Title: Hybrid estimation for an ergodic diffusion plus noise based on ultra high frequency data
Authors: Masayuki Uchida - Osaka University (Japan) [presenting]
Abstract: Hybrid estimation of both drift and volatility parameters for an ergodic diffusion processes plus noise based on ultra high frequency data is considered. Adaptive maximum likelihood type estimators (MLEs) of both drift and volatility parameters for a discretely observed ergodic diffusion processes plus noise have been proposed, and the asymptotic properties of the adaptive MLEs have been shown. In order to get the quasi MLE, it is crucial to choose a suitable initial estimator for optimization of the quasi likelihood function. From a computational point of view, we propose initial Bayes type estimators (initial BEs) of both drift and volatility parameters and the adaptive MLEs with the initial BEs, which are called hybrid estimators, are proposed. It is shown that the hybrid estimators with the initial BEs have asymptotic normality and convergence of moments. We also give an example and simulation results.