In this paper I derive the asymptotics of the exact, Euler, and Milstein ML
estimators for diffusion models, including general nonstationary diffusions. Though
there have been many estimators for the diffusion model, their asymptotic properties
were generally unknown. This is especially true for the nonstationary processes, even
though they are usually far from the standard ones. Using a new asymptotics with
respect to both the time span T and the sampling interval ยข, I find the asymptotics
of the estimators and also derive the conditions for the consistency. With this new
asymptotic result, I could show that this result can explain the properties of the
estimators more correctly than the existing asymptotics with respect only to the
sample size n. I also show that there are many possibilities to get a better estimator
utilizing this asymptotic result with a couple of examples, and in the second part of
the paper, I derive the higher order asymptotics which can be used in the bootstrap
analysis.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/ETD-TAMU-2335 |
| Date | 15 May 2009 |
| Creators | Jeong, Minsoo |
| Contributors | Park, Joon Y. |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | Book, Thesis, Electronic Dissertation, text |
| Format | electronic, application/pdf, born digital |
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