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The existing literature primarily examined the impact of unexpected events on the stock market at a single scale, posing the challenge of a lack of multiscale analysis. This paper investigates the impact of COVID-19 on stock markets (China, the U.S., and Hong Kong) from a multiscale perspective using an improved ensemble empirical mode decomposition (EEMD)-based event analysis method. First, the stock price series is decomposed into several independent intrinsic mode functions (IMFs) and a residue. Second, a novel composition method is proposed to reconstruct the IMFs into three components: high-frequency, low-frequency, and long-term trend. We find that the composition of low-frequency and long-term trend components is dominant, which is used to estimate the strength of COVID-19 impact on the stock markets. In addition, the outbreak of COVID-19 significantly increased the intensity of short-term fluctuations in stock prices. Finally, the high-frequency component is analyzed to capture the volatility spillover effects among the three stock markets by the BEKK(Baba-Engle-Kraft-Kroner)-GARCH model. The results show that before the outbreak, there are two-way volatility spillovers between any two of the three markets. After the outbreak, there is no spillover effect between China and Hong Kong, and Hong Kong has no spillover effect on the U.S. However, volatility in the U.S. market still has a significant spillover effect on the other two markets, implying that a mature market can absorb new information more quickly. [ABSTRACT FROM AUTHOR]