分段时变参数CIR模型及其实证研究

CIR Model with Segmented Time-varying Parameters:An empirical study

经济环境总体是变化的,但在一定阶段会保持局部稳定.鉴于此,提出了分段时变参数CIR模型的构想,并用它来建模短期利率与汇率.给出了CIR模型设定检验的广义残差拟合优度检验法,用之来检验模型的时变性.用数值模拟和实证分析来验证分段时变参数CIR模型进行利率、汇率建模的可行性和合理性.数值模拟表明,两组符合CIR(Cox-Ingersoll-Ross)模型的数据合在一起不一定还符合CIR模型.通过对短期国库券利率和加拿大元与美元汇率数据的实证分析,发现用分段时变参数CIR模型来描述短期利(汇)率比一般的固定常数CIR模型更加合理.

In general the economic environment is changing, but sometimes may keep local stability in a certain stage. In view of this, in the paper, we propose a concept of CIR model with time-varying parameters, and use it to model short-term interest rate and exchange rate. The generalized residual goodness of fit test of CIR model is given, which is used to test the time-varying characteristic of the model. Using numerical simulation and empirical analysis verify feasibility and rationality of CIR model with segmented time-varying parameters to describe interest and exchange rate modeling. Numerical simulation results show that if two groups of data which are in accordance with CIR（Cox-Ingersoll-Ross） model are combined together, and they may not conform to this model again. According to the data analysis for the weekly 6-month U.S. Treasury bill rate and the Canada / U.S. daily foreign exchange rates, we find that the CIR model with segmented time-varying parameters is more reasonable to describe the short-term interest（exchange） rate than the general constant coefficient CIR model.