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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.

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