Nonlinear dependence and information spillover between electricity and fuel source markets: New evidence from a multi-scale analysis

Physica A 537 (2020) 122298

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Nonlinear dependence and information spillover between electricity and fuel source markets: New evidence from a multi-scale analysis Tongshui Xia a , Qiang Ji b,c , Jiang-Bo Geng d ,

∗

a

Business School, Shandong Normal University, Jinan, Shandong, 250014, China Center for Energy and Environmental Policy research, Institutes of Science and Development, Chinese Academy of Sciences, Beijing 100190, China c School of Public Policy and Management, University of Chinese Academy of Sciences, Beijing 100049, China d School of Finance, Zhongnan University of Economics and Law, Wuhan 430073, China b

highlights • • • • •

Multi-scale nonlinear causality between PJM electricity and fuel returns is explored. Information spillover between them is examined using connectedness network. Causality direction between them behave differently across time horizons. Positive weak spillover from oil and uranium to electricity returns exists. Information spillover from the gas to electricity returns is relatively strong.

article

info

Article history: Received 6 May 2019 Received in revised form 25 July 2019 Available online 13 September 2019 Keywords: Electricity prices Fuel prices Ensemble empirical mode decomposition Nonlinear causality test Connectedness network

a b s t r a c t This study identifies nonlinear causality between electricity and fuel source returns based on a new multi-scale framework. The empirical results show that the causality direction between electricity and fuel returns behaves differently across time scales. Generally speaking, linear or nonlinear causality relationship between the electricity and gas markets exists for most time scales. The study also explores the magnitude of the feedback effects between electricity and fuel returns using the connectedness network. The results show that the degree of feedback effects between the electricity and fuel markets is relatively weak at the original data level. Across various time scales, there is positive but weak information spillover from the oil and uranium to electricity markets and reciprocal information spillover between the electricity and gas/coal markets at most time horizons. The information spillover from the gas to electricity returns is relatively strong. © 2019 Published by Elsevier B.V.

1. Introduction The challenge of low carbon development and environmental regulations has led many countries to close up some coal-fired power stations and increase the use of clean energy as a fuel source [1]. However, as the rise of the global power supply derived from renewable energy is relatively slow, natural gas as a kind of low carbon energy has received much ∗ Corresponding author. E-mail address: [email protected] (J.-B. Geng). https://doi.org/10.1016/j.physa.2019.122298 0378-4371/© 2019 Published by Elsevier B.V.

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T. Xia, Q. Ji and J.-B. Geng / Physica A 537 (2020) 122298

concern [2]. The proportion of gas in the power generation mix may rise and the proportion of coal may decrease with the further implementation of low carbon development. Changes now appearing in the power generation mix mean that regulators and energy policy makers need to make new portfolios or storage plans for power generation. It is, therefore, important to clarify the new feedback effects between the electricity and fuel source markets. Looking at the fuel mix of the Pennsylvania–New Jersey–Maryland (PJM) interconnection electricity market, more than 93%1 of electricity in that market is generated from coal, uranium and natural gas [3]. The four major sources of fuel for the PJM electricity market are coal, uranium, natural gas and crude oil — at 30.4%, 34.9%, 27.2% and 0.3%, respectively.2 As can be seen, the proportion of natural gas has been large, which may be resulted from the increase of shale gas in North America [4]. Therefore, the PJM electricity market was chosen as the research sample in this study. Clarifying the dependence structure and information spillover mechanism between the PJM electricity market and fuel source markets will help in formulating appropriate energy policies and commercial and trade strategies for sustainable and non-polluting power sources. The behaviour of energy policymakers and market participants may differ across various time horizons. As the evolution characteristics of energy prices may be different across various time scales [5–7], the dependence structure and information spillover mechanism between the electricity and power generation fuel markets may be sensitive to time horizons. In addition, nonlinear structural features should be considered vis-à-vis electricity and fuel prices [8–11]. Several prominent studies argue that nonlinear structural features are mainly the result of regime changes and significant emergencies (such as geopolitical wars, hurricanes and financial crises). The release and implementation of new policy of energy may cause structural changes in the electricity and fuel markets, thus showing nonlinear characteristics [12,13]. Therefore, this study uses nonlinear causality tests to explore the nonlinear dependence structure between the electricity and the fuel markets. This study contributes to the body of knowledge in three ways. First, under the new conditions with a high ratio of natural gas, the study offers new evidence as to how the dependence structure between the electricity and the fuel markets changes on various time scales. Secondly, the study clarifies the nonlinear linkage between each pair of decomposition series for the electricity and fuel markets. This information is compared with the results of linear causality tests. Thirdly, the connectedness network approach proposed by Diebold and Yilmaz [14] is employed for the first time to examine the information spillover between the electricity and fuel markets. In this way, the study is able to identify the extent to which electricity return variation is influenced by the dynamics of fuel source returns. The remainder of this paper is organised as follows. Section 2 consists of a literature review. Section 3 mainly describes the EEMD method, nonlinear Granger causality tests, the connectedness network method and the data sources. Section 4 consists of the empirical results and the discussion. Section 5 presents the conclusion and policy implications. 2. Literature review Existing studies have shown a high degree of convergence between the electricity and the fuel markets [15,16]. These studies have also found that the relationship between the electricity and the fuel markets varies significantly depending on the country and the specific market. The following section reviews the relevant research on this issue. For many countries, natural gas is one of the major fuels for power generation, and the natural gas and electricity markets often maintain a long-term dynamic linkage. Although some scholars have found that there does not exist Granger causality for gas and electricity markets [17], many others agree that gas market does exert considerable influence on the electricity market. In a study on the short- and long-term linkage for commodity and Spanish electricity markets, Moutinho et al. [18] found that the evolution of natural gas prices is able explain Spanish electricity prices. Studying the linkage between liquefied natural gas (LNG) and electricity markets in Korea, Chae et al. [19] found a strong unidirectional causal relationship from LNG to electricity prices in both the short and long term. Analysing the causal relationship between Spanish electricity futures and Belgian Zeebrugge port gas futures prices, Furió and Chuliá [20] found a unidirectional causality form the price volatility of gas and the electricity market. Nakajima and Hamori [21] analysed the Granger causality for electricity and gas markets in the southern United States and found unidirectional Granger causality between the two. Gal et al. [22] studied the effect of the uncertainty of natural gas prices on investment capacity and electricity market, pointing out that the natural gas price volatility tends to increase the market risk of independent electricity producers in the electricity market. However, other scholars have found a bidirectional linkage mechanism for the gas and electricity markets. When studying the Granger causality relationship for electricity and gas prices in California, Woo et al. [23] found bidirectional Granger causality between the two kinds of price series. Serletis and Shahmoradi [24] and Czamanski et al. [25] found a bidirectional linear and nonlinear causality for the power and gas markets in Alberta. Brown and Yücel [26] used data from 1997 to 2007 to show that a bidirectional effect existed between electricity and gas markets. Mjelde and Bessler [3] analysed the dynamic price information flow between electricity spot and gas markets in the United States. They found that electricity and gas prices had a reciprocal impact. Peng and Poudineh [27] pointed out that with the increased use of natural gas to generate power, the natural gas and electricity industries were experiencing a gradual merging [28–30]. 1 The data were collected in 2017 from the following website: http://www.pjm.com/markets-and-operations.aspx. 2 The data were collected in 2017 from the following website: http://www.pjm.com/markets-and-operations.aspx.

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Some scholars have analysed the linkage between the electricity and crude oil markets. Muñoz and Dickey [31] found that Spanish electricity prices were influenced by oil prices in a short period. Nakajima and Hamori [32] found that crude oil prices in Japan affected the power generation costs strongly. Furió and Chuliá [20] studied the causal relationship between Spanish electricity and Brent crude oil futures prices. Their results showed a unidirectional causality from the oil to electricity markets. Using the multivariable generalised autoregressive heteroscedasticity (GARCH) model and daily data from 2001 to 2013, Efimova and Serletis [33] analysed the fluctuation of crude oil and electricity prices for the United States and found a unidirectional relationship from the crude oil to electricity prices. As coal is the main fuel for power generation in many countries, some scholars have analysed the relationship between the electricity and coal markets. Mohammadi [34] analysed the long- and short-term dynamic linkage between electricity and coal markets in the United States and found a bidirectional long-term causal relationship. Liu et al. [35] pointed out the long-term relationship between China’s coal and electricity prices; however, this relationship was weak for residential electricity pricing. Proposing a new electricity price model, Zachmann [10] showed that although British electricity prices could be explained by coal and natural gas prices in the short term, German electricity prices could not. Some scholars have studied the relationship between the electricity and uranium markets. Amavilah’s study [36] showed that electricity prices had a direct negative impact on the demand for uranium as a fuel source. Kahouli [37] found that electricity prices have had a significant impact on the demand for uranium fuel since 1990. As can be seen from the above review, the existing literature has mainly analysed the relationship between the electricity and fuel markets on the original data level, which does not consider the multiple time scale characteristics that energy prices may exhibit. Therefore, this study addresses the multi-horizon nature of the linkage for the electricity and other fuel prices using the EEMD method. To further account for nonlinearity, this study also employs a nonlinear causality test proposed by Diks and Panchenko [38]. The study also uses the newly proposed connectedness network method to examine the magnitude and asymmetry of information spillover between the electricity and the fuel markets. 3. Methodology and data sources 3.1. EEMD model Using the EEMD method, the original market return series can be exhibited by independent intrinsic mode functions (IMFs) and one residual term [39], as follows: EleR(t) =

n ∑

ciEleR (t) + r EleR (t) and

(1)

i=1

FuelR(t) =

n ∑

ciFuelR (t) + r FuelR (t),

(2)

i=1

where EleR(t) and FuelR(t) represent the original electricity and fuel return series, respectively; n represents the number of IMFs; c(t) represents the independent IMFs that are orthogonal to one another; and r(t) represents the residual term. The total extracted number of IMFs is limited to log2 T, where T is the length of the electricity and fuel return series. 3.2. Nonlinear granger test using the GARCH (1,1) model Generally, considering that electricity and fuel returns contain a time-varying volatility, the GARCH effect should be eliminated in order to make the results of the nonlinear Granger causality test be robustness [40–42]. Therefore, the GARCH (1,1) model is used as follows [43]: yt = x′t γ + ut , ut ∼ N(0, σt2 ),

(3)

σt2 = a0 + a1 u2t −1 + β1 σt2−1 ,

(4)

where xt = (x1t , x2t , . . . , xkt )′ represents the explanatory variable vector and γ = (γ1 , γ2 , . . . , γk ) represents the coefficient vector. The nonlinear causality test is then performed for the GARCH (1,1) filtering residual series. 3.3. Connectedness network model The information or risk spillover effects always exist in financial or energy markets [44–47]. The connectedness network model has been widely used to analyse the information spillover effect related to financial markets or energy markets [48–50], which can identify the direction and the magnitude of spillover effects among different variables in the economic system. The impact degree of which a variable has on other variables is based on the results of the generalised variance decomposition [14,51]. Therefore, θijH can be used to represent the degree of the variablejcontributing to the

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T. Xia, Q. Ji and J.-B. Geng / Physica A 537 (2020) 122298 Table 1 Summary statistics of the electricity and fuel market returns. Mean Median Max Min Std. dev.

Electricity

Coal

Uranium

Gas

Oil

−0.241

0.032 0.000 18.232 −25.364 3.610

−0.125

−0.117

−0.070

0.000 18.232 −27.193 3.652

0.000 48.061 −41.753 8.297

0.248 25.253 −36.075 5.592

0.676 184.270 −169.821 35.906

variation for ∑ the variable i in its H period. Thus, the sum impact of the other variables to the variable i can be expressed k H as Fromi = j=1 θij , for j ̸ = i, whereas the total contribution degree of the variable i to the other variables can be

∑k

θjiH for j ̸= i. Therefore, the total spillover index can be defined as ∑k ∑k Toi i=1 Fromi Total = = i=1 .

represented as Toi =

j=1

k

k

The net total directional spillover measure (NDC ) for variable i can be calculated by the following formula: NDCi =

k ∑ j=i

θjiH −

k ∑

θijH ,

for i ̸ = j.

(5)

j=i

Thus, the net directional pairwise connectedness from the variable j to the variable i can be defined: Netij = θijH − θjiH . 3.4. Data sources This study uses weekly data. The data range is from July 17, 2006 to May 22, 2017. Electricity prices are extracted from the PJM interconnection electricity market, which is the world’s largest competitive power wholesale market [52]. In order to be comparable to the average daily spot prices of fuel sources, the study uses nonpeak electricity prices in the PJM market and the unit is U.S. dollars per megawatt. Both the nonpeak prices of the PJM electricity market and the coal and uranium prices are extracted from the Datastream database. Henry Hub spot prices and West Texas Intermediate (WTI) spot prices are obtained from the U.S. Energy Information Administration (EIA) website. All the data reflect Monday’s prices. Fig. 1 shows the spot price movements of electricity, coal, uranium fuel, gas and oil from July 17, 2006 to May 22, 2017. It can be seen that the PJM electricity and gas prices fluctuate more frequently and that the overall trends of coal, uranium and crude oil prices are similar. Table 1 shows the summary statistics of the electricity and fuel market returns. It is clear that the maximum and minimum value and the standard deviation value of the electricity and gas returns are higher than the coal, uranium and oil returns. This shows that the fluctuations of the electricity and gas markets are more obvious than for the other markets. It is mostly due to that the electricity and gas markets are vulnerable to seasonal effects. 4. Empirical results and discussion 4.1. Decomposition of electricity and fuel returns This study calculates the returns of electricity and fuel energy prices for further analyses. The decomposition results of the weekly returns of electricity markets are shown in Fig. 2. Six IMFs and one residual term were obtained using the EEMD method. The time scales and the importance of each decomposition mode series are presented in Table 2. Some results can be obtained from Table 2. IMF1 has an average duration of two to three weeks, containing the short market disequilibrium. The duration of IMFs 2 to 6 is from one month to one-and-a-half years. These series reflect the impact of irregular events such as hurricanes and other extreme weather or the effects of extreme events such as global financial crises. As electricity is the secondary energy source and the four fuels are the primary energy sources, electricity is the output product of the four power generation fuels. As a result, their respective market operating mechanisms are different, which means that the impact degree on electricity and fuel markets of different factors verify. Regarding the four fuel markets, the global economic environment and the geopolitical risk of oil-producing countries have great influence on the oil market [53,54]. As a regional market, the hurricanes or the emergence of the shale gas revolution may exert considerable influence on the natural gas market. Although their prices are often regulated, coal and uranium fuels are also impacted by dramatic changes in macroeconomic conditions. The residual series with the duration of about three years contain data with a long-term evolution trend. Similarly, for the electricity and the four fuel markets, their long-term trends exhibit different characteristics due to the impact of different factors. Electricity is the main source of secondary energy in terms of the economy; therefore, the long-term trend for electricity prices is largely influenced by the U.S. economic environment, and its price trend is largely in line with the U.S. economic cycle. For the four fuel markets, the

T. Xia, Q. Ji and J.-B. Geng / Physica A 537 (2020) 122298

Fig. 1. The weekly prices of electricity and fuel markets from July 17, 2006 to May 22, 2017.

Fig. 2. Decomposition results of the weekly returns of electricity markets.

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T. Xia, Q. Ji and J.-B. Geng / Physica A 537 (2020) 122298 Table 2 Measurements of the original data and extracted modes for returns. IMF1 (2–3) IMF (25–6) IMF3 (10–12) IMF4 (14–16) IMF5 (38–42) IMF6 (80–85) Residue (190)

Electricity

Coal

Uranium

Gas

Oil

54.38%a 22.33% 11.09% 3.72% 3.29% 2.07% 3.12%

28.59% 19.91% 13.90% 11.72% 9.72% 7.59% 8.57%

30.94% 20.33% 15.16% 11.79% 8.58% 6.39% 6.82%

41.96% 22.65% 12.69% 6.89% 6.28% 4.69% 4.83%

38.08% 19.15% 12.67% 10.50% 8.37% 5.65% 5.57%

Note: a Mode importance is calculated based on the proportion of the variance of each component that accounts for the total variances of IMFs and the residual item. Table 3 The Phillips and Perron unit test results. Original IMF1 IMF IMF3 IMF4 IMF5 IMF6 Residue

Electricity

Coal

Uranium

Gas

Oil

−83.611*** −65.249*** −21.814*** −4.664*** −7.248*** −5.308*** −3.641*** −1.877*

−22.404*** −80.864*** −20.424*** −4.391*** −5.234*** −3.111*** −2.380** −6.751***

−24.046*** −37.718*** −13.932*** −5.471*** −5.256*** −5.145*** −2.462** −5.050***

−26.821*** −47.864*** −10.427*** −4.218*** −5.405*** −4.597*** −3.077*** −2.290**

−25.390*** −49.351*** −13.486*** −3.956*** −5.276*** −4.258*** −2.512** −2.548**

Note: *Denote the significance at the 10% level. **Denote the significance at the 5% level. ***Denote the significance at the 1% level.

long-term trends of coal, uranium fuel and natural gas prices mainly is in pace with the evolution pattern of the crude oil market. The importance of IMFs and residual item to the original data series is identified by calculating the proportion of each variance for their total variances. The related results are also presented in Table 2. IMF1 contributes the largest to the total variances. Especially, the proportions of IMF1 for total market fluctuations are 54.38%, 28.59%, 30.94%, 41.96% and 38.08% for the electricity, coal, uranium, gas and oil returns, respectively. This indicates that IMF1 contributes the most to the behaviour of the electricity and the four fuel markets. The total fluctuation of IMFs 2 to 6 is also large. The residual item has the least share for the electricity and the four fuel markets. 4.2. Linear causality analysis Table 3 presents the results and finds that all series are stationary. Then, the VAR models for pairs of original time series and each pair of IMF series can be estimated to test the linear Granger causality. The optimal lag length of the model is determined according to the Akaike information criterion (AIC). Table 4 presents the linear causality for the electricity and fuel market returns at different time scales. At the original data level, there exists no linear causality between the electricity market and the coal, uranium and oil markets. However, bidirectional linear feedback effects for the electricity and gas markets are found. In the short term, no linear feedback effect can be found for the electricity and the coal, uranium and oil markets. However, unidirectional linear feedback effect exists for IMF1 from the electricity to gas markets. In the medium term, the existence of unidirectional linear feedback effect is supported from the electricity market to the coal market. For IMF3, there is only unidirectional linear feedback effect from the electricity to crude oil markets. In general, irregular or extreme events in the electricity market impact the coal and crude oil markets, whereas irregular or extreme events in the coal and crude oil markets have no effect on the electricity market. However, a unidirectional linear causality can be found from the uranium and gas markets to the electricity market for most cases. This also shows that irregular or extreme events in the uranium and natural gas markets may exert influence on the electricity market. For the long-term trend, the results show bidirectional linear Granger causality for the electricity market and the coal, gas and oil markets, which further emphasises that their long-term evolution patterns have reciprocal influences. However, the test results exhibit that only unidirectional linear feedback effect is present from the uranium to electricity markets, which further underlines the fact that the long-term evolution pattern of the electricity market would be impacted by that of the uranium market.

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Table 4 Multi-scale linear Granger causality between the electricity and fuel market returns. Series

Laga

H0 : electricity does not cause fuel source

H0 : fuel source does not cause electricity

Results

χ2

p-value

χ2

p-value

0.189 0.199 0.609 0.007 0.043 0.413 0.468 0.000

3.685 2.560 11.373 15.415 14.018 30.235 4.844 54.229

0.815 0.923 0.251 0.696 0.728 0.113 0.774 0.000

✕ ✕ ✕ electricity=>coal electricity=>coal ✕ ✕ electricity<=>coal

0.420 0.440 0.366 0.618 0.970 0.120 0.441 0.249

6.988 8.693 22.706 16.329 14.278 26.539 15.564 84.808

0.430 0.276 0.007 0.091 0.113 0.001 0.049 0.000

✕ ✕ electricity<=uranium electricity<=uranium ✕ electricity<=uranium electricity<=uranium electricity<=uranium

0.010 0.005 0.210 0.779 0.446 0.570 0.454 0.000

51.799 7.703 7.076 5.010 16.645 64.620 29.098 104.021

0.000 0.360 0.314 0.891 0.055 0.000 0.001 0.000

electricity<=>gas electricity=>gas ✕ ✕ electricity<=gas electricity<=gas electricity<=gas electricity<=>gas

0.206 0.338 0.261 0.0003 0.895 0.699 0.702 0.000

9.616 5.033 11.398 14.263 19.005 5.656 3.734 75.249

0.383 0.754 0.327 0.430 0.165 0.686 0.880 0.000

✕ ✕ ✕ electricity=>oil ✕ ✕ ✕ electricity<=>oil

The electricity and coal returns Original IMF1 IMF2 IMF3 IMF4 IMF5 IMF6 Residue

7 7 9 19 18 22 8 4

9.995 9.816 7.268 37.442 29.488 22.796 7.657 150.990

The electricity and uranium returns Original IMF1 IMF2 IMF3 IMF4 IMF5 IMF6 Residue

7 7 9 10 9 8 8 4

7.087 6.894 9.809 8.112 2.837 12.764 7.926 5.393

The electricity and gas returns Original IMF1 IMF2 IMF3 IMF4 IMF5 IMF6 Residue

7 7 6 10 9 21 9 4

18.382 20.507 8.407 6.414 8.912 19.232 8.818 37.293

The electricity and oil returns Original IMF1 IMF2 IMF3 IMF4 IMF5 IMF6 Residue

9 8 10 14 14 8 8 4

12.130 9.054 12.366 39.443 7.889 5.534 5.514 42.848

Note: a The optimal lag order is determined based on the AIC criterion.

4.3. Nonlinear causality analysis The results of multi-scale nonlinear causality between the electricity and fuel market returns are presented in Table 5.3 On the original data level, the results show that no nonlinear causality can be found between the electricity and the coal, uranium and oil markets, whereas a unidirectional nonlinear feedback effect is present from the gas to electricity markets. Additionally, in the short term, no nonlinear causality is present between the electricity and any of the fuel markets. It suggests that the short-term market fluctuations for the electricity and fuel have no reciprocal nonlinear interaction. In the medium term, bidirectional nonlinear causality between the electricity and all the fuel markets can be found. Significant events in the electricity and gas markets will impact each other. For example, when the frequent occurrence of extreme weather posed substantial threats to the PJM market during the 2014 North American polar vortex, the demand of natural gas raised in order to maintain the reliable operation of the power system without having an electricity shortage. The shale gas revolution in the North America that began in 2006 caused the share of gas used for power generation to increase significantly [4]. In the long term, no nonlinear causality can be found between the electricity and the coal, uranium and gas market returns, whereas unidirectional nonlinear feedback effect is presented from the electricity to crude oil markets.

3 The parameter for the bandwidth C is set to 8, the theoretical optimisation rate is set to 2/7 and the optimal bandwidth based on the sample size is set to 1.5.

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T. Xia, Q. Ji and J.-B. Geng / Physica A 537 (2020) 122298 Table 5 Multi-scale nonlinear Granger causality between the electricity and fuel market returns. Y-variables

X |Y

Y |X

Y-variables

Coal

Gas

Original IMF1 IMF2 IMF3 IMF4 IMF5 IMF6 Residue

Original IMF1 IMF2 IMF3 IMF4 IMF5 IMF6 Residue

** * *

**

Uranium

Oil

Original IMF1 IMF2 IMF3 IMF4 IMF5 IMF6 Residue

Original IMF1 IMF2 IMF3 IMF4 IMF5 IMF6 Residue

* ** ***

**

X |Y

Y |X

* *** * * *** ***

** *

** * *

***

Note: The test is made in two directions: X means the electricity returns; Y |X implies variable Y Granger-causes variable X; and X |Y implies variable X Granger-causes variable Y. *Denote the significance at the 10% level. **Denote the significance at the 5% level. ***Denote the significance at the 1% level. Table 6 The connectedness matrix for original returns. Electricity Coal Uranium Gas Oil To others Net

Electricity

Coal

Uranium

Gas

Oil

From others

94.317 0.780 0.543 5.100 0.725 7.148 1.465

0.348 89.367 1.628 2.052 5.022 9.050 −1.583

0.615 0.744 97.282 2.153 1.015 4.527 1.809

3.739 1.701 0.216 88.617 1.643 7.298 −4.085

0.981 7.410 0.331 2.078 91.595 10.800 2.394

5.683 10.633 2.718 11.383 8.405 7.765

Note: The number of lags for VAR models is determined according to the AIC and the optima lag for original returns is 4.

4.4. Connectedness network analysis

4.4.1. Spillover connectedness for the original returns Table 6 shows the connectedness matrix for the original returns. The total connectedness measure is 7.765%, which indicates that the electricity and fuel source markets are not highly correlated. For the original time series, the crude oil market contributed the most (10.80%) impact to the system, followed by the coal market (9.05%), the natural gas market (7.298%), the electricity market (7.148%) and the uranium fuel market (4.527%). In particular, 5.683% of the electricity return variation can be explained by the four fuel energy returns. The gas returns make the largest contribution to the electricity return variations (3.739%), followed by oil (0.981%), uranium (0.615%) and coal (0.348%). The electricity returns also contribute to 5.100% of natural gas variation, 0.780% of coal variation, 0.725% of oil variation and 0.543% of uranium variation. At the same time, the natural gas market is the largest information receiver (11.383%), followed by the coal market (10.633%), the crude oil market (8.405%) and the electricity market (5.683%). The results for net spillover present that the crude oil, uranium fuel and electricity markets are net information transmitters, whereas the natural gas and coal markets are net information receivers. The connectedness network for original returns is presented in Fig. 3. The red spots represent the information transmitter and the green spots represent the information receivers. The thickness of the arrows indicates the magnitude of information spillover between the electricity and the fuel markets. The oil and uranium markets have a low impact on the electricity market. The electricity market has the strongest influence on the gas market. The electricity market also has affected the coal market.

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Fig. 3. Connectedness network for original returns. (The red spots represent the information transmitter and the green spots represent the information receivers. The thickness of the arrows indicates the magnitude of information spillover between the electricity and the fuel markets.)

4.4.2. Multi-scale connectedness analysis for IMFs Multi-scale analysis of the connectedness network of the electricity and fuel markets would help us gain a deeper understanding of the information feedback effects between the electricity and fuel markets. Table 7 shows the multi-scale connectedness matrix for each IMF. The overall total spillover index at IMF2 is the largest (9.570%), whereas the total spillover index at other IMFs is small. Furthermore, the net spillover results can be obtained. For IMF1, the electricity and coal markets are net information transmitters, whereas the uranium, gas and oil markets are net information receivers. However, for IMFs 2 to 6, the electricity market is a net information receiver. Fig. 4 shows the directional net pairwise connectedness graph for each IMF. The spillover from the oil and uranium markets to the electricity market is positive for most of the IMFs. The spillover from the gas to electricity markets is the largest relative to the other fuel source markets and is positive for IMFs 4 to 6 and negative for IMFs 1 to 3. The spillover from the coal market is negative for IMFs 1 to 2 and IMF6 and positive for IMFs 3 to 4. Generally speaking, the oil and uranium markets have a positive spillover to the electricity market at most time horizons, but the spillover is relatively weak. There exists a reciprocal spillover between the electricity market and the gas and coal markets at most time horizons. The spillover from the gas to electricity markets is relatively strong. 5. Conclusions and policy implications In this paper, nonlinear dependence between the electricity and the fuel source markets is identified based on a new multi-scale framework using the PJM electricity market as a sample, with its high ratio of natural gas. For the original series, only bidirectional linear Granger causality can be found for the electricity and gas markets. In the short term, only unidirectional linear feedback effect is found from the electricity to gas markets. In the medium term, unidirectional causality exists from the uranium to electricity markets, whereas bidirectional nonlinear causality can be found between the electricity market and the coal and natural gas markets. In the long term, only unidirectional nonlinear Granger causality is presented from the gas and oil markets to the electricity market. The study also explores the information spillover effects for the electricity and the fuel markets using the connectedness network method. The degree of information spillover between the electricity and the fuel markets is relatively weak for the original series. On different time scales, the oil and uranium markets have a positive spillover to the electricity market at most time horizons, but the spillover is relatively weak. There is reciprocal information spillover between the electricity market and the gas and coal markets at most time horizons. The information spillover from the gas to electricity markets is relatively strong. The above results are based on the PJM electricity market with its high mix of clean power sources. To improve the power generation mix and move towards clean electricity, energy policymakers and market participants must be enlightened. Although the proportion of natural gas has increased, the short-term related intervention in the natural gas market does not affect the electricity market. In the medium term, in order to maintain reliable operation of the power system, policymakers need to develop detailed emergency plans in advance according to the historical impact of significant events in the coal, uranium and natural gas markets. In particular, they should focus on the shock of significant events for the natural gas market. Furthermore, the pattern change trends of the global crude oil market would influence the long-term policies of the coal and gas markets. Therefore, the long-term policy of the electricity market should focus not only on the evolution trend of the gas market but also on that of the oil market. Meanwhile, related information on the fuel source markets (especially the natural gas market) needs to be considered to better predict the long-term trend

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T. Xia, Q. Ji and J.-B. Geng / Physica A 537 (2020) 122298 Table 7 Multi-scale connectedness matrix for each IMF. Electricity

Coal

Uranium

Gas

Oil

From others

95.124 1.486 1.595 4.614 0.153 7.849 2.973

0.390 95.506 2.703 0.949 2.427 6.470 1.976

0.765 1.170 94.702 0.920 1.793 4.648 −0.650

2.790 0.224 0.280 92.846 1.216 4.511 −2.643

0.931 1.613 0.719 0.671 94.410 3.934 −1.656

4.876 4.494 5.298 7.154 5.590 5.482

90.675 1.520 1.934 1.445 2.233 7.132 −2.193

0.727 92.766 4.560 0.931 1.195 7.412 0.178

0.980 1.960 90.080 6.772 4.547 14.259 4.339

1.074 0.379 0.313 87.326 0.723 2.489 −10.185

6.544 3.375 3.112 3.527 91.303 16.558 7.861

9.325 7.234 9.920 12.674 8.697 9.570

94.704 0.543 2.495 0.731 0.185 3.954 −1.342

0.981 97.730 1.507 0.362 0.454 3.305 1.035

3.612 0.041 94.195 2.698 0.347 6.698 0.893

0.237 1.423 1.448 95.947 0.039 3.147 −0.906

0.466 0.264 0.354 0.262 98.975 1.346 0.320

5.296 2.270 5.805 4.053 1.025 3.690

86.614 0.572 0.269 0.191 0.010 1.042 −12.345

2.083 95.689 1.050 0.156 2.170 5.460 1.149

0.990 1.196 95.117 4.291 2.008 8.485 3.602

9.078 1.105 0.950 94.349 0.020 11.154 5.503

1.235 1.437 2.615 1.013 95.791 6.300 2.092

13.386 4.311 4.883 5.651 4.209 6.488

97.166 0.024 0.112 0.432 1.386 1.954 −0.880

0.022 97.397 2.377 0.006 2.335 4.738 2.135

0.262 0.939 97.040 0.029 0.176 1.406 −1.553

1.869 0.112 0.154 97.498 0.809 2.944 0.442

0.682 1.528 0.317 2.036 95.294 4.562 −0.144

2.834 2.603 2.960 2.502 4.706 3.121

92.261 0.447 0.328 4.553 0.592 5.919 −1.820

0.002 94.883 0.058 3.335 0.265 3.659 −1.458

2.924 1.740 95.919 0.641 0.349 5.654 1.574

4.695 2.725 2.254 89.907 0.030 9.704 −0.388

0.118 0.205 1.441 1.565 98.764 3.329 2.093

7.739 5.117 4.081 10.093 1.236 5.653

IMF1 Electricity Coal Uranium Gas Oil To others Net IMF2 Electricity Coal Uranium Gas Oil To others Net IMF3 Electricity Coal Uranium Gas Oil To others Net IMF4 Electricity Coal Uranium Gas Oil To others Net IMF5 Electricity Coal Uranium Gas Oil To others Net IMF6 Electricity Coal Uranium Gas Oil To others Net

Note: The number of lags is determined according to the AIC.

of the electricity market. The empirical results and policy implications depend on the power generation mix. The new analytical framework proposed in this study can be extended to other cases. An affordable, reliable and clean electricity generation system can be developed in the future by improving the proportion of clean power generation sources.

Acknowledgements

Supports from the National Natural Science Foundation of China under Grant No. 71874206, No. 71503274, No. 91546109, and No. 71774152, and the National Key Research and Development Program of China (Grant No. 2016YFA0602500) and China Postdoctoral Science Foundation (Grant No. 2016M591263) are acknowledged.

T. Xia, Q. Ji and J.-B. Geng / Physica A 537 (2020) 122298

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Fig. 4. Directional net spillover connectedness network for each IMF. (The red spots represent the information transmitter and the green spots represent the information receivers. The thickness of the arrows indicates the magnitude of information spillover between the electricity and the fuel markets.)

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