Efficient estimation for diffusions sampled at high frequency over a fixed time interval
arXiv:1507.06792 · doi:10.3150/15-BEJ799
Abstract
Parametric estimation for diffusion processes is considered for high frequency observations over a fixed time interval. The processes solve stochastic differential equations with an unknown parameter in the diffusion coefficient. We find easily verified conditions on approximate martingale estimating functions under which estimators are consistent, rate optimal, and efficient under high frequency (in-fill) asymptotics. The asymptotic distributions of the estimators are shown to be normal variance-mixtures, where the mixing distribution generally depends on the full sample path of the diffusion process over the observation time interval. Utilising the concept of stable convergence, we also obtain the more easily applicable result that for a suitable data dependent normalisation, the estimators converge in distribution to a standard normal distribution. The theory is illustrated by a simulation study comparing an efficient and a non-efficient estimating function for an ergodic and a non-ergodic model.
Published at http://projecteuclid.org/euclid.bj/1489737628 in the Bernoulli Journal ( see http://www.bernoulli-society.org/index.php/publications/bernoulli-journal/bernoulli-journal ) by the International Statistical Institute/Bernoulli Society ( see http://www.bernoulli-society.org )
References in corpus (5)
- ANOVA for diffusions and Itô processes
- Monte Carlo maximum likelihood estimation for discretely observed diffusion processes
- Simple simulation of diffusion bridges with application to likelihood inference for diffusions
- Closed-form likelihood expansions for multivariate diffusions
- A generative angular model of protein structure evolution