Statistical testing and estimation in continuous time interest rate models

The shape of drift function in continuous time interest rate models has beeninvestigated by many authors during the past decade. The main concerns have beenwhether the drift function is linear or nonlinear, but no convincing conclusions havebeen seen. In this dissertation, we investigate the reason for this problem and testseveral models of the drift function using a nonparametric test. Furthermore, westudy some related problems, including the empirical properties of the nonparametrictest.First, we propose regression models for the estimation of the drift function insome continuous time models. The limiting distribution of the parameter estimatorin the proposed regression model is derived under certain conditions. Based on ouranalyses, we conclude that the effect of drift function for some U.S. Treasury Bill yieldsdata is negligible. Therefore, neither linear nor nonlinear modeling has a significanteffect.Second, parametric linear and nonlinear proposed regression models are appliedand the correctness of those models is examined using the consistent nonparametricmodel specification test introduced by Li (1994) and Zheng (1996), henceforth the Jn test. The test results indicate that there is no strong statistical evidence against theassumed drift models. Furthermore, the constant drift model is not rejected either.Third, we compare the Jn and generalized likelihood ratio (GLR) tests throughMonte Carlo simulation studies concerning whether the sizes of tests are stable over arange of bandwidth values, which is an important indicator to measure the usefulnessof nonparametric tests. The GLR test was applied to testing the linear drift functionin continuous time models by Fan and Zhang (2003). Our simulation study showsthat the GLR test does not provide stable sizes over a grid of bandwidth values intesting the drift function of some continuous time models, whereas the Jn test usuallydoes.