**5. Conclusions**

This study analyzed return and volatility spillover effects from coal, natural gas, and crude oil fossil fuel markets to electricity spot and futures markets in Europe from 2 January 2007, to 2 January 2019, using a new empirical method in the time-frequency domain frameworks developed by Diebold and Yilmaz [17] and Barunik and Krehlik [18]. The study obtained the following major findings.

First, natural gas has the highest return spillover effect upon the electricity spot market and futures markets, followed by coal and crude oil. The results may be explained by two factors: (1) electricity production favoring one specific fossil fuel and; (2) the different storage cost of fossil fuels.

Second, due to increasing storage costs over time, the return spillovers from fossil fuel commodities to electricity futures with a long delivery period are higher than to electricity futures with a short delivery period. Meanwhile, compared to electricity futures markets, the spot market is more dependent on renewable energy infeed and electricity demand than fossil fuels such as natural gas and coal. Thus, the return spillover e ffect on electricity futures is higher than on electricity spot markets.

Third, in the frequency domain, we found that the majority of return spillover is generated in the short term which further implies that return shocks are transmitted from fossil fuel markets to electricity markets within only one week.

Contrary to expectations, we found that among the three fossil fuel markets, natural gas has the highest volatility spillover e ffect on electricity spot markets and monthly and quarterly futures, but not on yearly futures. Similarly, oil exhibits the weakest volatility spillover e ffect on all electricity markets, also except yearly futures markets.

Additionally, the volatility spillover from natural gas to monthly electricity futures is higher than for electricity futures with a longer delivery period. Meanwhile, crude oil and coal cause the highest volatility spillovers to yearly electricity futures, followed by monthly and then quarterly futures. Except for natural gas, the volatility spillovers from coal and crude oil to electricity futures are higher than in the electricity spot market, which is the same result as that found in the analysis of return spillovers.

In the frequency domain, the majority of volatility spillover is produced in the long term which further indicates that transmitted shocks from fluctuations in fossil fuels have long-lasting e ffects on electricity market volatility.

Furthermore, we also explored dynamic spillovers by adopting the 400-day moving window method. We found there is a similar pattern in the dynamics of return spillovers from fossil fuel commodities to electricity futures with long delivery periods, and to electricity generation from natural gas. However, we found the dynamic volatility spillovers from fossil fuels to electricity markets are more sensitive to extreme events such as the 2008 global financial crisis, the 2014 international oil price's violent shock, and the 2016 rise in coal and natural gas prices, as shown by volatility spillovers varying sharply when the extreme events occurred.

The results in this paper may be helpful for investors with di fferent investment horizons in Europe to diversify their portfolios, hedge their strategies, and make their risk managemen<sup>t</sup> plans. For short term investors, constructing well-diversified portfolios consisting of fossil fuels futures, electricity spot and futures is a complicated task, especially in times of financial turmoil. On the other hand, for long-term investors, including the fossil fuels in portfolios composed primarily of electricity spot and futures with di fferent delivery periods could enable them to obtain the long-term diversification benefits.

**Author Contributions:** Conceptualization, T.N. and S.H.; investigation, T.L. and X.H.; writing—original draft preparation, T.L.; 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 Keukwan Ryu and two anonymous referees for helpful comments and suggestions.

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

**Appendix A**
