Diffusion Process Of Diagnosis

Nowadays, diffusion process is widely used in finance modeling and econometrics, and the statistical analysis for diffusion process has became an important research field in statistics. This article mainly studied the statistical diagnosis method for parametric diffusion process. For Black-Scholes model, we first discretized the model so that it was similar to regression model, and then used the Generalized Method of Moments Estimation to estimate the parameters. Then we established the case deletion model to obtain the generalized cook distance and generalized moment distance. By simulation, we validated our results. For general parametric diffusion process, we first discretized the model and then used the maximum likelihood estimation method to estimate the parameters. Then we discussed the statistical diagnosis method. Again, we took O-U process for example to construct the generalized cook distance and the likelihood distance, also we obtained the mean shift model and the influencers Score testing statistics SCi like the parametric regression. Then we obtained the perturbation model and discussed the local influence analysis for O-U process based on likelihood distance, similarly, we used simulations to prove our results. Finally, we confirmed the application of our method by example.