*2.3. General Spillover Risks*

First and foremost, the connectedness between decentralization policy and spillover effects is mentioned in study of Ogawa and Wildasin (2009) as well as Feder (2018). In these researches, the authors emphasized that decentralization might lead to spillovers among heterogeneous status. Second, when it comes to the decentralization in cryptocurrency market mentioned before, this means that these cryptocurrencies have a 'peer-to-peer' position in purchasing, selling, and trading without central control or concentrated authorization. Thus, the spillover effects might easily happen in terms of a decentralized context with unrestricted transactions.

### *J. Risk Financial Manag.* **2019**, *12*, 52

The test of spillover risks is usually to test for many different stocks, equity markets, as well as different kinds of financial assets. In this subsection, we will acknowledge the previous studies regarding the extent of relevant models to our study. Primarily, there is also an empirical study regarding contagion risk through the Structural Vector Autoregression (SVAR) model. Dungey et al. (2011) asserted that the liquidity and volatility of JP Morgan indices measured by credit risk with spread2, as well as a country risk by idiosyncratic shocks. Therefore, this study also emphasized the role of SVAR in identifying contagion risk through transmission of shocks from one country to another country. In the previous period, Diebold and Yilmaz (2008) suggested a method to measure the interdependent features among many assets. It is based on "own variance shares", which are estimated by error variances in forecasting. Latter, Yilmaz (2010) applied this method for measuring risks and volatility among East Asian stock markets. Similarly, there are plenty of works using Granger causality on the VAR basis to indicate the spillover risks such as Zhang et al. (2010). This study used Granger causality tests to indicate that change in the Dow Jones Industrial Average Index significantly causes changes in the Shanghai Stock Exchange Composite Index. This is one of the fundamental concepts for us to employ Granger causality for further investigation. Besides, the work of Shabri Abd. Majid et al. (2009) integrated the Generalized Method of Moments (GMM) in panel data to test contagion risks in 5 emerging markets among ASEAN countries. Additionally, Ding (2010) also checked the co-movements with Granger causality for the US and the Asia Pacific stock markets, while Central and Eastern Europe are the scope of study by Tudor (2011). Then, there is also a country research, employing this methodology of Vinh (2014) and Su (2017).

In order to observe the spillover risks, Christodoulakis and Satchell (2002), Engle (2002), as well as Tse and Tsui (2002) proposed the methodology of time-varying conditional correlations to examine whether the spillover risks happen in the market or not. There are many innovations from the previous traditional model. For example, Kundu and Sarkar (2016) introduced the STVAR-BTGARCH-M model for examining contagion risks. Afterward, Bouri et al. (2018a) built on previous studies, investigating the spillover risks between Bitcoin and financial assets (such as MSCI indices, commodity, energy, gold, US dollar, and US Treasury). One of the most impressive points in this study is to divide the sample into two regimes, for instance, bull and bear market. Additionally, Cong et al. (2008) employed multivariate VAR to indicate the transmission between oil price shocks and the equity market in China. Afterward, the study of Narayan and Narayan (2010) reexamined this approach for country research in Vietnam. Interestingly, Park and Ratti (2008) expanded their sample to the US and European countries by using Johnson and Juselius' cointegration tests before the empirical findings of Maghyereh and Al-Kandari (2007) by nonlinear cointegration analysis for Gulf Cooperation Council (GCC) countries. Another country research is from Hammoudeh and Aleisa (2004), who used VAR, likelihood ratio, and cointegration tests to examine the equity markets and New York Mercantile Exchange (NYMEX) oil futures.

One of the modern methodologies to measure the dependence structure is Copulas. Noticeably, in the equity market, Nguyen and Bhatti (2012) took advantage of the characteristics of marginal distribution and bivariate analysis to estimate the dependence structure, which is also known as spillover risks. In the early period, Bae et al. (2003) and Boyson et al. (2010) shed new light on estimating tail (or extreme) events of market returns as contagion risks. Later, the study of Luo et al. (2011) approached this methodology to explain how Chinese stock markets transmitted their risks to the other equity markets. Interestingly, Hiang Liow (2012) presented the results of the co-movements in securitized real estate and stock markets by Copulas. Following this work, Boubaker and Sghaier (2013) also implemented their Copulas results with portfolio managemen<sup>t</sup> implications for the US financial assets, whereas Ghorbel and Trabelsi (2014) contributed a piece of empirical evidence for energy portfolio using Copulas. Besides, the research of Al Rahahleh and Bhatti (2017)

<sup>2</sup> It was measured by the gap between the US industrial yields and the US Treasury bond.

demonstrated that there is a relationship between the information transmission and international stock markets in co-movements by Copulas.

To sum up, our literature review regarding spillover effects only focuses on three main points: (i) Granger causality test to estimate spillover risks; (ii) other time-varying models to examine contagion phenomenon; and (iii) the applications of Copulas in spillover risks.

### *2.4. Relevant Studies in Terms of Spillover Risks on the Cryptocurrency Markets*

The study of Koutmos (2018a) investigated the relationship among cryptocurrencies by employing a multivariable vector autoregression (VAR). These findings sugges<sup>t</sup> that there exists the spillover pattern in cryptocurrency markets, which represents interdependencies among these coins. However, this study only examines the covariates rather than joint distribution between each pair of cryptocurrencies. Therefore, it is encouraged to have further researches in distribution characteristics.

By using the value-at-risk and expected shortfall, the study of Gkillas and Katsiampa (2018) investigated tail behaviors among the five largest coins in the exchange market. This study shares some similarities in findings with Brauneis and Mestel (2018) regarding tail risks. Interestingly, the study of Brauneis and Mestel (2018) uses a rich set of quantitative techniques, such as the Ljung and Box (1978) test for autocorrelation, Wald and Wolfowitz (1940) test for random order, bootstrapped variance ratio by Chow and Denning (1993), etc. Nevertheless, these studies might miss capturing the tail dependence structure among these cryptocurrencies. In brief, the findings are quite consistent in that there exist spillover risks among these kinds of assets.

Interestingly, Corbet et al. (2017) examined the idiosyncratic characteristics of Bitcoin and came into conclusion that there exist the spillover effects among cryptocurrencies. However, this study applied the GARCH approach to investigate the volatility spillovers. Later, by using LASSO-VAR<sup>3</sup> approach, Yi et al. (2018) indicated that there is interconnection among cryptocurrencies in terms of returns and volatilities. This study failed to confirm that Bitcoin is the dominant element for this transmission. Therefore, Yi et al. (2018) confirmed that the spillover effects happen in cryptocurrency markets; however, this study does not emphasize the tail dependence structure. Recently, Bouri et al. (2018a, 2018b) applied the test from Phillips et al. (2015) called generalized sup Augmented Dickey–Fuller (GSADF) test for proving the multiple bubbles as well as co-explosivity in the cryptocurrency market. Once again, this study skipped the tail structure in capturing the extreme value, which might cause spillover risks. The study of Tu and Xue (2018) is entirely new, and employs Granger causality to check interrelationship between Bitcoin and Litecoin. However, this study limits two coins without more expansion for many coins. Finally, Huynh et al. (2018) asserted that there exist the contagion risks among cryptocurrency markets by using nonparametric (chi-plots and Kendall-plots) and parametric (Copulas with Normal, Clayton, and Gumbel) approaches. This study is one of the fundamental concepts for us to develop to use further quantitative techniques in examining the spillover risks.

Recently, Trabelsi (2018) investigated the volatility spillover effects among cryptocurrencies with a time–frequency–dynamic connectedness nature. The results are quite interesting to the readers because it contributes to the empirical evidences regarding connectedness within the cryptocurrency markets. Especially, this study also introduces the time of decomposition of the total spillover index, emphasized in 2–4 days. However, Trabelsi (2018) employed VAR methodology, which is good to forecast in linear shape rather structural dependence or complex structures of asset distribution. Although this study is a review, we would like to investigate insights by using quantitative techniques specifically structural VAR and Copulas for further estimation.

To the best of our knowledge, there was no further investigation among cryptocurrencies using Granger causality on the theme of VAR and SVAR. Furthermore, the previous studies only took normal

<sup>3</sup> Least Absolute Shrinkage and Selection Operator and Vector Autoregressive Model.

Copulas with a normal distribution to capture the left-tail dependence and fail to explain the extreme value, which only Student's-t Copulas fits. Therefore, our research will bridge the shortage of previous studies on the three following main points. (i) Review the previous studies in cryptocurrencies in terms of spillover or contagion risks; (ii) contribute to new approach of Granger causality on the theme of VAR (or linear) and SVAR (or structural dependence); and (iii) reexamine the joint distribution between each pair of cryptocurrencies with Gaussian and Student's-t Copulas allowing to capture the extreme value.
