Parameter Estimation For The CIR Integrated Diffusion Process With High Frequency Sampling

Nowadays,the digital economy based on data has become a new form of economic and social development,and big data analysis is the key to sustainable economic development in the digital financial neighborhood.The diffusion process model uses high-frequency information data to describe Asset price fluctuations play an important role.Since the diffusion process is mainly described by drift parameters and diffusion parameters,the inference and estimation of parameters is the key to theoretical application.In this paper,the parameter contrast estimators of the Cox-Ingersoll-Ross integrated diffusion process are derived by applying the contrast function of the integrated diffusion process,and the asymptotic properties of the estimators are discussed by using the mixing properties of the process.We firstly give the tail probability exponential inequality of the high-frequency sampling mixing sequence,and then use this inequality to prove the strong consistency of the contrast estimators of the drift parameters and the diffusion parameter of the CIR integrated diffusion process.In order to obtain this asymptotic property,we require relatively low order r of the negative power moment E|X_t^-1|^r of the diffusion process.In the existing literature,r>9 is required to obtain the weak consistency of the estimators.In our theorems,only r>2 is required for the strong consistency of the diffusion parameter estimator,while r>4 for the strong consistency of the drift parameter estimators.In the numerical simulation analysis,we use the Euler discrete algorithm and the Milstein discrete algorithm.The simulation results show that the optimal sampling intervals are around n ^1/3,and as the sample size increases,the standard deviations of the estimators get smaller.In the empirical analysis,we use the daily log price data of the CSI 300 Index to estimate the CIR integrated diffusion model,and build the log price Bootstrap prediction model and prediction confidence interval.The results show that the prediction effect of the model is good.