Abstract: The variational mode decomposition method is used to decompose the raw return series into sub-sequences with different investment horizons.Based on the dynamic Copula function， the conditional value at risk index(VaR and CoVaR) are quantified to analyze the short- and long-term tail risk spillovers between oil market and stock market in the bear and bull markets. The empirical research results show that there is a two-way tail risk spillover effect between the oil market and the stock market. Firstly， in terms of the intensity of risk spillover， the tail risk spillover effect of the oil market on the stock market is significantly stronger than that of the stock market on the oil market. Secondly， in terms of the direction of risk spillover， the tail risk spillovers from the stock market to the oil market are all positive， the upside risk spillovers from the oil market to the stock markets of most countries are positive， and the downside risk spillovers from the oil market to the stock markets of all countries are positive. Finally， the long-term tail risk spillover effect between the oil market and the stock markets of most countries is stronger than the short-term tail risk spillover effect.The research results are beneficial to the formulation of relevant market investment strategies and the prevention of extreme risk contagion.

Key words: stock market; oil market; tail risk spillover; variational mode decomposition; Copula function