Stock market, government bond market and corporate bond market are important components of my country's financial market. It is of great significance to study stock market price fluctuations and their forecasting methods, and to reveal the risk transmission path between them. The first part of this paper mainly studies the construction of the index price prediction model, and makes a comprehensive comparison of the high-frequency fluctuation characteristics, long-term trend characteristics and average trend characteristics of the EMD decomposition results of the Shanghai Composite Index, the SSE Government Bond Index, and the SSE Corporate Bond Index. The LSTM prediction model and the EMD-LSTM prediction model were established for the three sequences respectively, and the prediction effects of the models were comprehensively compared by calculating the RMSE and MAPE of the predicted values of the test set. The results show that after the introduction of the EMD method, the prediction effects of the SSE Composite Index and the SSE Corporate Bond Index prediction model have been greatly improved, but the prediction effect of the SSE Government Bond Index prediction model is far inferior to that of the LSTM model. The second part of this paper mainly studies the financial market risk analysis and transmission path. First, the fluctuation risk analysis and stationarity analysis of the logarithmic return series of the three index price series are carried out. The yield series are stable. Then, the LSTM models based on different training data predict three index price series and compare the prediction results to study the similarity of the price fluctuation mechanism of the three financial markets. The results show that the price fluctuation mechanism of the stock market is similar to that of the corporate bond market, and the price fluctuation mechanism of the government bond market is more similar to the corporate bond market than the stock market. The paper conducts E-G cointegration test on three logarithmic return series that have been tested for stationarity to study the long-term equilibrium relationship between the three markets and finds that there is a cointegration relationship between the SSE Composite Index and the SSE Government Bond Index, as well as the SSE Government Bond Index and the SSE Corporate Bond Index. Finally, the Granger causality test is carried out between the sequences with cointegration relationship, and the result shows that the risk transmission mechanism between the national debt market and the corporate bond market is strong, while the risk transmission mechanism between the stock market and the bond market is weak.
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