[SOLVED] CS finance flex chain algorithm Energy Economics 81 (2019) 10421055

Energy Economics 81 (2019) 10421055
Contents lists available at ScienceDirect Energy Economics
journal homepage: www.elsevier.com/locate/eneeco
Information interdependence among energy, cryptocurrency and major commodity markets
Qiang Ji a,b,c, Elie Bouri d,, David Roubaud e, Ladislav Kristoufek f
a BusinessSchool,ShandongNormalUniversity,Jinan,Shandong,250014,China
b InstitutesofScienceandDevelopment,ChineseAcademyofSciences,Beijing100190,China
c SchoolofPublicPolicyandManagement,UniversityofChineseAcademyofSciences,Beijing100049,China d HolySpiritUniversityofKaslik,Lebanon
e MontpelierBusinessSchool,Montpelier,France
f Institute of Economic Studies, Faculty of Social Sciences, Charles University, Prague, Czech Republic
article info
Article history:
Received 10 February 2019
Received in revised form 13 May 2019 Accepted 8 June 2019
Available online 14 June 2019
Keywords:
Transfer entropy Commodity market Cryptocurrency Information spillover Integration
1. Introduction
With the emergence of Bitcoin as an investment option due to its tradability as a unit of value, a heated debate has ensued over whether this prominent digital coin is a currency, a commodity or a synthetic commodity (Yermack, 2013; Lo and Wang, 2014; Polasik et al., 2015; Popper, 2015; Selgin, 2015; Blau, 2017).1 Some studies have revealed evidence of a weak connection between Bitcoin and commodities such as gold and crude oil (Bouri et al., 2018a, 2018b; Ji et al., 2018a).2 With the development of new cryptocurrencies other than Bitcoin, the debate has only intensified.3 Still, it is not clear whether the diversified cryptocurrency market that now consists of various leading cryptocurrenciessuch as Ethereum, Ripple, Stellar and Litecoinis connected or disconnected from the commodity markets (e.g., for en- ergy, metals and agricultural commodities).
Correspondingauthor.
E-mail address: [email protected] (E. Bouri).
1 For example, Selgin (2015) indicates that Bitcoin combines features of commodities (e.g., gold) and fiat currencies.
2 Ji et al. (2018a) also report evidence of instability in the relationship through an anal- ysis across sub-sample periods.
3 Most cryptocurrencies are based on the backbone of Bitcoin, which is blockchain technology.
https://doi.org/10.1016/j.eneco.2019.06.005
0140-9883/ 2019 Elsevier B.V. All rights reserved.
2019 Elsevier B.V. All rights reserved.
From a theoretical point of view, different channels and factors which have been previously identified in the literature on inter- market relationships may play a role in forming a connection between the cryptocurrency market and the commodity markets. The first among these is the correlated-information channel (Kodres and Pritsker, 2002), through which connections occur via the price- discovery process. The second is the risk premium channel, through which a shock in one market may adversely affect the willingness of market participants to hold risk in any market (Acharya and Pedersen, 2005). Both channels can be relevant to the case of cryptocurrencies and commodities. Interestingly, some prior studies highlight an associ- ation between the commodity markets and the cryptocurrency market, as represented by Bitcoin, while providing additional theoretical under- pinnings and reasons for this. Hayes (2017) indicates a possible linkage between energy and Bitcoin markets based on the rationale that energy, in the form of electricity, is the main cost of Bitcoin production (i.e., for mining).4 Particularly, the discussions in Bouri et al. (2018b) and Shahzad et al. (2019) provide interesting arguments that clarify the need for and appropriateness of studying the connection between Bitcoin and commodity markets. Other studies examine potential
4 Bouri et al. (2017) also build on the rationale of Hayes (2017) and provide evidence that Bitcoin and energy commodities move more in tandem after December 2013.
abstract
The relationship between conventional and digital assets has become a prominent research topic, a focus partially emerging from the establishment of some large cryptocurrencies as legitimate financial assets. In this paper, we examine the information interdependence among various commoditiessuch as energy, metals and agricultural commoditiesand leading cryptocurrencies. We use a time-varying entropy-based approach to identify the di- rection of return spillovers, and the results show that the nature of information spillovers changes over time, with cryptocurrencies becoming more connected and more prominent within the system; in contrast, the role of energy commodities is dependent on their price dynamics. We also apply a minimum spanning tree (MST) and various centrality measures, which reveal that agricultural and energy commodities form the core of the commodities network. The basic skeleton of the network remains rather stable over time even though the de- tailed connections are rather volatile. Our findings generally suggest that cryptocurrencies are integrated within broadly-defined commodity markets.

associations among commodities and Bitcoin arising from the similarity of some characteristics of cryptocurrencies and metals commodities (e.g., gold). For example, Henriques and Sadorsky (2018), Klein et al. (2018), Selmi et al. (2018) and Shahzad et al. (2019) compare the vir- tues of gold and Bitcoin; however, these studies provide mixed evidence and results.
Most of the existing research still focuses on the interdependent re- lationship among commodity markets and between commodity and fi- nancial markets (Wang et al., 2018; Ma et al., 2019a, 2019b, 2019c; Zhang and Broadstock, 2018; Zhang et al., 2019), while the relationship between the cryptocurrency market and commodity markets has been given increasing attention by researchers of late. Previous studies have shown that commodities enjoy a strong network structure that is also intertwined with financial assets. Kristoufek et al. (2012) were the first to study the properties of commodity market networks. Even though their study primarily focuses on the place of biofuels in the net- works, Kristoufek et al. (2012) show not only that the separations be- tween clusters can be very clear but also that they can vary in time considerably. Regarding more recent studies, Filip et al. (2016) study a network of 33 assets covering commodities (including energy, agricul- tural and fuel commodities), stock indices, interest rates and exchange rates and mostly confirm the qualitative results of Kristoufek et al. (2012), but on a larger scale.
Two observations are noteworthy from the existing literature on cryptocurrencies (e.g., Bitcoin) and commodities (e.g., gold and crude oil). The first is that in the existing studies beginning with Hayes (2017) and ending with Shahzad et al. (2019), Bitcoin is considered the sole representative of the cryptocurrency market. Consequently, they disregard other leading cryptocurrencies, such as Ethereum, Rip- ple, Stellar and Litecoin, which have recently eroded the dominance of Bitcoin in the cryptocurrency market5; these cryptocurrencies have be- come alternative digital investments that are attracting the attention of scholars focusing on the relationship between the leading players in the cryptocurrency market (Brauneis and Mestel, 2018; Ji et al., 2018b; Koutmos, 2018). The year 2017 was not only the year of Bitcoin and its unprecedented appreciation but also the year of the so-called altcoinscoins derived from the core Bitcoin features as well as other original coins and derived tokens (first and foremost, the case of Ethereum and its smart-contract-based tokens). This enlarged the pool of cryptoassets (i.e., coins and tokens) appropriate and useful for fi- nancial analysis that we are able to make use of in our analysis. The sec- ond noteworthy observation is that most prior studies that examine the relationship between commodities and Bitcoin do not look at the time variability in that relationship (e.g., Ji et al., 2018a) despite empirical ev- idence that the inter-market relationships among conventional assets are rather dynamic, which necessitates a thorough examination of the time-varying networks of connectedness between commodities and Bitcoin and, thus, among various commodities and cryptocurrencies.
In this context, the aim of this paper is to examine information spill- overs (i.e., interdependence) and market integration among various commodities and cryptocurrencies. Our dataset covers three groups of commoditiesenergy, metals and agricultural commoditiesand their individual commodity components, as well as five leading cryptocurrencies (Bitcoin, Ethereum, Ripple, Stellar and Litecoin).
With regard to methodology, we use an entropy-based network ap- proach to capture the direction of spillovers within the information net- work, from both static and dynamic perspectives. We apply minimum spanning trees (MST) to capture the intensity of such spillovers and the stability and evolution of the integration structure for the informa- tion flow. We also use several network indicators (degree centrality, closeness centrality and betweenness centrality) to identify the impor- tance of each variable being studied within the global information flow.
5 For example, the market share of Bitcoin decreased from more than 80% in early 2017 to 45% in the last quarter of 2018.
Our empirical analysis is essential reading for policymakers who are concerned with the stability of financial markets. Evidence of increased or unstable interdependence between the commodity and cryptocurrency markets suggests the need for continuous monitoring of the connectedness network for the sake of different economic actors. Our empirical analysis also has implications that go beyond policymakers, affecting investors and risk managers. Increasing con- nectedness between commodity and cryptocurrency markets weakens the attractiveness of portfolio diversification across these markets. As for evidence of significant time variability in the interdependence be- tween various commodities and cryptocurrencies, our analysis may suggest that market participants should maintain a perspective of dy- namic hedging or periodic rebalancing. This is important in light of ear- lier findings about the importance of combining Bitcoin with commodities to reduce risk and maximise returns (e.g., Bouri et al., 2017).
The major empirical results arising from our empirical analyses are as follows. First, we show that energy and agricultural commodities are the driving forces of the whole system, both from the perspective of spillovers and from the network perspective. Second, cryptocurrencies are not detached from the system and are more con- nected to the global commodity markets than are metals (including gold). Third, cryptocurrencies are not strongly affected by energy com- modities, which goes against the basic idea that electricity prices form an important part of cryptocurrency production costs. We argue that this is connected to the development of the cryptocurrency mining mar- ket, which reacted only slowly to the surge of 2017. Fourth, cryptocurrencies become more connected to and more important within the overall network over time. Fifth, energy commodities be- come less important over time as they are evidently connected to the price dynamics of crude oil as a representative commodity. And sixth, we discuss the implications of these results for portfolio management, arguing that the role of cryptocurrencies as diversifiers is not necessarily as strong as is commonly believed, at least during times of general asset appreciation.
The rest of the paper is structured as follows. Section 2 describes the methods that we use, namely the connectedness approach based on en- tropy, the MSTs and various centrality measures. Section 3 provides em- pirical results and a detailed discussion in the light of prior studies. Section 4 offers concluding remarks and directions for future research.
2. Methods
Network-based modelling has recently come into common use as a methodological framework to investigate information transmission and systemic risk in the energy and financial fields (Diebold and Yilmaz, 2014; Ji and Fan, 2016; Ji et al., 2018c; Zhang, 2017; Zhang and Broadstock, 2018). The biggest advantage of the network analysis approach is that it can efficiently present a clear dependence structure and intuitively reflect the complex information linkages among assets. The key point of network modelling is to build the pairwise linkages be- tween assets. The most frequently used measures are summarised below.
Billio et al. (2012) propose using Granger causality networks to study connectedness and systemic risk in the finance and insurance sec- tors. They affirm that Granger causality can accurately measure the pre- dictive relationship between the past values of one variable and the future values of another, which is a simple measure of unconditional correlation (Castagneto-Gissey et al., 2014). However, the significance of Granger causality heavily depends on the selected number of lags, which may be inconsistent for different pairs of assets. Moreover, Granger causality networks are measured as unweighted networks, meaning they cannot investigate the magnitude of information trans- mission among assets.
Another popular approach was recently developed by Diebold and Yilmaz (2014), who build a connectedness network employing the
Q. Ji et al. / Energy Economics 81 (2019) 10421055 1043

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Q. Ji et al. / Energy Economics 81 (2019) 10421055
Table 1
Summary statistics of asset returns.
Cryptocurrency
Metals
Energy
Agricultural
Bitcoin Ethereum Ripple
Stellar Litecoin
Gold
Silver Aluminium Copper Nickel Natural Gas Heating Oil Unleaded Gas Crude Oil Live Cattle Cocoa
Coffee
Corn
Cotton
Lean Hogs Orange Juice Soybeans Wheat Sugar
Mean Std.Dev Skewness Kurtosis
0.395 4.609 0.184 7.677 0.706 8.390 0.733 8.353 0.504 8.402 2.490 18.800 0.569 10.376 3.347 37.409 0.339 6.828 1.582 16.221 0.008 0.807 0.221 6.426 0.009 1.413 0.394 6.153 0.009 1.461 0.593 12.666 0.001 1.642 0.359 14.280 0.008 2.343 0.090 10.892 0.009 2.577 0.002 5.392 0.000 2.223 0.355 7.689 0.006 2.259 0.413 7.901 0.058 2.290 0.309 5.407 0.035 1.443 2.444 24.438 0.018 2.298 0.183 14.598 0.024 2.088 1.370 23.446 0.005 1.771 1.444 25.445 0.016 1.766 1.858 22.876 0.013 2.524 1.696 29.730 0.030 2.593 0.070 19.145 0.010 1.727 0.081 16.153 0.005 2.438 0.730 30.274 0.013 2.278 0.162 9.832
Risk adjusted returns
0.086 0.084 0.060 0.055 0.050 0.010 0.006 0.006 0.001 0.003 0.003 0.000 0.003 0.025 0.024 0.008 0.011 0.003 0.009 0.005 0.012 0.006 0.002 0.006
Jarque-Bera
750.025*** 1050.066*** 9353.356*** 41,881.720*** 6298.512*** 406.733*** 359.956*** 3232.469*** 4354.021*** 2123.715*** 194.962*** 766.657*** 841.871*** 210.525*** 16,478.850*** 4589.531*** 14,503.990*** 17,454.570*** 13,934.850*** 24,744.970*** 8885.038*** 5897.060*** 25,426.870*** 1594.346***
ADF test
27.833*** 26.013*** 16.331*** 26.914*** 26.137*** 29.052*** 30.487*** 29.364*** 29.417*** 29.797*** 28.901*** 30.346*** 28.690*** 29.993*** 26.903*** 29.368*** 26.462*** 28.440*** 27.254*** 28.644*** 26.860*** 28.768*** 27.889*** 28.351***
PP test
27.859*** 26.013*** 25.514*** 26.985*** 26.132*** 26.061*** 30.429*** 29.352*** 29.417*** 29.803*** 28.902*** 31.675*** 29.279*** 29.994*** 26.884*** 29.371*** 26.585*** 29.034*** 27.241*** 29.436*** 26.839*** 28.874*** 27.953*** 28.402***
Note: This table presents the summary statistics of the daily returns of the variables under study. The sample period is from 15 August 2015 to 27 September 2018. The JarqueBera sta- tistics test nulls the hypothesis that the distribution of each return series is Gaussian. *** denotes significance at 1% level.
vector autoregressive model (VAR) and the generalised forecasting error variance decomposition (FEVD) method. This is based on the sim- ple idea of reorganising the FEVD results to provide an intuitive way to interpret the VAR results, which has been widely used in the field of en- ergy finance (Luo and Ji, 2018). However, the VAR model is limited by the number of sample variables and cannot deal with high- dimensional network issues.
Other methodologies such as conditional value at risk (CoVaR) and similar approaches can accurately estimate the risk spillovers between two assets (Ji et al., 2018d, 2019) but suffer from complexity issues re- garding the coefficient estimation process. More importantly, such ap- proaches lack a clear definition extending them from pairwise to network-level analysis.
In this paper, we employ the transfer entropy approach, which avoids the limitations of the above-mentioned studies, specifically the curse of dimensionality and coefficient estimation complexity. The transfer entropy approach is flexible in dealing with asymmetric and nonlinear processes (Altiparmak and Dengiz, 2009; Bekiros et al., 2017). In addition, the transfer entropy approach has specific advan- tages in measuring information spillovers among assets as it can be eas- ily estimated and it ignores variable dimension issues. Particularly, the transfer entropy between two variables is generally asymmetric, which can provide useful information on the spillover direction be- tween variables. In this section, we extend the pairwise transfer entropy estimation to a network analysis with reference to Diebold and Yilmazs (2014) idea of the connectedness framework. We build new network construction rules by converting pairwise transfer entropy into a direc- tional transfer entropy spillover network (details can be seen in Subsection 2.2.1). In the constructed network, the transmission chan- nels and direction of information spillover can be intuitively explored. The following section contains the detailed modelling procedure for the transfer entropy approach.
2.1. Transfer entropy
Transfer entropy, originally introduced by Schreiber (2000), can measure the directionality of a variable with respect to time, based on the theory of information proposed by Shannon (1948).
Let us consider a discrete and stationary process, I(t), with p(i) being the prior probability of i. Then, according to Shannon, the average num- ber of bits needed to optimally encode I(t) without taking into account possible correlations is given by
X
i
where H(I) is called Shannon entropy.
Then, the difference between the Shannon entropy of neighbouring
orders constitutes the conditional entropy:
hIm 14 HIm 1HIm 2
where h(I(m)) denotes the average amount of information transmitted by the latest observation I(m + 1), given that the last m observations of I are known and their information has been completely exploited. Then, h (I(m)) can be rewritten as
HI 14 Hp1; p2; ; pk 14
pi logpi 1
hIm14
X  
p i1;i2;;im1 logp im1 i1;i2;;im 3
where p(im+1|i1,i2,,im) = p(i1,i2,,im,im+1)/p(i1,i2,,im) explains the concept of conditional entropy.
When we extend the concept of conditional entropy to two different sequences, transfer entropy is employed to measure the information flow from one stationary Markov process to another. Let X be a station- ary Markov process of order k; then, the probability of X at time t + 1 is conditional on k previous observations, that is, p(xt+1|xt, , xtk+1) = p (xt+1|xt, ,xtk). The measure of information flow from process Y to X can then be quantified as the deviation from the following generalised Markov property: p(it+1|i(t k)) = p(it+1|i(t k), j(t l)).
The transfer entropy that relates k previous samples of process X and l previous samples of process Y is defined as follows:
  k l X  k l p it1it ;jt
TYXk;l14 p it1;it ;jt log  k 4 p it1it

Q. Ji et al. / Energy Economics 81 (2019) 10421055 1045
Table 2
Information spillover among energy, cryptocurrencies and commodity markets.
1
2 0.10
3 0.12
4 0.11
5 0.16
6 0.11
7 0.23
8 0.24
9 0.22
10 0.26
11 0.20
12 0.20
13 0.22
14 0.27
15 0.13
16 0.21
17 0.28
18 0.19
19 0.20
20 0.23
21 0.24
22 0.17
23 0.22
24 0.26
To 4.56 Net 0.37
0.17 0.12 0.17 0.11 0.10 0.12 0.15
0.19 0.11 0.16 0.17 0.21 0.17 0.21 0.15 0.21 0.09 0.13 0.16 0.11 0.14 0.17 0.16 0.12 0.15 0.20 0.17 0.19 0.17 0.18 0.20 0.17 0.20 0.24 0.12 0.14 0.22 0.18 0.11 0.17 0.07 0.13 0.15
0.23 0.22 0.15 0.13 0.15 0.12 0.16 0.15 0.18 0.18 0.14 0.15 0.15 0.14 0.16 0.05 0.05 0.02 0.21 0.12 0.14 0.15 0.06 0.09 0.19 0.07 0.17 0.22 0.16 0.20 0.28 0.24 0.25 0.17 0.19 0.23 0.16 0.22 0.19
0.18 0.21 0.16 0.18 0.21 0.24 0.18 0.18 0.13 0.13 0.22 0.20 0.18 0.18 0.21 0.13 0.20 0.15 0.16 0.12 0.17 0.18 0.13 0.19 0.12 0.08 0.05 0.03 0.04 0.06 0.08 0.12 0.11 0.16 0.05 0.10 0.02 0.09 0.10 0.14 0.09 0.04 0.06 0.13 0.10 0.20 0.19 0.15 0.18 0.23 0.27 0.27 0.27 0.28 0.32 0.21 0.15 0.18 0.17 0.18 0.17 0.15 0.20 0.21 0.22 0.23 0.17 0.15 0.24 0.20 0.12 0.09 0.08 0.18 0.16 0.15 0.14 0.16 0.25 0.30
0.13 0.17 0.17 3.26 0.21 0.14 0.20 4.15 0.16 0.10 0.18 3.32 0.18 0.19 0.15 3.52 0.06 0.01 0.05 1.65
0.09 0.13 0.17 3.26
0.10 0.08 0.11 2.69
0.07 0.05 0.12 3.14 0.17 0.20 0.20 4.58 0.26 0.24 0.25 5.66 0.16 0.17 0.21 4.29 0.14 0.24 0.22 4.66 0.17 0.27 0.24 4.67 0.11 0.12 0.13 3.53 0.15 0.13 0.19 4.70 0.15 0.26 0.24 4.56 0.09 0.07 0.11 2.63 0.09 0.08 0.12 2.80 0.14 0.23 0.20 4.62 0.14 0.22 0.18 4.36
1
2 3 4
5 6 7 8 9 10 11 12 13
14 15 16
17 18 19 20 21
22 23 24 From 0.24 0.19 0.16 4.19
0.12 0.14
0.16 0.18 0.15 0.15 0.22 0.21 0.30 0.20 0.24 0.22 0.19 0.23 0.23 0.24 0.26 0.22 0.26 0.28 0.20 0.23 0.23 0.21 0.25 0.22 0.26 0.30 0.29 0.24 0.21 0.20 0.22 0.26 0.30 0.22 0.24 0.26 0.19 0.26 0.31 0.17 0.23 0.21 0.21 0.19 0.20 0.20 0.24 0.24 0.20 0.26 0.23 0.27 0.22 0.24 0.23 0.26 0.32 0.27 0.31 0.24 4.78 5.11 5.28 1.52 0.96 1.96
0.08 0.18 0.17 0.14 0.14 0.18 0.12 0.12 0.18 0.04 0.02 0.03 0.04 0.10 0.04 0.02 0.28 0.02 0.07 0.08 0.11 0.17 0.07 0.11 0.15 0.03 0.10 0.05 0.11 0.13 0.08 0.12 0.23 0.07 0.12 0.07 0.16 0.14 0.19 0.12 0.21 0.08 0.19 0.15 0.18 0.23 0.19 0.20 0.22 0.19 0.23 0.22 0.24 0.21 0.26 0.30 0.22 0.09 0.15 0.20 0.15 0.25 0.22 0.10 0.27 0.13 0.20 0.14 0.15 0.22 0.26 0.09
0.28 0.13 0.16 0.14 0.20 0.24 0.24 0.08 0.10 0.23 0.07 0.11 0.08 0.13 0.13 0.21 0.10 0.20 0.22 0.17 0.20 0.13 0.19 0.29 0.24 0.23 0.21 0.26 0.06 0.10 0.14 0.14 0.22 0.23 0.24 0.19 0.12 0.05 0.13 0.06 0.04 0.09 0.19 0.15 0.10 0.20 0.08 0.12 0.03 0.10 0.09 0.18 0.09 0.16 0.27 0.12 0.14 0.11 0.12 0.22 0.28 0.21 0.24 0.23 0.09 0.16 0.16 0.12 0.19 0.20 0.24 0.23 0.14 0.03 0.06 0.08 0.04 0.08 0.13 0.15 0.09 0.21 0.07 0.16 0.08 0.12 0.26 0.30 0.21 0.26 0.30 0.18 0.21 0.21 0.25 0.27 0.26 0.27 0.30 4.83 2.32 3.50 2.90 3.10 4.01 4.48 3.61 3.93
0.22 0.29 0.14 0.23
1.32 0.67 0.25 0.21
0.03 0.57 1.18 0.68 0.73 0.47 0.17 0.72 0.82 0.57 0.33
0.65 0.35 0.70
0.89 1.62
Note: The element in the table is the pairwise transfer entropy. 1 = Bitcoin, 2 = Ethereum, 3 = Ripple, 4 = Stellar, 5 = Litecoin, 6 = Gold, 7 = Silver, 8 = Aluminium, 9 = Copper, 10 = Nickel, 11 = Natural Gas, 12 = Heating Oil, 13 = Unleaded Gas, 14 = Crude Oil,15 = Live Cattle, 16 = Cocoa, 17 = Coffee, 18 = Corn, 19 = Cotton, 20 = Lean Hogs, 21 = Orange Juice, 22 = Soybeans, 23 = Wheat and 24 = Sugar.
0.26 0.18
0.23 0.20 0.18 0.09 0.04 0.12 0.12 0.03 0.14 0.20 0.19 0.22 0.26 0.18 0.20 0.13 0.07 0.08 0.21 0.10 0.20 0.30 0.24 0.30 4.20 3.36 3.99
0.12 0.17 0.20 0.21 0.11 0.03 0.11 0.14 0.09 0.10 0.12 0.06 0.22 0.19 0.13 0.26 0.19 0.11 0.12 0.19
0.07 0.10 0.05 0.13 0.11 0.18 0.08 0.13 0.22 0.21 0.24 0.14 0.20 0.22 0.27 3.74 3.20 3.13 3.97 4.02
0.03 0.10 2.59 0.11 0.25 4.41
0.16 0.18
5.57
3.29 3.52 3.95

1046 Q. Ji et al. / Energy Economics 81 (2019) 10421055
where l is the order of the assumed Markov process for Y, and TYX(k,l) is defined as the information flow from source Y on the next state of X that cannot be explained by the past state of X. Following the previous lit-
erature, we assume l = k = 1 (Bekiros et al., 2017). Similarly, TXY k; l 14
out X Di 14
j
2.2.2. Information integration network
In addition to the information spillover network, we also construct an information integration network to measure the centrality of infor- mation integration among assets. Following Yang and Zhou (2017), in the information integration network, we ignore the direction of spill- over, focusing instead on the intensity of co-movement. Therefore, we first transform the transfer entropy spillover matrix T into a symmetric transfer entropy intensity matrixT~, in which the diagonal elements are zeros and the off-diagonal elements are the sum of two pairwise trans-
fer entropies (Tf 14 Tf 14 T T ). Subsequently, to filter the necessary ij ji ij ji
information and identify the redundant information disturbed by some unimportant linkages, we employ an MST to depict the core link- ages among the assets. As indicated by Ji et al. (2018a), an MST is a con- nected spanning tree that has the minimum total edge weight. It has advantages compared with other tree structures, such as the planar maximally filtered graph, because it contains the most relevant connec- tions of each element in the set, with a simpleness and robustness struc- ture that has been widely applied in the financial field for market integration (see also Kristoufek et al., 2012). Detailed information about how to construct an MST can be found in most of the relevant lit- erature and involves the use of Prims algorithm (Prim, 1957). In gen- eral, for N markets, the MST only contains N1 links with the closest distance.
Following Ji and Fan (2016) and Ji et al. (2018a), three centrality measures are introduced to identify the most important node in the net- work, which are constructed as follows:
t1
. Obviously, the transfer entropy is
pj jjl;ik ; jl; ik log t1 t t
P
pj
2.2. Entropy-based networks and different measures
In this study, two different networks are built: an information spill-
over network and an information integration network. The former focuses on the direction of information spillover among assets, while the latter highlights the centrality of market integration among assets.
2.2.1. Information spillover network
In this section, the information spillover network is constructed. First,
we construct a transfer entropy spillover matrix T = [Tij], in which
Tijdenotes the transfer entropy from asset j to asset i, that is, Tij = Tji. Sim-
ilar to Diebold and Yilmazs (2014) connectedness measures, pairwise net
transfer entropy N(Tij) is measured by Tij Tji. Transfer entropy From
andToarecalculatedbytherowsumT =N T ,j=iandcolumn i j=1 ij
sum T = N T , i = j, respectively, of the transfer entropy spillover ma- j i=1 ij
trix T. The total net transfer entropy of variable i is defined as Ti = Ti Ti, and the system total spillover index is defined as T total
14 N1 Ni ; j 14 1 T i j ; i = j .
Second, the information spillover network is constructed based on the pairwise net transfer entropy. There exists a directional edge,Eji, in the information spillover network if and only if N(Tji) 0. At this point, we can easily identify the structure of information flow among different assets.
In this network, degree centrality is used to analyse the influence of the node in the system. Therefore, the weighted in-degree and out- degree centralities of a node in the network are measured. Weighted in-degree and out-degree centrality are respectively defined as follows:
t t pj
asymmetric for the pairwise (X, Y) and (Y, X). Therefore, it can provide useful information about the direction of interdependence between two time series.
Din14XTT; if andonlyif TT0 iijji ijji
5
Metals
3.978 1.716 3.644 6.505 14.127 0.534
j
Table 3
Information spillover among different types of assets. Panel A: Pairwise spillover
Cryptocurrency Metals
Energy Agricultural
To Net
Panel B: Net pairwise spillover
Cryptocurrency Metals
Energy Agricultural
2.759 5.555 4.740 11.512 21.807 6.130
Cryptocurrency
Energy
3.229 2.713 2.260 8.014 13.956 3.060
Agricultural
8.470 5.325 8.632 13.738 22.427 3.604
From
15.677 13.593 17.016 26.031
Agricultural
0
0 0.618 0
TjiTij; if and only if TjiTij0 6
jjl t1 t
degree centrality : closeness centrality :
Xn j141
ki 14 CCi 14
aij ; X
i; j
Rij; 2
7 i=j; and 8
Bi 14
X jli ; i= j=l; 9 NN1j;l jl
betweenness centrality :
where aij = 1 if and only if vertex i and vertex j have an edge in the MST,
Cryptocurrency
0 1.577 1.511 3.042
Metals
0
0 0.931 1.180
Energy
0 0 0 0
Note: In this table, information spillover between groups of assets is calculated based on the pairwise transfer entropy from Table 2. For example, the value of the diagonal element (Cryptocurrency, Cryptocurrency) is calculated as the average of the sum of all the pairwise transfer entropy values between the five cryptocurrencies. Similarly, the value of the off-di- agonal element (Cryptocurrency, Metal) is calculated as the average of the sum of all the pairwise transfer entropy values between the five cryptocurrencies and four metal commodities (i.e., a total of 5 4 = 20 combinations).

Q. Ji et al. / Energy Economics 81 (2019) 10421055 1047
a. Energy, cryptocurrency, and major commodity markets
b. Energy and Cryptocurrencies c. Energy and Metals
d. Energy and Agricultural
Fig. 1. Entropy-based network based on net pairwise spillover among energy, cryptocurrency and commodity markets. Note: Figs. 1(b), (c) and (d) are the subgraphs of Fig. 1(a), which only retains the edges between energy and other types of assets. For example, for Fig. 1(b), only the edge with one node belonging to Energy and another node belonging to Cryptocurrency is retained. Node size is calculated using the weighted out-degree of the pairwise net transfer entropy, while edge size is measured using the pairwise net transfer entropy. Nodes are coloured from blue to orange, according to the node size ranking, intuitively indicating that blue nodes act as large information transmitters and orange notes act as large information recipients, which is consistent with the node size.

1048 Q. Ji et al. / Energy Economics 81 (2019) 10421055
Rijis the shortest path from i to j in the MST, jl(i) is the number of shortest paths from j to l that pass through i, and jl is the number of shortest paths from j to l. Moreover, we use the normalised tree length
(Lt 14 1 X eij) to measure the degree of system integration, in N1eijMST
which eij is the edge in the MST. 3. Empirical results
3.1. Sample analysis
We use daily price data covering leading cryptocurrencies (Bitcoin, Ethereum, Ripple, Stellar and Litecoin)6 and three commodity groups (energy, metals and agricultural commodities). Energy includes natural gas, heating oil, unleaded gas and crude oil; metals include gold, silver, aluminium, copper and nickel; and agricultural commodities include live cattle, cocoa, coffee, corn, cotton, lean hogs, orange juice, soybeans, wheat and sugar. Price data on cryptocurrencies come from https:// coinmarketcap.com/, whereas price data on commodities come from Datastream. The sample period is from 15 August 2015 to 27 September 2018, resulting in 819 daily common observations across various com- modities and cryptocurrencies. The starting point, 15 August 2015, was dictated by data availability for the cryptocurrencies. We conduct the empirical analyses with daily returns calculated as 100 times the first difference of the logarithmic closing prices. Summary statistics of the daily returns are provided in Table 1. All return series depart from normality. Notably, the average returns and standard deviations of the returns for the five cryptocurrencies are substantially higher than those in the three commodity groups. The risk-adjusted returns are pos- itive for cryptocurrency, energy and gold, although they are higher in cryptocurrency. Within the cryptocurrency market, Ethereum has the highest return, while Stellar is the most volatile. However, in terms of the risk-adjusted returns, Bitcoin is the most attractive. All energy com- modities have a positive average return. Metals and agricultural com- modities, except gold, exhibit negative average returns. Nonetheless, the average return of all commodities is close to zero. Moreover, the augmented DickeyFuller (ADF) and PhillipsPerron (PP) tests show that the stationarity of all the return series cannot be rejected.
3.2. Information spillover network analysis
In this section, we present the information spillovers among the returns of the different variables, from both static and dynamic perspec- tives. We consider various measures of transfer entropy networks with the aim of discovering the structure, direction and strength of the network.
3.2.1. Static results
Table 2 presents measures of information spillovers among the ex- amined variables in three forms: pairwise net, To and From. It appears that the largest pairwise information spillovers are from orange juice to natural gas (0.32) and cocoa (0.30); from Stellar to wheat (0.32) and coffee (0.31); from Ripple to sugar (0.31) and unleaded gas (0.30); from Litecoin to sugar (0.30); from natural gas to wheat (0.30); from unleaded gas to natural gas (0.30) and sugar (0.30); from crude oil to sugar (0.30); from cocoa to sugar (0.30) and crude oil (0.29); and from nickel to cocoa (0.29). Conversely, the smallest pairwise informa- tion spillovers are from wheat to gold (0.01); from gold to silver (0.02) and aluminium (0.03); from aluminium to gold (0.02); from unleaded gas to gold (0.02); from cocoa to gold (0.02); from cotton to gold (0.02); from corn to aluminium (0.02); from copper to gold (0.03); and from live cattle to cotton (0.03).
6 The five cryptocurrencies represent more than 78% of the overall cryptocurrency mar- ket and attract more than 82% of the 24-hour trade volume.
5
4.5
4
3.5
3
Total spillover index
Fig. 2. Total spillover index among energy, cryptocurrency and commodity markets.
Looking at the overall results, we observe two general patterns. First, the cryptocurrencies are not outside of the system, and the information flow from them is reflected in the rest of the system. This does not nec- essarily mean that the cryptocurrencies actually influence the commod- ities in a strict sense but that the information affecting cryptocurrencies also has a specific effect on agricultural commodities, albeit with a delay. This delay is inherent to agricultural commodities, as they are depen- dent on production and growing cycles that have various costs, many of them fixed, which can be adjusted only with a pronounced delay (Janda et al., 2012; Janda and Kristoufek, 2019). And second, the most frequently and most strongly influenced commodities are the agricul- tural ones. This is connected to the previous point about the delayed cost adjustments, and it is well documented in the literature (Filip et al., 2017). The evidence related to the very weak dependence of gold on cryptocurrencies and commodities is not surprising, given its role as a safe-haven and the particularity of the factors that affect its returns and volatility (Baur and McDermott, 2010, 2016).
Focusing on the line titled To, which indicates the total information spillover from each variable to the other variables, Stellar and Ripple are the largest contributors, with values of 5.28 and 5.11, respectively. Con- versely, gold and aluminium are the smallest contributors, with total in- formation spillover values of 2.32 and 2.90, respectively. Based on the last row, titled From, it appears that natural gas and sugar receive the highest amount of information spillover from other variables, with values of 5.66 and 5.57, respectively. In contrast, gold and soybeans re- ceive the lowest amount of information spillover from other variables, with values of 1.65 and 2.59, respectively. Gold thus retains its safe- haven property even from this more aggregated perspective. As for the last line, titled Net, which measures the difference between total information spillover values (i.e., To minus From), the net values are positive in the cases of Bitcoin, Ethereum, Ripple, Stellar, Litecoin, gold, silver, aluminium, corn, cotton and orange juice. The most positive values are reported for Stellar and Ethereum, suggesting these variables are the leading contributors to the global information flow among the examined variables and thereby to market integration. This is in accor- dance with cryptocurrencies being the most volatile of the analysed samples as well as their quick reactions and, frequently, overreactions to news. Conversely, negative net information spillover is reported for the rest of the variables. Specifically, the main net receivers of informa- tion in the global information flow are sugar and natural gas, suggesting the isolation (i.e., segmentation) of these two agricultural commodities.
We also provide a summary of the results of the pairwise informa- tion spillover analysis while considering the five cryptocurrencies as a single Cryptocurrency group and three commodity groups (Metals, En- ergy and Agricultural). The largest pairwise information spillovers are from the Cryptocurrency to Agricultural groups (11.512), from Agricul- tural to Energy (8.632) and Cryptocurrency (8.470), and from Energy to Agricultural (8.014). This underlines the results reported for the sepa- rate commodities (i.e., the integration of cryptocurrencies into the

Q. Ji et al. / Energy Economics 81 (2019) 10421055 1049
Fig. 3. Net spillover index for each type of assets. Note: The net spillover index for each type of asset is calculated as the sum of all the net spillover indexes of assets in the same group.
market as well as the strong interaction between agricultural and en- ergy commodities). The smallest pairwise information spillovers are from Energy to Metals (2.713), Energy to Cryptocurrency (3.229), Metals to Energy (3.644) and Metals to Cryptocurrency (3.978). The low spillovers from Energy to Cryptocurrency are particularly interest- ing because electricity prices, which are highly dependent on the prices of production factors (e.g., coal and gas), play a crucial role in the pro- duction (i.e., mining) costs of cryptocurrencies. As all the analysed cryptocurrencies are based on the proof-of-work conceptin which the transactions are confirmed and verified by solving computationally intensive hashes that are physically verified by specialised chipselec- tricity price is a competitive factor in cryptocurrency production. How- ever, it is reasonable to assume that similar conclusions are true for other cryptocurrencies as well because mining was highly profitable up until the first half of 2016 and during the boom of 2017 (specifically, between Q2 and Q4 of 2014), when the margin between electricity costs and the price of mined bitcoins was above 1000%. In the middle of 2018, the margin dropped to around 100%. It is easy to see that in the earlier period, electricity price was not relevant, as cryptocurrency mining was profitable for practically anyone, even with average household electricity prices. As the mining difficulty has increased and cryptocurrency prices have undergone a correction since the surge of 2017, electricity prices have become more and more relevant. In fact, the year 2018and mainly the second halfwas characterised by some big mining companies (e.g., Bitmain) and mining initial coin offer- ings (ICOs) experiencing trouble or even halting or closing their busi- nesses. The weak connection between cryptocurrencies and energy commodities, seen from the global perspective, is not, therefore, completely surprising, and it only highlights the need for dynamic anal- ysis of the connections between the commodities groups, which we provide further below.
Moving to the highest and lowest receivers of information from other groups, the Agricultural group is in first place (26.031), far ahead of Energy (17.016), which is in second place. Conversely, Metals is the lowest receiver of information spillover from other groups (13.593). Regarding net receivers/transmitters of information, the
main net transmitter is Cryptocurrency (6.130), whereas Agricultural and Energy are net receivers, with values of 3.604 and 3.06, respec- tively. Interestingly, and as shown in Panel B of Table 3, Cryptocurrency is a net transmitter to each of the three groups, while Metals is a net transmitter to Energy and Agricultural. Cryptocurrencies thus play an important role in the entire system, as they react to the arriving infor- mation the fastest and are clearly the most sensitive to news in the group of analysed assets. This goes against the popular conception of cryptocurrencies being either completely or, at least, strongly detached from all other financial assets. Based on our results, this is not the case. The implications for practical portfolio diversification are quite straight- forward, as cryptocurrencies being influenced by similar information to that which influences the rest of the system (or at least the part of the global assets network we study here) lowers their diversification poten- tial and benefits.
For better visualisation of the information spillover network ema- nating from the pairwise net transfer entropy, an infographic illustra- tion is provided in Fig. 1.7 It is comprised of nodes and edges. The size of the node reflects the strength of the information spillover, whereas the colour indicates the structure hierarchy of the information flow net- work. Net transmitters are shown in blueviolet, whereas net receivers are shown in orange. The edge size reflects the magnitude of the pairwise net transfer entropy and has an arrow that indicates the direc- tion of the information flow. Fig. 1a considers energy, cryptocurrency and major commodity markets. It shows that nodes introduce distinct information spillover contributions to the network, where Stellar has the largest spillover contribution to the system and sugar is the com- modity most affected by system information. Interestingly, the role of leading cryptocurrencies other than Bitcoin is important. This was also the case for the information flow between the Energy and Cryptocurrency groups (Fig. 1b). As for the information flow between Energy and Metals (Fig. 1c), it shows that gold and, to a lesser extent, sil- ver play the role of transmitters. The network of information flow
7 Notably, for the existence of an arrow edge from one variable to another, there must be a pairwise net transfer entropy from that variable to the other that is larger than zero.

1050 Q. Ji et al. / Energy Economics 81 (2019) 10421055
Table 4
Summary statistics for the in-degree, out-degree and net spillover index of each asset.
Ethereum Cryptocurrency Ripple Stellar
Metals Aluminium Copper
Energy
Nickel Natural Gas Heating Oil Unleaded Gas Crude Oil Live Cattle Cocoa
Coffee
Corn
Cotton
Lean Hogs Orange Juice Soybeans Wheat
Sugar
0.349 0.515 0.325 0.372 0.653 0.250 0.595 0.591 0.457 0.081 1.074 0.887 0.962 0.265 0.650 0.638 0.378 0.676 0.880 0.481 0.744 0.328 0.280 0.593 0.455 0.271 0.252 0.322 0.554 0.232 0.351 0.348 1.108 0.103 0.481 0.140 1.028 0.369 0.635 0.915 0.265 0.029
Agricultural
*** Denotes significance at 1% level.
Bitcoin
0.320 0.186 0.045 0.037 0.237 0.170 0.091 0.128 0.173 0.193 0.816 0.249 1.030 0.301 1.300 0.360 0.923 0.230 1.057 0.350 0.675 0.297 1.025 0.430 1.101 0.396 0.816 0.481 1.342 0.198 1.057 0.268 1.198 0.301 0.944 0.235 1.141 0.145 0.940 0.319 0.969 0.220 0.903 0.153 1.390 0.283 1.293 0.190
0.402 2.198 0.806 2.939 0.323 2.019 1.505 4.436 0.957 2.659 0.117 2.314 0.370 2.285 0.076 2.146 0.073 1.897 0.237 1.997 0.386 1.805 0.032 1.955 0.157 1.754 0.558 1.927 0.414 2.450 0.765 2.958 0.035 2.397 0.138 2.214 0.310 2.774 0.003 2.001 0.303 3.351 0.822 4.089 0.763 2.778 0.090 2.846
30.574*** 61.671*** 32.691*** 263.811*** 89.550*** 12.460*** 25.102*** 17.851*** 29.340*** 29.157*** 48.004*** 25.998*** 39.150*** 56.810*** 23.422*** 55.567*** 8.751** 16.434*** 10.327*** 23.647*** 11.609*** 92.197*** 56.392*** 1.328
1.686 0.552 0.655 2.099 0.261 0.138 1.573 0.466 0.631 2.015 0.417 0.527 1.754 0.706 0.023 1.158 0.429 0.346 0.579 0.170 0.144 0.602 0.290 0.292 0.637 0.237 0.070 0.572 0.224 0.781 1.024 0.255 0.136 0.653 0.248 0.552 0.506 0.221 0.802 0.735 0.607 1.103 0.380 0.104 0.796 0.418 0.147 0.048 0.318 0.223 1.351 0.616 0.236 0.403 0.686 0.226 0.161 0.618 0.254 0.458 0.618 0.232 0.009 0.800 0.362 0.460 0.362 0.115 0.657 0.378 0.137 0.296
2.208 55.584*** 1.890 31.029*** 2.052 59.067*** 2.166 42.797*** 1.470 55.524*** 1.511 63.898*** 2.124 20.129*** 1.630 52.634*** 1.890 29.662*** 2.814 58.739*** 2.395 10.428*** 2.409 37.132*** 2.682 63.433*** 2.764 116.667*** 3.574 67.944*** 1.973 25.235*** 3.767 187.113*** 2.052 36.677*** 1.999 26.231*** 2.428 27.677*** 2.314 11.181*** 2.548 24.893*** 3.138 41.378*** 2.647 11.263***
1.366 0.712 0.400 2.054 0.288 0.075 1.335 0.615 0.476 1.924 0.529 0.696 1.581 0.880 0.147 0.341 0.526 0.651
1.953 41.135*** 1.891 29.672*** 1.838 53.506*** 2.203 61.041*** 1.575 50.190*** 2.468 46.835*** 1.800 39.054*** 2.003 54.135*** 3.207 1.063 2.245 24.571*** 1.871 40.258*** 1.918 33.716*** 2.000 43.469*** 2.364 84.148*** 2.695 42.233*** 2.649 46.250*** 3.059 52.626*** 3.808 48.794*** 3.092 6.214** 2.017 28.003*** 4.062 143.180*** 2.925 2.004 2.637 41.396*** 2.813 0.906
Litecoin Gold Silver
0.452 0.406 0.227 0.698 0.539 0.568 0.286 0.311 0.023 0.484 0.530 0.341
In-degree
Out-degree
Net
Mean Std.dev Skewness Kurtosis
J-B
Mean Std.dev Skewness
Kurtosis J-B
Mean Std.dev Skewness
Kurtosis J-B

between Energy and Agricultural (Fig. 1d) shows more interactions be- tween the commodities, with energy commodities showing more con- nections among themselves and with some agricultural commodities. Apparently, agricultural commodities such as orange juice, lean hogs, wheat and sugar exhibit weakness in terms of power and magnitude of connection with others and with themselves.
3.2.2. Dynamic results
Although the results presented in Subsection 3.2.1 help in uncovering the network of information transmission among the exam- ined variables, they provide no indication of whether the interdepen- dence among the examined variables is static or time variant. Abundant evidence suggests the possibility that structural changes af- fect the stability of the information flow among financial markets (e.g., Ji et al., 2018b), which renders it dynamic rather than static. To re- veal the time variability in the total spillover index, we apply a rolling window analysis8 and present the results in Fig. 2. The results from this measure of information spillover for the whole network demon- strate clear variability during the sample period and, importantly, gen- erally exhibit a declining trend. After peaking in early 2017, there is a steady decline towards March and into April 2018, when it bottoms out and then begins to slightly increase.
We also present the time-varying net spillover index for each group in Fig. 3, where time variation is omnipresent in all four groups but the signs of net spillover are dissimilar. For the Energy group, the net spill- over index (i.e., net transfer entropy) declines from the beginning of the sample period and switches to negative territory from Q3 of 2017 onwards, with a downward slope. The switch of the net spillover from positive to negative suggests a switch in the contribution of energy to the global flow of information from a net transmitter status to a net re- ceiver one. This is likely connected to the decreasing price of crude oil and, consequently, other energy commodities between 2015 and
8 We use a window size of 250 days, corresponding to a one-year period.
2016, when the West Texas Intermediate (WTI) crude oil price went from $110 per barrel to around $35 per barrel. The driving force behind energy commodities seems to be closely connected to this price, as the net spillover index starts growing with the increasing price in 2017 and 2018. Interestingly, the Cryptocurrency group is consistently a net transmitter of information during all sample periods, with evidence of an increase in its contribution to the global transmission of information during the period from early 2017 to mid-2018. The role of cryptocurrencies has thus had an evident increasing tendency. How- ever, this might be a similar situation to that of energy commodities, as the cryptocurrencies appreciate in price for most of the examined pe- riod and the net spillover index stabilises at the end of the period, when the rolling windows get to the correction year of 2018. As for the Metals group, it spends the whole sample period in negative territory (i.e., as a net receiver of information), except for a short period ranging from March to April 2017. As for the Agricultural group, its net spillover index swings but remains in the negative area, making it a consistent net receiver of information during all sample periods.
In Table 4, we also present the summary statistics for the in-degree, out-degree and net spillover index of each variable under study. The
Q. Ji et al. / Energy Economics 81 (2019) 10421055 1051
Fig. 4. MST based on pairwise transfer entropy information.
Table 5
Integration degree among different types of assets. Cryptocurrency Metals
Energy
Agricultural
Cryptocurrency Metals
Energy
Agricultural
External integration
6.299
6.925 7.846
5.601 5.329 3.195
5.876 6.016 3.490 4.106 18.402 18.27 14.42 15.382
Note: The value of each element in the table is calculated as the average of the sum of all the pairwise shortest paths between the variables in the pairwise types of assets. For ex- ample, the value of the element Cryptocurrency, Metals is calculated as the average of the sum of all the pairwise shortest paths between one node in Cryptocurrency and an- other node in Metals.

1052 Q. Ji et al. / Energy Economics 81 (2019) 10421055
highest weighted average in-degree values in each of the four groups are as follows: Bitcoin (0.320) in Cryptocurrency; aluminium (1.300) in Metals; unleaded gas (1.101) in Energy; and wheat (1.390) in Agri- cultural commodities. The central cryptocurrency of Bitcoin being a cen- tral node is not surprising, as Bitcoin is usually synonymous with the whole cryptomarket. Until 2017, Bitcoin capitalisation comprised be- tween 80% and 90% of all cryptomarket capitalisation. It was only in 2017, the year that experienced the unleashing of altcoins and tokens, that the dominant role of Bitcoin was diminished. In energy commodi- ties, even though unleaded gas has the highest statistics, it is on a similar level with other commoditiesspecifically, heating oil and crude oil and it seems there is no strong central point in this group of commodi- ties. A similar outcome is found for agricultural commodities. As for the
highest weighted average out-degree values, they are reported for Ethereum (2.099) in the Cryptocurrency group; gold (1.158) in Metals; natural gas (1.024) in Energy; and soybeans (0.800) in Agricultural commodities. Regarding the net spillover index, Ethereum and Stellar have the largest values in the Cryptocurrency group, which is a net transmitter of information (see also Fig. 3). Gold is a net transmitter, whereas the rest of the commodities in the Metals group are net re- ceivers of information, especially aluminium (0.698). In the Energy group, natural gas is the only net transmitter, whereas the largest net re- ceiver is unleaded gas. In the Agricultural group, which contains only net receivers, live cattle and sugar are the two largest net receivers. Ethereum being a receiver of information reflects its role as a smart con- tract cryptocurrency. In the boom of 2017, many projects launched their
Fig. 5. System integration index based on the time-varying MST.
Fig. 6. Integration index for each type of asset based on the time-varying MST. Note: The value of the integration index for each type of asset is calculated as the average of the sum of all the pairwise shortest paths between one node in one type and another node in the other types.

ICOs, and most of them were based on the Ethereum platform. As long as the cryptomarket was booming, ICO issues were booming as well, which led to skyrocketing demand for Ethereum as their most popular host platform. Gold holds its position as a safe-haven asset.
3.3. Centrality network analysis
While the above analyses consider the information spillover net- work by giving special attention to the direction of spillover, the analy- ses in this section consider the information integration network by emphasising the intensity of the spillover.9 Specifically, we construct both static and dynamic MSTs to highlight the importance of each indi- vidual variable (or group of variables) and the stability and evolution of the integration structure for the information flow.
3.3.1. Static results
Focusing on the core connections among all the variables under study, Fig. 4 illustrates the MST based on pairwise information spillovers. It shows that some commodities and cryptocurrencies are clustered together. However, the most important cluster in the network is centred on natural gas, suggesting that this energy commod- ity is a predominant commodity and has a powerful influence in the MST.
Table 5 presents results related to the degree of integration among the four groups (i.e., Cryptocurrency, Energy, Metals and Agricultural), which could facilitate a better understanding than can connections be- tween separate assets. First, we see that energy commodities are the most central ones in the network, closely followed by agricultural com- modities. This is in accordance with the previous observation of energy and agricultural commodities being tightly interconnected. Second, the energy and agricultural commodities are also quite closely connected within their respective groups, meaning that energy commodities tend to move together, as do agricultural commodities. A much weaker connection is observed among metal commodities and among cryptocurrencies. And third, the most detached group in terms of the network structure is the Metals group. Cryptocurrency has the largest external integration value of 18.402, showing a weaker connection with commodities within the system.
3.3.2. Dynamic results
Unlike the static results above, these results reveal evidence of time variability. Similar to Subsection 3.2.2, we use a rolling window with a duration of 250 days. Fig. 5 shows the system integration index, which is based on the time-varying MST. It appears that the integration degree of the cryptocurrency-commodity system is relatively stable during the period of 2016 to 2017 and then exhibits a decreasing trend from the beginning of 2018,10 which might be produced by changes in individual market conditions or common external shocks (Ji et al., 2018a).
We also focus on the evolution of the importance of each group in the information integration network. As shown in Fig. 6, the importance of the Energy commodity group continues to increase since the energy integration index reaches a peak experienced in October 2016. This is not the case for the Cryptocurrency and Metals groups, which experi- ence large fluctuations. As for the Agricultural group, it exhibits narrower variability.
We conducted further analysis to detect the identity of the most im- portant or central commodity/cryptocurrency in the network structure. Although the existing literature presents mixed views about what cen- trality is and how it is measured, we apply three measures of centrality that have been extensively used in academic research: degree
9 This is done while ignoring the direction of spillover (Yang and Zhou, 2017).
10 Note that the system integration index is an opposite indicator calculated by the
shortest paths.
Table 6
Summary statistics of centrality measures.
Q. Ji et al. / Energy Economics 81 (2019) 10421055
1053
Degree centrality
Mean Std.
dev dev
Closeness centrality
Betweenness centrality
Mean Std. dev
0.016 0.056 0.000 0.010 0.013 0.058 0.000 0.000 0.000 0.000 0.073 0.064 0.184 0.172 0.118 0.135 0.116 0.169 0.189 0.192 0.161 0.204 0.334 0.248 0.280 0.238
0.226 0.228 0.293 0.248 0.376 0.221 0.130 0.143 0.099 0.156 0.048 0.067 0.118 0.183 0.168 0.200 0.092 0.126 0.287 0.268 0.226 0.209
Cryptocurrency
Metals
Energy
Agricultural
Bitcoin Ethereum Ripple Stellar Litecoin Gold
Silver Aluminium Copper Nickel NaturalGas HeatingOil Unleaded Gas
Crude Oil LiveCattle Cocoa Coffee
Corn
Cotton LeanHogs OrangeJuice Soybeans Wheat Sugar
1.132 0.438 1.002 0.042 1.063 0.244 1.000 0.000 1.000 0.000 1.842 0.738 2.467 0.949 2.037 1.085 1.664 0.912 2.079 0.978 1.979 1.157 2.743 1.175 2.678 1.206
2.295 1.307 2.631 1.183 3.167 1.192 1.989 0.894 1.622 0.794 1.522 0.687 1.508 0.732 1.754 0.820 1.745 0.760 2.640 1.613 2.467 1.233
167.852 25.706 166.097 27.351 164.019 28.300 166.087 29.102 168.176 26.203 149.616 27.863 132.334 27.177 136.277 22.945 141.175 29.665 128.696 22.742 135.689 31.311 118.263 26.519 122.964 29.028
125.818 27.361 119.890 30.443 109.953 22.689 139.364 23.191 138.606 25.976 148.510 26.738 137.540 28.722 134.333 28.322 135.923 22.374 123.081 30.708 127.474 27.279
Mean Std.
centrality, closeness centrality and betweenness centrality (Ji and Fan, 2016; Ji et al., 2018a).
Table 6 presents the summary statistics of those three centrality measures. The results from the measure of degree centrality show that cocoa is the most important node in the MST, followed by heating oil. This suggests that information spillover from these two commodities plays a central role in influencing the other variables. The highest value for closeness centrality is that of Litecoin, suggesting a low degree of co-movement between this cryptocurrency and the other variables under study and, thus, a peripheral position in the MST. In contrast, cocoa has the lowest measure of closeness centrality, which indicates tight connections with the other variables and a central position in the MST. Regarding the betweenness centrality measure, cocoa and heating oil play important roles in connectedness in the information flow. The results for the measures of closeness and betweenness centrality, which highlight the importance of each variable, are generally consis- tent with the results for degree centrality.
4. Concluding remarks
Despite some early studies on the relationship between Bitcoin and commodity markets, the issue of the information spillovers and system integration of various energy and non-energy commodities and leading digital currencies remains a puzzle to investors, practitioners and policymakers. Motivated by a growing literature on the possible associ- ation between certain commodities (e.g., gold and crude oil) and lead- ing cryptocurrencies (e.g., Bitcoin) emanating from some similarities in the features of commodities and cryptocurrencies, this study applies various network-based methods and centrality measures to examine in- formation spillovers among the returns of energy, cryptocurrency and major commodities. This is accomplished by considering both the direc- tion and intensity of spillovers from static and dynamic perspectives. The results of the directional spillover analysis suggest that the most im- portant movers in the system are agricultural and energy commodities, whereas metals react the least to information flow in the system.

1054 Q. Ji et al. / Energy Economics 81 (2019) 10421055
Cryptocurrencies inhabit the mid-range in terms of importance but are well established within the system.
Interestingly, the connection between cryptocurrencies and energy commodities is rather weak, which runs contrary to the common belief that energy plays an essential role in cryptocurrency pricing. A rolling- window approach reveals evidence of dynamic characteristics in the transfer entropy in most cases. We use a time-varying entropy-based approach to identify the direction of return spillovers, and the results show that the nature of information spillovers changes over time, with cryptocurrencies becoming the largest net transmitter of spill- overs; in contrast, the spillover contribution of energy commodities to the system is dependent on their price dynamics. Regarding the inten- sity of spillovers, results from the MST highlight the importance of en- ergy and agricultural commodities, which form the backbone of the entire system. The least connected of the groups is the Metals group. Cryptocurrencies are well integrated within the network, but as a group, they show strong signs of heterogeneity. The core structure of this network hierarchy does not change much over time even though the detailed connections are rather volatile and unstable.
Our empirical analyses have major implications for decision-makers as investors and policymakers are very concerned with information spillovers across commodities and other markets, including the cryptocurrency market. A major implication is that commodity (or cryptocurrency) investors should not neglect information spillovers from the cryptocurrency (or commodity) market when building invest- ment strategies that involve designing portfolios and risk-management measures. Given the evidence of time variability in information spill- overs, investment decisions and policy measures must pay special at- tention to ensuring a dynamic approach in portfolio rebalancing and risk inferences. Even though cryptocurrencies have very specific statis- tical and correlative properties within the system, their diversification benefits do not seem to be miraculous as they seem to be quite well con- nected to the commodities network even though they are certainly not central to the overall system. However, this will likely only be the case until the next global market cooling, when the true nature of cryptocurrencies diversification potential may be seen; this is because the analysed period still mostly falls within the aftermath of the global financial crisis and the subsequent quantitative easing and booming of the prices of practically all financial assets, which occurred after the wave of cheap money provided by the most important central banks.
There are several interesting future avenues one might take when studying the static and dynamic connections within the system of cryptocurrencies and commodities. First, other entropy measures such as effective transfer entropy, Renyi transfer entropy and effective Renyi transfer entropy (He and Shang, 2017) can be utilised to check the robustness of the results. Second, the results can be materialised in practical portfolio construction. Third, the cryptocurrency part of the system calls for a more detailed network analysis not only connected to its price dynamics and spillovers but also to the dynamics and con- nections between prices, volatility, liquidity as well as mining costs. Even though there are some expected results to be found as various groups of cryptocurrencies are bound to be tightly connected together with respect to their protocols and mining algorithms, a detailed study of such interconnections is still missing. Overall, the cryptocurrency market and its rich network structure provide a wealth of possibilities for future research, and most of the related questions are far from being answered.
Acknowledgement
The first author acknowledges supports from the National Natural Science Foundation of China (Grant No. 71774152, No. 91546109) and the Youth Innovation Promotion Association of Chinese Academy of Sci- ences (Grant No. Y7X0231505). The last author acknowledges supports from the Charles University PRIMUS program (project PRIMUS/19/ HUM/17).
Appendix A. Supplementary data
Supplementary data to this article can be found online at https://doi. org/10.1016/j.eneco.2019.06.005.
References
Acharya, V., Pedersen, L.A., 2005. Asset pricing with liquidity risk. J. Financ. Econ. 77, 375410.
Altiparmak, F., Dengiz, B., 2009. A cross entropy approach to design of reliable networks. Eur. J. Oper. Res. 199 (2), 542552.
Baur, D.G., McDermott, T.K.J., 2010. Is gold a safe haven? International evidence. J. Bank. Financ. 34, 18861898.
Baur, D.G., McDermott, T.K.J., 2016. Why is gold a safe haven? J. Behav. Exp. Financ. 10, 6371.
Bekiros, S., Nguyen, D., Junior, L.S., Uddin, G.S., 2017. Information diffusion, cluster forma- tion and entropy-based network dynamics in equity and commodity markets. Eur. J. Oper. Res. 256, 945961.
Billio, M., Getmansky, M., W. Lo, A., Pelizzon, L., 2012. Econometric measures of connect- edness and systemic risk in the finance and insurance sectors. J. Financ. Econ., 104, 535559.
Blau, B.M., 2017. Price dynamics and speculative trading in bitcoin. Res. Int. Bus. Financ. 41, 493499.
Bouri, E., Jalkh, N., Molnar, P., Roubaud, D., 2017. Bitcoin for energy commodities before and after the December 2013 crash: diversifier, hedge or safe haven. Appl. Econ. 49 (50), 50635073.
Bouri, E., Das, M., Gupta, R., Roubaud, D., 2018a. Spillovers between bitcoin and other as- sets during bear and bull markets. Appl. Econ. 50 (55), 59355949.
Bouri, E., Gupta, R., Lahiani, A., Shahbaz, M., 2018b. Testing for asymmetric nonlinear short-and long-run relationships between bitcoin, aggregate commodity and gold prices. Resources Policy 57, 224235.
Brauneis, A., Mestel, R., 2018. Price discovery of cryptocurrencies: bitcoin and beyond. Econ. Lett. 165, 5861.
Castagneto-Gissey, G., Chavez, M., De Vico Fallani, F., 2014. Dynamic Granger-causal net- works of electricity spot prices: a novel approach to market integration. Energy Econ. 44, 422432.
Diebold, F.X., Yilmaz, K., 2014. On the network topology of variance decompositions: measuring the connectedness of financial firms. J. Econ. 182, 119134.
Filip, O., Janda, K., Kristoufek, L., Zilberman, D., 2016. Dynamics and evolution of the role of biofuels in global commodity and financial markets. Nat. Energy 1, 16169.
Filip, O., Janda, K., Kristoufek, L., Zilberman, D., 2017. Food versus fuel: an updated and ex- panded evidence. Energy Economics https://doi.org/10.1016/j.eneco.2017.10.033. Hayes, A., 2017. Cryptocurrency value formation: an empirical analysis leading to a cost of
production model for valuing bitcoin. Telematics Inform. 34 (7), 13081321.
He, J., Shang, P., 2017. Comparison of transfer entropy methods for financial time series.
Physica A: Statistical Mechanics and its Applications 482, 772785.
Henriques, I., Sadorsky, P., 2018. Can bitcoin replace gold in an investment portfolio? Jour-
nal of Risk Financial Management 11 (3), 48.
Janda, K., Kristoufek, L., 2019. The Relationship between Fuel and Food Prices: Methods
and Outcomes. Annual Review of Resource Economics (in print).
Janda, K., Kristoufek, L., Zilberman, D., 2012. Biofuels: policies and impacts. Agricultural
Economics Czech 58 (8), 372386.
Ji, Q., Fan, Y., 2016. Evolution of the world crude oil market integration: a graph theory
analysis. Energy Econ. 53, 90100.
Ji, Q., Bouri, E., Gupta, R., Roubaud, D., 2018a. Network causality structures among bitcoin
and other financial assets: a directed acyclic graph approach. The Quarterly Review of
Economics and Finance 70, 203213.
Ji, Q., Bouri, E., Lau, M.C.K., Roubaud, D., 2018b. Dynamic connectedness and integration in
cryptocurrency markets. Int. Rev. Financ. Anal. 63, 257272.
Ji, Q., Bouri, E., Roubaud, D., 2018c. Dynamic network of implied volatility transmission
among US equities, strategic commodities, and BRICS equities. Int. Rev. Financ.
Anal. 57, 112.
Ji, Q., Bouri, E., Roubaud, D., Shahzad, S.J.H., 2018d. Risk spillover between energy and ag-
ricultural commodity markets: a dependence-switching CoVaR-copula model. En-
ergy Econ. 75, 1427.
Ji, Q., Liu, B., Fan, Y., 2019. Risk dependence of CoVaR and structural change between oil
prices and exchange rates: a time-varying copula model. Energy Econ. 77, 8092. Klein, T., Thu, H.P., Walther, T., 2018. Bitcoin is not the new golda comparison of volatil-
ity, correlation, and portfolio performance. Int. Rev. Financ. Anal. 59, 105116. Kodres, L., Pritsker, M., 2002. A rational expectations model of financial contagion.
J. Financ. 57, 769800.
Koutmos, D., 2018. Return and volatility spillovers among cryptocurrencies. Econ. Lett.
173, 122127.
Kristoufek, L., Janda, K., Zilberman, D., 2012. Correlations between biofuels and related
commodities before and during the food crisis: a taxonomy perspective. Energy
Econ. 34 (5), 13801391.
Lo, S., Wang, C. J., 2014. Bitcoin as Money? Current Policy Perspectives, No. 144, Federal
Reserve Bank of Boston, Boston, MA. 2014.
Luo, J., Ji, Q., 2018. High-frequency volatility connectedness between the US crude oil mar-
ket and Chinas agricultural commodity markets. Energy Econ. 76, 424438.
Ma, F., Zhang, Y., Wahab, M.I.M., Lai, X., 2019a. The role of jumps in the agricultural futures market on forecasting stock market volatility: new evidence. J. Forecast. https://doi.
org/10.1002/for.2569.

Ma, Y., Ji, Q., Pan, J., 2019b. Oil financialisation and volatility forecast: evidence from mul- tidimensional predictors. J. Forecast. https://doi.org/10.1002/for.2577
Ma, Y., Zhang, D., Ji, Q., Pan, J., 2019c. Spillovers between oil and stock returns in the US energy sector: does idiosyncratic information matter? Energy Econ. 81, 536544. Polasik, M., Piotrowska, A.I., Wisniewski, T.P., Kotkowski, R., Lightfoot, G., 2015. Price fluc-
tuations and the use of bitcoin: an empirical inquiry. Int. J. Electron. Commer. 20 (1),
949.
Popper, N., 2015. Digital Gold: The Untold Story of Bitcoin. Penguin, London.
Prim, R.C., 1957. Shortest connection networks and some generalizations. Bell Syst. Tech.
J. 36 (6), 13891401.
Schreiber, T., 2000. Measuring information transfer. Phys. Rev. Lett. 85, 461464.
Selgin, G., 2015. Synthetic commodity money. J. Financ. Stab. 17, 9299.
Selmi, R., Mensi, W., Hammoudeh, S., Bouoiyour, J., 2018. Is bitcoin a hedge, a safe haven
or a diversifier for oil price movements? A comparison with gold. Energy Econ. 74,
787801.
Shahzad, S.J.H., Bouri, E., Roubaud, D., Kristoufek, L., Lucey, B., 2019. Is bitcoin a better safe-
haven investment than gold and commodities? Int. Rev. Financ. Anal. 63, 322330.
Shannon, C.E., 1948. A mathematical theory of communication. Bell System Technical Journal, 27, 379423, 623656.
Wang, Y., Wei, Y., Wu, C., Yin, L., 2018. Oil and the short-term predictability of stock return volatility. J. Empir. Financ. 47, 90104.
Yang, Z., Zhou, Y., 2017. Quantitative easing and volatility spillovers across countries and asset classes. Manag. Sci. 63 (2), 333354.
Yermack, D., 2013. Is bitcoin a real currency? An economic appraisal. No. w19747. Na- tional Bureau of Economic Research 2013.
Zhang, D., 2017. Oil shocks and stock markets revisited: measuring connectedness from a global perspective. Energy Econ. 62, 323333.
Zhang, D., Broadstock, D.C., 2018. Global financial crisis and rising connectedness in the international commodity markets. Int. Rev. Financ. Anal. https://doi.org/10.1016/j. irfa.2018.08.003
Zhang, D., Ji, Q., Kutan, A., 2019. Dynamic transmission mechanisms in global crude oil prices: estimation and implications. Energy 175, 11811193.
Q. Ji et al. / Energy Economics 81 (2019) 10421055 1055