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Abstract:
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This paper derives the asymptotics of the maximum likelihood estimators for jump-diffusion models. We propose the decomposition of the discrete-time likelihood function by Radon-Nikodym derivative, which plays an important role in the derivation for the asymptotics. Then we derive the corresponding score and Hessian functions. The asymptotic theory is therefore established as the sampling interval goes to zero and the time span goes to infinity. Our theory reveals that the asymptotic distributions of drift and diffusion parameters are independent of the jump parameters, and they are the same as those under the pure diffusion models in form. The accuracy of our theory is illustrated through some representative examples.
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