Title: Adaptive maximum-likelihood-type estimation for discretely and noisily observed diffusion processes
Authors: Shogo Nakakita - Osaka University (Japan) [presenting]
Masayuki Uchida - Osaka University (Japan)
Abstract: An ergodic diffusion process is considered which is defined by the following stochastic differential equation and parametric inference with discrete and noisy observation. While the estimation with short-term high-frequency and noisy observation has been one of the central topics in the context of financial data analysis, the focus is on the long-term observation scheme to estimate the parametric drift term of the stochastic differential equation. To extract the state of the latent process, we compose the sequence of local means with respect to large numbers of partitions of observation. With this sequence, we construct two quasi-likelihood functions for diffusion and drift parameters respectively. It is possible to optimise these quasi-likelihoods separately, and this adaptive procedure has an advantage over the existent simultaneous one from the viewpoint of computational burden. We show that both the estimators have asymptotic properties such as consistency, asymptotic normality with different convergence rate and asymptotic independence.