Reference : Asymptotic normality of randomized periodogram for estimating quadratic variation in ...
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Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/26393
Asymptotic normality of randomized periodogram for estimating quadratic variation in mixed Brownian-fractional Brownian model
English
Azmoodeh, Ehsan [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Sottinen, Tommi []
Viitasaari, Lauri []
2014
No
[en] 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 H of the fractional part satisfies H∈(3/4,1), the central limit theorem holds. In the nonsemimartingale case, that is, where H∈(1/2,3/4], the convergence toward the normal distribution with a nonzero mean still holds if H=3/4, whereas for the other values, that is, H∈(1/2,3/4), the central convergence does not take place. We also provide Berry--Esseen estimates for the estimator.
http://hdl.handle.net/10993/26393
http://arxiv.org/abs/1411.4499

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