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Asymptotic normality of randomized periodogram for estimating quadratic variation in mixed Brownian–fractional Brownian model
Volume 2, Issue 1 (2015), pp. 29–49
Ehsan Azmoodeh   Tommi Sottinen   Lauri Viitasaari  

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https://doi.org/10.15559/15-VMSTA24
Pub. online: 11 May 2015      Type: Research Article      Open accessOpen Access

Received
17 November 2014
Revised
30 March 2015
Accepted
24 April 2015
Published
11 May 2015

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 H of the fractional part satisfies $H\in (3/4,1)$, the central limit theorem holds. In the nonsemimartingale case, that is, where $H\in (1/2,3/4]$, the convergence toward the normal distribution with a nonzero mean still holds if $H=3/4$, whereas for the other values, that is, $H\in (1/2,3/4)$, the central convergence does not take place. We also provide Berry–Esseen estimates for the estimator.

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Copyright
© 2015 The Author(s). Published by VTeX
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Open access article under the CC BY license.

Keywords
Central limit theorem multiple Wiener integrals Malliavin calculus fractional Brownian motion quadratic variation randomized periodogram

MSC2010
60G15 60H07 62F12

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  • Online ISSN: 2351-6054
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