We derive the asymptotics of the maximum likelihood estimators for diffusion models. The models considered in the paper are very general, including both stationary and nonstationary diffusions. For such a broad class of diffusion models, we establish the consistency and derive the limit distributions of the exact maximum likelihood estimator, and also the quasi and approximate maximum likelihood estimators based on various versions of approximated transition densities. Our asymptotics are two dimensional, requiring the sampling interval to decrease as well as the time span of sample to increase. The two dimensional asymptotics provide a unifying framework for such a broad class of estimators for both stationary and nonstationary diffusion models. More importantly, they yield the primary asymptotics that are very useful to analyze the exact, quasi and approximate maximum likelihood estimators of the diffusion models, if the samples are collected at high frequency intervals over modest lengths of sampling horizons as in the case of many practical applications.
Keywords: Diffusion; Maximum likelihood estimation; Nonstationarity; Asymptotics
Biography: Dr Joon Y. Park is a professor with the department of Economics, Indiana University, USA.