**4. Data**

We use daily data for the natural gas, crude oil, and electricity utility sector indices of Europe and North America from 4 August 2009 to 16 August 2019, without uncommon business days. Because the data and CAC Utilities Index (USD) extends from 4 August 2009 to 16 August 2019, in order to consolidate the time for all data, we chose this time period. To avoid the influence of the exchange rate on our results, we consolidated the currency units of the variables into a dollar currency unit. Specifically, the variables we use are shown in Table 1.


**Table 1.** Variables in the model.

For the North American market, we use the daily prices of the Henry Hub Natural Gas Futures from Bloomberg for the natural gas market. For the crude oil market, we employ the Crude Oil WTI Futures from Bloomberg. With exports grown in Europe, South America, and Asia, the New York Mercantile Exchange (NYMEX) Henry Hub Natural Gas futures have become a global price benchmark for natural gas trading. WTI, a medium crude oil and futures contract launched by the NYMEX in 1983, has long been a benchmark for international crude oil prices, thus making an important contribution to the development of the global crude oil market. For the stock market, we use the electricity utilities in the US and Canada. For the US, we use the Standard and Poors 500 Utilities (S&P 500) which is composed of electricity and energy companies included in the S&P 500. This is classified as members of the Global Industry Classification Standard (GICS) utilities sector, such as the American Electric Power Company (AEP), Duke Energy Company (DU), Consolidated Edison Company (ED), and 28 other companies in total. The S&P/TSX Capped Utilities Sector Index (TSX) is a market-value-weighted index obtained from 16 electricity and energy companies, such as Emera Inc. (EMA) and Fortis Inc. (FTS).

For Europe, we use the daily price of the Intercontinental Exchange (ICE) UK Natural Gas Futures for the natural gas market and the ICE Brent Futures for the crude oil market. The ICE UK Natural Gas Futures contract is used for physical delivery by transfer of natural gas rights at the National Balancing Point (NBP) virtual trading point operated by the National Grid, a UK transmission system operator. This is the second most common liquid gas trading point in Europe. Brent Oil is the primary trading category for sweet light crude and serves as a benchmark price for oil purchases in the world. For stock markets, in Germany, we use the Dax subsector All Electricity (DAX), calculated by Deutsche Börse. DAX is a market-value-weighted index that includes companies with an average daily trading volume of at least €1 million to qualify. In the UK, we use the market-value-weighted FTSE 350 Electricity Index (FTSE 350), which includes three companies: DRAXGROUP, SSE (Scottish and Southern Electricity), and Contour global, all of which are large electricity enterprises in the UK. In France, we use the CAC Utilities Index (CAC), a market-value-weighted index that comprises 10 electricity and energy companies, including EDF and ENGIE. In Italy, we use the FTSE ITALIA ALL-SHARE UTILITIES Index (FTSE Italia), which includes 14 electricity and energy companies, such as ENEL (an Italian multinational energy company working in the field of power generation and distribution).

Figure 1a shows images of the prices of natural gas, crude oil, and the electricity utility sector indices in North America. Figure 1b illustrates the natural gas, crude oil, and electricity utility sector indices in Europe. As we can see, in the North America market, the price of the natural gas, crude oil, and electricity utility sector index in Canada follow similar trends and fluctuate violently. These trends dropped dramatically from 2014 to 2016 due to the international oil price crisis. In general, the electricity utility sector index in the US increased continuously from 2009 to 2019, after the global financial crisis of 2007–2009. Relatively, in the European market, Figure 1b shows that the prices of natural gas, crude oil, and the electricity utility sector index follow a semblable non-stationary trend. Moreover, due to international oil price crisis of 2014–2016, energy prices dropped to varying degrees during this time period.

In our analysis, we calculated the closing price of the North American market and the European logarithmic difference as the daily return data, as shown in Figure 2a,b. Furthermore, we use the Ljung-Box, which has a lag of 20 to test the time variations of the return series and confirm that the return of all variables is not a white noise series with 10% significance. We use the ARMA (Autoregressive Moving Average)–GARCH model to calculate the volatilities of four assets in North America and six assets in Europe, and the plots are shown in Figure 3a,b. Additionally, the lag of the GARCH model is determined on the basis of the Akaike Information Criterion (AIC).

The descriptive basic statistics of the return and volatility series are shown in Table 2, Table 3. In North America, we find that the mean returns of natural gas and crude oil have negative values. However, the others have positive mean returns. Furthermore, natural gas has the largest maximum daily return and the largest minimum daily return. Specifically, we find that natural gas is the most volatile, followed by crude oil, TSX (Canada), and the S&P 500 (US). Moreover, based on skewness, we find that, except for natural gas, the returns are left-skewed, whereas the return of natural gas is right-skewed. Meanwhile, according to kurtosis, the volatility of the four assets are right-skewed. Regarding kurtosis, the returns and volatilities of the four assets are leptokurtic, which means that the four variables will show more peaked and fat tails. Finally, as the most commonly used unit root testing method, the augmented Dickey–Fuller (ADF), proposed in 1981, tests the null hypothesis that a variable has a unit root, which means that the variable is nonstationary. From the ADF results, the null hypothesis is rejected at 1% significance level for all variables.

**Figure 1.** (**a**) Time-variations of the price series in North America. Notes: Henry Hub indicates natural gas; WTI indicates crude oil; US indicates the S&P 500 Utilities Index; CANADA indicates the S&P/TSX Capped Utilities Sector Index. (**b**) Time-variations of the price series in Europe. Notes: NBP indicates natural gas; BRENT indicates crude oil; GERMANY indicates the DAX subsector for all electricity; UK indicates the FTSE 350 Electricity Index; FRANCE indicates the CAC Utilities Index; ITALY indicates FTSE Italia All-Share Utilities Index.

Meanwhile, in the European market, in contrast to the North America market, we see that the mean returns of crude oil, DAX (Germany), FTSE 350 (UK), and CAC (France) have negative values. However, the others have positive mean returns. Natural gas has the largest maximum daily return, and FTSE 350 (the UK) has the largest minimum daily return. However, we find that natural gas is the most volatile, followed by crude oil, DAX (Germany), CAC (France), FTSE Italia (Italy), FTSE 350 (UK), and DAX (Germany). On the basis of skewness, the returns of natural gas and crude oil are right-skewed, but the others are left-skewed. In addition, the volatilities of the six assets are right-skewed. Regarding kurtosis, except for the return of CAC (France), which is platykurtic, the returns of the others are

leptokurtic. Moreover, the volatilities of the six assets are leptokurtic. Eventually, based on the ADF results, we reject the null hypothesis of a unit root at 1% significance level for all series.

**Figure 2.** (**a**) Time-variations of the return series in North America. Notes: Henry Hub indicates natural gas; WTI indicates crude oil; US indicates the S&P 500 Utilities Index; CANADA indicates the S&P/TSX Capped Utilities Sector Index. (**b**) Time-variations of return series in Europe. Notes: NBP indicates natural gas; BRENT indicates crude oil; GERMANY indicates the DAX subsector for all electricity; UK indicates the FTSE 350 Electricity Index; FRANCE indicates the CAC Utilities Index; ITALY indicates FTSE Italia All-Share Utilities Index.

**Figure 3.** (**a**) Time-variations of the volatility series in North America. Notes: Henry Hub indicates natural gas; WTI indicates crude oil; US indicates the S&P 500 Utilities Index; CANADA indicates the S&P/TSX Capped Utilities Sector Index. (**b**) Time-variations of volatility series in Europe. Notes: NBP indicates natural gas; BRENT indicates crude oil; GERMANY indicates the DAX subsector for all electricity; UK indicates the FTSE 350 Electricity Index; FRANCE indicates the CAC Utilities Index; ITALY indicates FTSE Italia All-Share Utilities Index.


Note: ADF: Augmented Dickey and Fuller Unit Root Test (1979); \*\*\* denotes a rejection of the null hypothesis at 1% significance level.

> **Table 3.** Descriptive statistics for return and volatility in Europe.


Note: ADF: Augmented Dickey and Fuller Unit Root Test (1979); \*\*\* denotes a rejection of the null hypothesis at 1% significance level.

#### **5. Empirical Results**

#### *5.1. Spillover Results*

We followed Diebold and Yilmaz [1] (hence, DY12) to obtain the spillover effects in the time domain. We first estimated the four variables in our VAR model in the North American market and the six variables in our VAR model in the European market. Then, we used the generalized variance decomposition for a forecast error to set up the spillover table to measure the direction and intensity of spillover across the selected markets.

Next, in frequency domain, following Barunik and Krehlik [2] (hence, BK18), we used Fourier transform to decompose the spillover table in the DY12 model into three different frequency bands, stated in Toyoshima and Hamori [20] as the short-term, "Fre S," roughly corresponding to 1 to 5 days; the medium-term, "Fre M," roughly corresponding to 6 to 21 days; and the long-term, "Fre L," roughly corresponding to 22 days to infinity.

In this study, the lag length of the VAR model is based on the AIC. According to our BK18 model, if the forecasting horizon is (H) < 100, the method is invalid. Consequently, we used a 100-day ahead forecasting horizon (H) for variance decomposition.

In Table 4, Table 5, we show the return spillover results from DY12 and BK18, which include the two markets: North America and Europe. Specifically, Tables 4 and 5 includes four sub-tables. At the top are the results of the DY12, followed by the short-term, the medium-term, and the long-term results from the BK18. In each sub-table, the values in the *i*th row and the *j*th column equate to the strength of the spillover effect from the *j*th market to the *i*th market. For example, in the DY12 return spillover results in the North American market, the strength of the spillover effect in the third column (US) and the second row (WTI) is 2.264. The values in the last row called "TO" indicate the mean value of the spillover effect on the other markets, whereas the values in the last column called "FROM" indicate the mean value of the spillover effect from the other markets. The total spillover is the summary of all "TO" or "FROM" (for example, 17.165, as shown in the lower right corner).


**Table 4.** The return spillover table of DY, 2012 and BK, 2016 (North America).


**Table 4.** *Cont.*

Note: Freq S: the spillover at "Freq S" roughly corresponds to 1 to 5 days; Freq M: the spillover at "Freq M" roughly corresponds to 6 to 21 days; Freq L: the spillover at "Freq L" roughly corresponds to 22 to infinite days.

**Table 5.** Return spillover table of DY (2012) and BK (2018) (Europe).


Note: Freq S: the spillover at "Freq S" roughly corresponds to 1 to 5 days; Freq M: the spillover at "Freq M" roughly corresponds to 6 to 21 days; Freq L: the spillover at "Freq L" roughly corresponds to 22 to infinite days.

Next, we identify some specifics when we compare the di fference between the return spillover effect in North America and in Europe using the pure time-domain approach of DY12. First, for the total return spillover e ffect, we can see that the total return spillover e ffect in Europe (30.245%) is stronger than that in North America (17.165%). This demonstrates that the return connectedness of natural gas, crude oil, and the electricity utility sector index in Europe is stronger than that in North America. Whether in North America or Europe, the total return spillover of crude oil contributes more than natural gas to the electricity utility stock market in each country. Further, in North America, Canada receives a greater e ffect from the two energy futures (0.318% from natural gas and 11.8% from crude oil) compared with the US in the time domain. In contrast, Canada exerts a greater e ffect on the natural gas (0.394%) and crude oil (13.697%) sectors in the time domain. In Europe, the UK receives the greatest e ffect from the two energy futures (0.757% from natural gas and 3.889% from crude oil) compared with the other three countries in the time domain. The UK transmits the greatest e ffect on natural gas (1.249%), but France transmits the greatest e ffect on crude oil (6.353%) in the time domain, which contrasts with the situation in North America. Finally, we find that there are some di fferences in the return spillover e ffect among the two commodity markets and the stock market in North America and Europe, respectively. In North America, we find that the US receives a greater return spillover effect on natural gas (0.163%) and transmits less of an e ffect (0.147%). In contrast to the US, Canada transmits more of a return spillover e ffect on natural gas (0.394%) and receives a smaller e ffect (0.318%). In contrast to the natural gas market, the US transmits more of a return spillover e ffect on crude oil (2.264%) and receives a smaller e ffect (2.242%). In the same vein as the US, Canada also transmits more of a return spillover e ffect on crude oil (13.697%) and receives a smaller e ffect (11.8%).

In Europe, except for Germany, the other three stock markets transmit more of a return spillover effect on natural gas and receive a smaller e ffect. In the same vein as the situation for natural gas, except for Germany, the other three stock markets transmit more of a return spillover e ffect on crude oil and receive a smaller e ffect. In terms of frequency, Tables 4 and 5 reveal that looking at either North America or Europe, the total return spillover in the short-term (Frequency S 1–5 Days) is the highest, followed by the medium-term (Frequency M 6–21 Days) and the long-term (Frequency L 22–Infinity Days). These results sugges<sup>t</sup> that the return shocks from any market transmitted to another market will not exceed one week.

Table 6, Table 7 show the volatility spillover results of DY12 and BK18 with the same construction. Table 6 shows the volatility spillover e ffect in North America, and Table 7 shows the e ffect in Europe. In time domain of DY12, we find the following. The total volatility spillover e ffect in Europe (27.929%) is stronger than that in in North America (20.216%). This situation is the same for the total return spillover; whether in North America or Europe, the total volatility spillover of crude oil transmits more than natural gas to the electricity utility stock market in each country. In North America, between the two stock markets, Canada receives the greatest spillover e ffect from natural gas (0.664%), and the US receives the greatest e ffect from crude oil (6.771%) in the time domain. Among the two commodity markets, WTI is the most influential market on the stock market, transmitting the largest volatility spillover to the US (6.771%) and Canada (6.302%) and is also the market that receives the largest volatility spillover from the US (4.373%) and Canada (19.036%) compared with the natural gas market.

In the European market, among the four stock markets, the UK receives the largest e ffect from natural gas (0.785%), and Germany receives the largest e ffect from crude oil (4.56%) in the time domain. However, the UK transmits the largest e ffect on crude oil (8.843%), and Germany transmits the largest effect on natural gas (2.374%) compared with other countries in the time domain. In addition, in terms of frequency and in contrast to the return spillover, Tables 6 and 7 reveal that in both North America and Europe, the total volatility spillover for the long-term (Frequency L 22–Infinity Days) is the highest, followed by the medium-term (Frequency M 6–21 Days) and the short-term (Frequency S 1–5 Days). These results imply that volatility shocks have a long-lasting e ffect.


**Table 6.** Volatility spillover table of DY12 and BK18 (North America).

Note: Freq S: the spillover at "Freq S" roughly corresponds to 1 to 5 days; Freq M: the spillover at "Freq M" roughly corresponds to 6 to 21 days; Freq L: the spillover at "Freq L" roughly corresponds to 22 to infinite days.

#### *5.2. Dynamic (Moving-Window) Analysis*

We have useful results on the total spillover e ffects from our full sample. However, these results are not helpful in analyzing how connectedness changes over time. If we only focus on the static results, the VAR estimated over the whole sample may smooth out the results when there is time variation in the relationship between the variables (Lovcha [21]). In order to better understand the dynamics of spillover e ffects, we employ a moving-window to analyze the spillover results of DY12 and BK18. For the moving-window method, we keep the forecast horizon at 100, which is used in the static analysis. For example, Toyoshima and Hamori [20] employ 100–day rolling samples. Jorion [32] sets a 20–day window for estimation. Blanchard et al. [33] used a five–year rolling standard deviation of output growth in the US. Similarly, we set the length of the window at 250 trading days, 370 trading days, and 500 trading days, and find that the plots of these trading days have almost the same trends. We put the results into Appendix A. For this reason, we chose 500 trading days for the length of the moving-window to keep the rolling sample large enough to ensure the stationarity of the series in each VAR estimation.


**Table 7.** Volatility spillover table of) DY12 and BK18 (Europe).

Note: Freq S: the spillover at "Freq S" roughly corresponds to 1 to 5 days; Freq M: the spillover at "Freq M" roughly corresponds to 6 to 21 days; Freq L: the spillover at "Freq L" roughly corresponds to 22 to infinite days.

As displayed in Figure 4a,b, we find some characteristics from the dynamics of the total return spillover and the frequency decomposition of North America and Europe. In both North America and Europe, the total return spillover occurs in the short-term. Moreover, two dynamic return spillover figures have a similar trend. In Europe, the total spillover of the DY12 model for the return series varies between 20% and 45%, which is wider than that in North America (between 10% and 30%). From 2009 to mid–2013, whether in North America or Europe, the total return spillover retains high stability, which may be a consequence of the effect of the 2008 global financial crisis or the 2010 European sovereign debt crisis. The total return spillover in both North America and Europe began to increase steadily until around 2017, which could be influenced by the 2014 international crude oil crisis.

**Figure 4.** (**a**) The total return spillover of DY12 andBK18 in North America (Windows 500). (**b**) The total return spillover of DY12 and BK18 in Europe (Windows 500). Note: The yellow line indicates the total spillover index of the DY12 model; the red line indicates the total spillover index at "Freq S" of the BK18 model; the green line indicates the total spillover index at "Freq M" of the BK18 model; the blue line indicates the total spillover index at "Freq L" of the BK18 model. The vertical axis variable unit is in percentages.

As seen in Figure 5a,b, which shows the dynamics of total volatility spillover and frequency decomposition for North America and Europe, the total spillover fluctuates more than the total return spillover. Moreover, the total volatility spillover reacts more violently to extreme events than that of the returns. In contrast with the total return spillover, the total volatility spillover develops over the long-term. This means that the total volatility spillover is more sensitive to shocks and extreme events; unlike the total return spillover, whether in North America or Europe, the total volatility spillover of DY12 shifts between 0% and 60%. From 2009 to mid-2013, whether in North America or Europe, the total volatility spillover retained its stability, which may be a consequence of the 2008 global financial crisis and the 2009 European sovereign debt crisis. In North America, we identified some sudden fluctuations, such as a sharp increase in 2015 and 2016, an increasing trend from 2017 to 2018, and a sudden rise in 2019. These fluctuations may have been influenced by the 2014 international crude

oil crisis, the 2016 Organization of the Petroleum Exporting Countries announcement to cut supplies at the end of 2017, the 2017 summer Hurricane Irma, and the 2019 trade war between China and the US. However, in Europe, we see almost the same fluctuations from mid-2013 to 2016; around 2015 to mid-2016, there are two sudden fluctuations that may be a result of some extreme events, such as the 2014 international crude oil crisis and the 2016 Brexit event. We also investigated the dynamics of the total return and volatility spillover in different windows and the pairwise directional return and volatility spillover in two regions. The results are given in Appendix A.

**Figure 5.** (**a**) The total volatility spillover of DY12 and BK18 in North America (Windows 500). (**b**) The total volatility spillover of DY12 and BK18 in Europe (Windows 500). Note: The yellow line indicates the total spillover index of the DY12 model; the red line indicates the total spillover index at "Freq S" of the BK18 model; the green line indicates the total spillover index at "Freq M" of the BK18 model; the blue line indicates the total spillover index at "Freq L" of the BK18 model. The vertical axis variable unit is in percentages.

#### **6. Concluding Remarks**

Our paper discusses the return and volatility spillover across the natural gas market, crude oil market, and stock market from 4 August 2009 to 16 August 2019 to assess the information transmission and risk transmission among the three markets by employing a new method for time–frequency developed by Diebold and Yilmaz [1] and Barunik and Krehlik [2]. It is crucial to investigate the spillover e ffects not only for investors to adjust their investment programs but also for governmen<sup>t</sup> authorities to make proper economic decisions. The contributions of our paper to the literature are as follows.

First, in time domain, the total return and volatility spillover in Europe are stronger than in North America. Moreover, whether in North America or in Europe, the spillover table reveals that crude oil, rather than natural gas, has the greatest e ffect on electricity utility stock markets. In North America, Canada not only receives a larger return spillover e ffect from the two energy futures (0.318% from natural gas, 11.8% from crude oil) compared with the US but also transmits a greater e ffect on the two energy futures. Regarding volatility spillover, Canada still has the largest spillover e ffect on the other two energy futures and receives the largest volatility e ffect from natural gas. However, the US receives the largest volatility spillover e ffect from crude oil (6.771%). In Europe, the UK receives the greatest return spillover e ffect from the two energy futures (0.757% from natural gas and 3.889% from crude oil) compared with the other three countries. The UK transmits the largest e ffect on natural gas (1.249%), but France transmits the largest e ffect on crude oil (6.353%) in the time domain, which is di fferent than the situation in North America. Regarding volatility spillover, the UK receives the largest e ffect from natural gas (0.785%), and Germany receives the largest from crude oil (4.56%). However, FTSE350 (the UK) transmits the largest e ffect on crude oil (8.843%), and Germany transmits the largest e ffect on natural gas (2.374%) compared to the other countries.

Second, in terms of frequency, our results show that the short-term has the largest e ffect on return spillover; however, the long-term has the largest e ffect on volatility spillover in both North America and Europe. These results imply that the return shocks from any market transmitted to another market will not exceed one week, whereas the results of volatility spillovers imply that volatility shocks have a long-lasting e ffect. This conclusion is consistent with the results of Barunik and Krehlik [2] and Tiwari et al. [34].

Third, in terms of return spillover transmission, all markets respond to return shocks immediately. The total return spillover e ffect in the short-term was the greatest. In this case, it is di fficult to determine the impact of a particular market on another market. Unlike return spillover transmissions, the total volatility spillover e ffect in the long-term was the greatest. Policymakers have su fficient time to prevent the impact of extreme volatility shocks on other markets. In addition, based on a summary of the results above, the volatility of natural gas is less than that of oil, which suggests that compared with oil, natural gas investors may have a greater opportunity to make a profit.

Forth, some interesting results are displayed in the rolling analyses. For example, because of the subsequent e ffect of the 2008 global financial crisis and the 2010 European sovereign debt crisis, the return and volatility spillover in both North America and Europe maintained a high level. Due to the later 2014 international oil crisis, both North America and Europe fluctuated fiercely around 2015. Around mid-2016, the Brexit event made the volatility spillover in Europe increase suddenly.

**Author Contributions:** Conceptualization, T.N. and S.H.; investigation, W.Z. and X.H.; writing—original draft preparation, W.Z.; writing—review and editing, X.H., T.N., and S.H.; project administration, S.H.; funding acquisition, S.H. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by JSPS KAKENHI Grant Number 17H00983.

**Acknowledgments:** We are grateful to Mehmet H. Bilgin and four anonymous referees for helpful comments and suggestions.

**Conflicts of Interest:** The authors declare no conflict of interest.
