2012/12/10 by Jacod, Jean, Mathieu Rosenbaum, Jean Jacod +1
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Spectral Theory in Mathematical Physics #Stochastic processes and financial applications #math.PR
paper · pdf · doi:10.48550/arxiv.1212.1997
arXiv admin note: substantial text overlap with arXiv:1207.3757
arxiv created 2012/12/10 · openalex publication_date 2012/12/10 · arxiv updated 2012/12/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a multidimensional Ito semimartingale regularly sampled on [0,t] at high frequency 1/Δn, with Δn going to zero. The goal of this paper is to provide an estimator for the integral over [0,t] of a given function of the volatility matrix, with the optimal rate 1/√(Δn) and minimal asymptotic variance. To achieve this we use spot volatility estimators based on observations within time intervals of length knΔn. In [5] this was done with kn tending to infinity and kn√(Δn) tending to 0, and a central limit theorem was given after suitable de-biasing. Here we do the same with kn of order 1/√(Δn). This results in a smaller bias, although more difficult to eliminate.