Asymmetric Multifractal Of Modified MF-ADCCA Method And Study On MFI-EMD-BP Model Prediction

With the development of nonlinear scientific theories such as fractal and chaos,many new research methods have emerged in financial markets.As one of the representative methods,multifractal has been widely used in the research of financial markets because it can describe the fluctuation range in different time scales,which provides a new way of thinking for a deeper understanding of the operating rules of financial markets.The main work and conclusions of this paper are as follows:Firstly,the oscillation trend is introduced into the two-state MF-ADCCA method by nonlinear method,and a modified MF-ADCCA method is proposed to analyze the asymmetric multifractal correlation between two time series under three trend states.Taking Shanghai and Shenzhen stock markets as the representative,the empirical analysis results show that there is asymmetric multifractal correlation between the two markets under any trend state.Specifically,in the state of oscillation and downtrend,there is a long correlation between the two markets in small fluctuations,and there is an anti-persistence feature in large fluctuations.In the uptrend,there is multifractal characteristic of time-varying fluctuation between the two markets.At the same time,the accuracy and robustness of the modified MF-ADCCA method are tested.The test results show that the two-state MF-ADCCA method underestimates the multifractal strength under the rising trend and overestimates the multifractal strength under the falling trend.The modified MF-ADCCa method is more accurate in describing the fractal strength.The robustness results also showed that the modified MF-ADCCA method was robust.Secondly,a modified MF-ADCC method based on EMD decomposition is proposed,which decomposes non-stationary and non-linear time series into eigenmode functions with different frequencies,reconstructs the eigenmode functions into high-frequency and low-frequency time series according to the frequency level,and then uses the modified MF-ADCC method to measure the asymmetric multifractal correlation of high-frequency and low-frequency time series under three trend states of rising,oscillating and falling respectively.The empirical results show that the time series with different frequencies have asymmetric multifractal correlations under different trend states,and there are significant differences among the multifractal indicators.It is confirmed that the modified MF-ADCCA method based on EMD decomposition can analyze the multifractal characteristics of the market from different frequencies and multi-trend angles.Finally,based on the multifractal indexes of different multifractal methods under three trend states and two frequency information,a variety of neural network prediction models are constructed,including BP model,integral fractal model,MFI-BP model,MFI-EMD-BP model,and the accuracy of the models is evaluated through the mean absolute error,the mean absolute error rate and the mean square error.The empirical results show that the accuracy of the prediction model based on the multifractal indexes is higher than that of the traditional BP model in the four models,and the accuracy of the MFI-EMD-BP prediction model is the highest.