Research On Long-term Memory Of Chinese Bond Market Based On Fractal Market Theory

The long-term memory of financial time series is one of the hot research di rections of modern finance.Based on the fractal market theory,the long-term me mory between elements in the process of financial time series can be effectively portrayed.As an important part of the financial market,Long-term memory resea rch on the Chinese bond market can not only help us understand and analyze m arket characteristics,but also predict the trend of asset price changes,which has important practical significance.Therefore,based on the fractal market theory,thi s article uses the fractal analysis method and the time series analysis method to study the bond market in my country as follows.Use two distribution feature test methods to check the normality of the sample data and use Q statistics and BDS test methods to verify the correlation of the sample data;then use the classic R/S analysis method,modified R/S analysis method and DFA analysis method test the long-term memory of the sample;Finally,the v statistic calculated by the classic R/S analysis method is used to estimate the duration of long-term memory.The results display that the national debt index and the corporate bond index do not satisfy the normal distribution and have the distribution characteristics of peaks and thick tails and non-linear correlation structure.The long-term memory is stronger than the national debt index.The minimum cycle of Treasury bond index and corporate bond index yield fluctuation is 24 days and 55 days respectively,and the maximum cycle period is 244 days and 330 days respectively.Considering the impact of time variable on the results of the long-term memory inspect,the long-term memory of the sample data is tested and estimated under different time scales and different interval lengths.The results show that different sample interval lengths and different time scales will affect the long-term memory estimation,the sample data of this paper have long-term memory under different interval lengths and time scales.Aiming at the long-term memory characteristics of the national debt index and corporate debt index,a parameter model that can describe the long-term memory of the time series is used to fit and forecast the daily closing prices of the above two indexes: ARFIMA model and ARTFIMA model.The results show that,from the perspective of spectral density fitting,the ARTFIMA model performs a better fit on the data at low frequencies under the effect of harmonic parameters;from the perspective of prediction,the ARTFIMA model performs better in predicting the closing price of the national debt index.Finally,the comparative analysis method verifies that the ARTFIMA model has an advantage in predicting time series processes with weak long-term memory,while the ARFIMA model has an advantage in predicting time series with strong long-term memory.