Parameter Estimations For Two-type SCIR Model With Small Noises

As we all know,Cox-Ingersoll-Ross(CIR)is widely used in the international financial environment,and it is a model to describe the evolution of interest rate in financial mathematics.CIR model driven by stationary process is stationary CIR(SCIR)model,which is also a special form of continuous state branching process with immigrants.SCIR model has been widely used in financial mathematics at present.SCIR model is also a CIR model with jumps and diffusion.Compared with one-type SCIR model,two-type SCIR model contains interactive terms and more possible jumping terms.Stochastic phenomena of different interest rate term changes can be more accurately described by two-type SCIR model.Therefore,it is of great significance to study the properties of two-type SCIR model.At present,many scholars have studied the parameter estimation of CIR model and SCIR model.Therefore,it has a wide application prospect for studying the parameter estimation of two-type SCIR model.In this essay,mainly explores the least square estimation of two-type SCIR model when is very small.First,the high-order moment of two-type SCIR model is given,and it is verified that the r-order moment of two-type SCIR model is finite by It(?)’s formula and three inequalities.Then,the least square estimation of drift term and interaction term in twodimensional SCIR model when is very small is estimated.By finding the partial derivative of contrast function,the estimated values of the drift term and the interaction term are obtained,and the asymptotic behavior of the more accurate estimator is proved by Lévy-It(?) and the error equation between the parameter estimator and the real value.Finally,the theoretical results are simulated by R software,and the average absolute error of the estimator of random number estimation parameters is randomly generated by the density function of-stable distribution.The data model and chart analysis of the theoretical results show that the simulation effect is good.