Open Access
August 2017 Efficient estimation for diffusions sampled at high frequency over a fixed time interval
Nina Munkholt Jakobsen, Michael Sørensen
Bernoulli 23(3): 1874-1910 (August 2017). DOI: 10.3150/15-BEJ799


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.


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Nina Munkholt Jakobsen. Michael Sørensen. "Efficient estimation for diffusions sampled at high frequency over a fixed time interval." Bernoulli 23 (3) 1874 - 1910, August 2017.


Received: 1 July 2015; Revised: 1 November 2015; Published: August 2017
First available in Project Euclid: 17 March 2017

zbMATH: 06714322
MathSciNet: MR3624881
Digital Object Identifier: 10.3150/15-BEJ799

Keywords: approximate martingale estimating functions , discrete time sampling of diffusions , in-fill asymptotics , normal variance-mixtures , optimal rate , random Fisher information , stable convergence , Stochastic differential equation

Rights: Copyright © 2017 Bernoulli Society for Mathematical Statistics and Probability

Vol.23 • No. 3 • August 2017
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