Variance estimator for fractional diffusions with variance and drift depending on time

Abstract

We propose punctual and functional estimators for the local variance of pseudo-diffusions driven by Gaussian noises. The consistency and asymptotic normality are shown. The proofs are simplified by using the Central Limit Theorem for non-linear functionals belonging to Itô-Wiener’s Chaos, of Peccati-Nualart-Tudor. Besides, a simulation study is made to assess the performance of those estimators. This study reveals, through various examples, that the estimators give good approximations for the true local variance.