**5. Conclusions**

We have adopted Diebold and Yilmaz's [15] approach to examine the spillover effects among natural gas and wholesale electricity markets using their futures with different maturities and their spot prices. We used daily data from January 5, 2009, to December 31, 2018, and employed the Henry Hub and the PJM Western Hub Peak as the natural gas price indicator and the wholesale electricity price indicator, respectively. We obtained each commodity's spot prices and 12 types of futures with one to twelve months maturities. In other words, we analyzed the relationships between 26 types of economic variables.

The main results of our analyses are fourfold. First, we find that there are mutual spillover effects amongs<sup>t</sup> natural gas futures returns showing that the natural gas futures market is integrated. The possession of futures with many different maturities has a low diversification effect on a portfolio, although it is effective for directly hedging the spot trading at the applicable maturity. It is reasonable to hold the futures with two-, three-, and four-month period maturities, because these futures largely affect the other variables (see the row Others and columns G2 to G4 in Table 3) and all futures are equally affected by the other variables (see rows G1 to G12 and the column Others in Table 3).

Second, our results show that there are spillover effects from natural gas futures returns to natural gas spot returns, although no spillover effects from natural gas spot returns to natural gas futures returns are evident. From this, we conclude that futures markets have better natural gas price discovery capabilities than spot markets. The natural gas futures markets indicate the prices expected from the long-term economic environment surrounding natural gas. The natural gas spot prices often deviate from their fundamentals because the storage cost is extremely expensive, and the spot prices depend on their fluctuations in supply and demand at that immediate time. Therefore, the futures prices must be utilized when formulating governmen<sup>t</sup> policies and/or business plans.

Third, we observe spillover effects from natural gas spot returns to electricity spot returns as well as spillover effects from natural gas futures returns to electricity futures returns. The spillover effects from natural gas spot returns to electricity spot returns are larger than the spillover effect from natural gas spot returns to natural gas futures returns. We thus argue that the marginal cost of power generation (natural gas prices) is passed through to electricity prices. The natural gas futures markets are extremely useful in order to control the risks from the electricity markets.

Finally, our results do not show any spillover effects amongs<sup>t</sup> electricity futures returns, except for some combinations, or any spillover effects from electricity futures returns to natural gas futures returns. We confirm the presence of spillover effects between futures with a maturity difference of six months only, concluding these as merely a singular phenomenon. This means it is not caused by arbitrage trading. The maximum power load, which is the main determinant of the prices, has an almost semi-annual seasonality. Thus, we conclude that the electricity futures market is not integrated. We might expect diversification effects by the possession of the futures with many different maturities. However, it is necessary to pay attention to the seasonality in the selection.

**Author Contributions:** Conceptualization, T.N.; Data curation, T.N.; Formal analysis, T.N.; Validation, Y.T.; Visualization, T.N.; Writing—original draft, T.N.; Writing—review & editing, T.N. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Acknowledgments:** The authors would like to thank the anonymous reviewers, whose valuable comments helped improve an earlier version of this paper.

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