The Cir Model Statistical Diagnostics

It's been a long time for the study of statistical inference for financial model, and there have been a lot of maturity theories about the study. But there are few people to study the introduction of statistical diagnose to financial model in the world. Up to now, only the diagnosis for time series has been applied to finance, but the theory is not matured. And there are few paper which introduce regression diagnose to finance too. In order to extend regression diagnose to diffusion model, this paper applies the regression diagnose to CIR model, and proposes the diagnosis methods for CIR.Firstly, this paper reviews the research status of the estimation of diffusion model and statistical diagnose, then studies the diagnosis for CIR model as followed:This paper applies the Gisanov theorem and Ito theorem, under the equivalent probability defined in this paper, to obtain a linear regression model about CIR model, and gives the Cook distance, WK statistic and AP statistic. As the error term in the linear regression is more complex than the one in classical regression diagnose model, we use numerical simulation to examine the effect of the diagnostic statistics above in two ways. We first use the diagnose statistics above to indentify the outliers from the simulated data, then delete the outliers and reestimate the parameter of the diffusion term of CIR model, and the result is better. Secondly we change the values of some data to make them obviously deviate from the simulated track, and then reestimate the parameter, the result is not better. So we conclude that the diagnose statistics above is reasonable. In this paper, we also study about the diagnosis of mean-shift outlier model and likelihood distance for CIR model.In the chapter 4, we take the ShangHai Interbank Offered Rate (SHIBOR) overnight quote as the study object, and detect the outliers. Then we compare the outliers to the date when the monetary policies released by government to examine the effect of the statistical diagnosis for CIR model. And the result show that the diagnosis for CIR model is effective.