Abstract
The present paper concerns the parametric estimation for the fractional Gaussian noise in a high-frequency observation scheme. The sequence of Le Cam’s one-step maximum likelihood estimators (OSMLE) is studied. This sequence is defined by an initial sequence of quadratic generalized variations-based estimators (QGV) and a single Fisher scoring step. The sequence of OSMLE is proved to be asymptotically efficient as the sequence of maximum likelihood estimators but is much less computationally demanding. It is also advantageous with respect to the QGV which is not variance efficient. Performances of the estimators on finite size observation samples are illustrated by means of Monte-Carlo simulations.
Highlights
Beyond the classical model of independent and identically distributed Gaussian random variables for the returns of an asset price, several extensions have been proposed to describe the observed stylized facts by means of heteroscedasticity, non-Gaussianity and/or dependence
We focus on the fractional Gaussian noise which is characterized by a standard deviation parameter and a dependence parameter (Hurst exponent)
Contrary to the large sample setting, the Local Asymptotic Normal (LAN) property of the likelihoods cannot be deduced from the previous results in the high-frequency scheme, where the time horizon is fixed and the mesh size tends to zero
Summary
Beyond the classical model of independent and identically distributed Gaussian random variables for the returns of an asset price, several extensions have been proposed to describe the observed stylized facts by means of heteroscedasticity, non-Gaussianity and/or dependence. Contrary to the large sample setting, the LAN property of the likelihoods cannot be deduced from the previous results in the high-frequency scheme (infill asymptotics), where the time horizon is fixed and the mesh size tends to zero. In this setting, the joint estimation of the volatility and the self-similarity index is singular and no confidence interval of the pair could be obtained [2, 16]. Performances of the estimators for samples of medium size are illustrated by means of Monte-Carlo simulations
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
