Asymptotic normality of randomized periodogram for estimating quadratic variation in mixed Brownian--fractional Brownian model
arXiv:1411.4499 · doi:10.15559/15-VMSTA24
Abstract
We study asymptotic normality of the randomized periodogram estimator of quadratic variation in the mixed Brownian--fractional Brownian model. In the semimartingale case, that is, where the Hurst parameter of the fractional part satisfies , the central limit theorem holds. In the nonsemimartingale case, that is, where , the convergence toward the normal distribution with a nonzero mean still holds if , whereas for the other values, that is, , the central convergence does not take place. We also provide Berry--Esseen estimates for the estimator.
Published at http://dx.doi.org/10.15559/15-VMSTA24 in the Modern Stochastics: Theory and Applications (https://www.i-journals.org/vtxpp/VMSTA) by VTeX (http://www.vtex.lt/)