The shape of drift function in continuous time interest rate models has been
investigated by many authors during the past decade. The main concerns have been
whether the drift function is linear or nonlinear, but no convincing conclusions have
been seen. In this dissertation, we investigate the reason for this problem and test
several models of the drift function using a nonparametric test. Furthermore, we
study some related problems, including the empirical properties of the nonparametric
test.
First, we propose regression models for the estimation of the drift function in
some continuous time models. The limiting distribution of the parameter estimator
in the proposed regression model is derived under certain conditions. Based on our
analyses, we conclude that the effect of drift function for some U.S. Treasury Bill yields
data is negligible. Therefore, neither linear nor nonlinear modeling has a significant
effect.
Second, parametric linear and nonlinear proposed regression models are applied
and the correctness of those models is examined using the consistent nonparametric
model 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 the
assumed drift models. Furthermore, the constant drift model is not rejected either.
Third, we compare the Jn and generalized likelihood ratio (GLR) tests through
Monte Carlo simulation studies concerning whether the sizes of tests are stable over a
range of bandwidth values, which is an important indicator to measure the usefulness
of nonparametric tests. The GLR test was applied to testing the linear drift function
in continuous time models by Fan and Zhang (2003). Our simulation study shows
that the GLR test does not provide stable sizes over a grid of bandwidth values in
testing the drift function of some continuous time models, whereas the Jn test usually
does.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/4189 |
| Date | 30 October 2006 |
| Creators | Kim, Myung Suk |
| Contributors | Wang, Suojin |
| Publisher | Texas A&M University |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | Electronic Dissertation, text |
| Format | 536282 bytes, electronic, application/pdf, born digital |
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