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    Asymptotics for the maximum likelihood estimators of diffusion models

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    JEONG-DISSERTATION.pdf (563.5Kb)
    Date
    2009-05-15
    Author
    Jeong, Minsoo
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    Abstract
    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 ¢, 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.
    URI
    http://hdl.handle.net/1969.1/ETD-TAMU-2335
    Subject
    nonstationary diffusion process
    mixed normal limit theory
    Milstein scheme
    Euler scheme
    maximum likelihood estimation
    true transition density
    hypothesis testing
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    • Electronic Theses, Dissertations, and Records of Study (2002– )
    Citation
    Jeong, Minsoo (2008). Asymptotics for the maximum likelihood estimators of diffusion models. Doctoral dissertation, Texas A&M University. Available electronically from http : / /hdl .handle .net /1969 .1 /ETD -TAMU -2335.

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