Abstract: In order to solve the problem of nonlinearity in high frequency data，the LMD ( Local Mean Decomposition) method is proposed to estimate the volatility of high frequency data． Firstly，high-frequency simulation data are used to verify the feasibility of the estimation method． Secondly，taking the closing price of Shanghai and Shenzhen 300 index at different frequencies as the research object，the volatility is estimated by LMD method，and the relative error statistics are calculated． The results show that the LMD method can effectively estimate the volatility of high-frequency data and solve the nonlinear problems in high frequency data．With the increase of sample frequency，the estimation accuracy gradually improves． The method of LMD provides a new idea for non-parametric estimation of volatility in high frequency data．

Key words: high frequency financial data, volatility estimation, logarithmic return rate, local mean decomposition ( LMD)