This study investigates the time–frequency dynamics of return and volatility spillovers between the stock market and three commodity markets: natural gas, crude oil, and gold via a comparative analysis between the United States and China is conducted with the help of new empirical methods. Our findings are as follows. First, in terms of time, return spillovers between crude oil and the stock market are strongest in two of the three commodity markets. Crude oil emits a net negative return spillover to the US stock market, and a net positive return spillover to the Chinese stock market. By contrast, the strongest volatility spillover effect is transmitted to the stock markets of both countries through gold. However, gold has a net positive volatility spillover effect on the US stock market and a net negative effect on the Chinese stock market. In the frequency domain, most of the return spillover is produced in the short term, and most of the volatility spillover occurs in the long term. In addition, the moving-window method reveals the dynamic nature of the spillover effect. Some extreme events can have a dramatic effect on the spillover index. Conversely, the spillover effect differs significantly between the two countries and is characterized by time variation and frequency dependence.

Our study analyzes the return and volatility spillover among the natural gas, crude oil, and electricity utility stock indices in North America and Europe from 4 August 2009 to 16 August 2019. First, in time domain, both total return and volatility spillover are stronger in Europe than in North America. Furthermore, compared to natural gas, crude oil has a greater volatility spillover on the electricity utility stock indices in North America and Europe. Second, in frequency domain, most of the return spillover occurs in the short-term, while most of the volatility spillover occurs over a longer period. Third, the rolling analyses indicate that the return and volatility from 2009 to late 2013 remained stable in North America and Europe, which may be a result of the 2008 global financial crisis, and started to fluctuate after late 2013 due to some extreme events, indicating that extreme events can significantly influence spillover effects. Moreover, investors should monitor current events to diversify their portfolios properly and hedge their risks.

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Using a fresh empirical approach to time-frequency domain frameworks, this study analyzes the return and volatility spillovers from fossil fuel markets (coal, natural gas, and crude oil) to electricity spot and futures markets in Europe. In the time domain, by an approach developed by Diebold and Yilmaz (2012) which can analyze the directional spillover effect across different markets, we find natural gas has the highest return spillover effect on electricity markets followed by coal and oil. We also find that return spillovers increase with the length of the delivery period of electricity futures. In the frequency domain, using the methodology proposed by Barunik and Krehlik (2018) that can decompose the spillover effect into different frequency bands, we find most of the return spillovers from fossil fuels to electricity are produced in the short term while most of the volatility spillovers are generated in the long term. Additionally, dynamic return spillovers have patterns corresponding to the use of natural gas for electricity generation, while volatility spillovers are sensitive to extreme financial events.