Robust Statistical Study Of Non-stationary Financial High-frequency Data

In the financial field,the risk of financial assets is one of the most concerned issues,which plays an important role in the financial asset pricing and risk management.At present,diffusion model is a very important method to depict the price change process of financial assets,in which the diffusion coefficient or its square term volatility of the model describes the fluctuation of the price,which is a good description of the risk of financial assets.Therefore,related research is widely concerned in the academic circle and the industry.However,with the development of computer technology,financial data has been changing in the form of high frequency.The current study shows that high frequency financial data is usually not stationary,and will be more vulnerable to sudden events and the influence of financial market microstructure.These features cause more jumps in the data,and the distribution of financial data also has obvious thick tail.These characteristics of high frequency financial data cause the traditional estimation methods are no longer robust in the estimation of volatility,and the estimation results may produce wrong conclusions.On the other hand,due to the complexity of nonstationary jump-diffusion model structure,the traditional random analysis method is no longer applicable,and the frequency and size of jump can not be accurately estimated,which brings a great challenge to prove the large sample properties of the robust estimation.Based on the above background,this paper explores the robust estimation of diffusion coefficient of jump-diffusion model.The former chapters systematically introduce the existing research methods and problems from different perspectives,and summarize feasible treatment methods for the existing problems.Based on this,considering the superior characteristics of second-order jump-diffusion model in the nonstationary financial data,this paper introduces a threshold function to eliminate the influence of large fluctuations in the data,and then obtains the robust estimation result of diffusion coefficient of second-order jump-diffusion model by M-estimation method.In the investigation of the new estimation method,this paper compares the new estimation method with the existing estimation method under different conditions by numerical simulation.Numerical simulation results show that,compared with local linear estimation,threshold local linear estimation and traditional M-estimation,the new estimation method proposed in this paper can effectively deal with outliers and jumps in the data.In the case of large sampling time span,high sampling frequency,and tendency to take relatively large jumps,the estimation’s accuracy and robustness are better than the other three methods.At the same time,this paper explores the large sample property of the new estimation by means of QQ plot,and illustrates the distribution characteristics of the estimation.In addition,the results of numerical simulation in this paper also show that when there are many outliers in the data,especially when the value of jump tends to be large,the effect of introducing threshold into the estimation method is better than using M-estimation directly.