic can lead to severe consequences and bankruptcy. Innovations from ETC and XRP (despite their lower extent) appeared to have the largest footprints in the system. Hence, policymakers can counter ETC innovations before they become widespread and cause market turbulence.

Finally, in predicting the TCI level among cryptocurrencies, the MSFE-adjusted statistics confirmed the improved predictability of the model containing information on the FGCI, ADS, GPR, EPU, and TEU conditions at multiple investment horizons with high significance. This means policymakers can use our metrics to forecast periods with notably high TCI and take the necessary measures to mitigate financial contagion and preserve financial stability. This finding does not comply with the notion of increasing cryptos' efficiency, as Noda (2021) argued. Hence, our study provides new evidence of the inefficiency of cryptocurrencies.