Asymptotic normality of randomized periodogram for estimating quadratic variation in mixed Brownian–fractional Brownian model
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 nons...
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2015-05-01
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| Series: | Modern Stochastics: Theory and Applications |
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| Online Access: | https://vmsta.vtex.vmt/doi/10.15559/15-VMSTA24 |
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doaj-47a84cee15b845ccafd3b206439061bb2020-11-24T21:53:22ZengVTeXModern Stochastics: Theory and Applications2351-60462351-60542015-05-0121294910.15559/15-VMSTA24Asymptotic normality of randomized periodogram for estimating quadratic variation in mixed Brownian–fractional Brownian modelEhsan Azmoodeh0Tommi Sottinen1Lauri Viitasaari2Mathematics Research Unit, Luxembourg University, P.O. Box L-1359, LuxembourgDepartment of Mathematics and Statistics, University of Vaasa, P.O. Box 700, FIN-65101 Vaasa, FinlandDepartment of Mathematics and System Analysis, Aalto University School of Science, Helsinki, P.O. Box 11100, FIN-00076 Aalto, Finland; Department of Mathematics, Saarland University, Post-fach 151150, D-66041 Saarbrücken, GermanyWe 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.https://vmsta.vtex.vmt/doi/10.15559/15-VMSTA24Central limit theoremmultiple Wiener integralsMalliavin calculusfractional Brownian motionquadratic variationrandomized periodogram |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Ehsan Azmoodeh Tommi Sottinen Lauri Viitasaari |
| spellingShingle |
Ehsan Azmoodeh Tommi Sottinen Lauri Viitasaari Asymptotic normality of randomized periodogram for estimating quadratic variation in mixed Brownian–fractional Brownian model Modern Stochastics: Theory and Applications Central limit theorem multiple Wiener integrals Malliavin calculus fractional Brownian motion quadratic variation randomized periodogram |
| author_facet |
Ehsan Azmoodeh Tommi Sottinen Lauri Viitasaari |
| author_sort |
Ehsan Azmoodeh |
| title |
Asymptotic normality of randomized periodogram for estimating quadratic variation in mixed Brownian–fractional Brownian model |
| title_short |
Asymptotic normality of randomized periodogram for estimating quadratic variation in mixed Brownian–fractional Brownian model |
| title_full |
Asymptotic normality of randomized periodogram for estimating quadratic variation in mixed Brownian–fractional Brownian model |
| title_fullStr |
Asymptotic normality of randomized periodogram for estimating quadratic variation in mixed Brownian–fractional Brownian model |
| title_full_unstemmed |
Asymptotic normality of randomized periodogram for estimating quadratic variation in mixed Brownian–fractional Brownian model |
| title_sort |
asymptotic normality of randomized periodogram for estimating quadratic variation in mixed brownian–fractional brownian model |
| publisher |
VTeX |
| series |
Modern Stochastics: Theory and Applications |
| issn |
2351-6046 2351-6054 |
| publishDate |
2015-05-01 |
| description |
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. |
| topic |
Central limit theorem multiple Wiener integrals Malliavin calculus fractional Brownian motion quadratic variation randomized periodogram |
| url |
https://vmsta.vtex.vmt/doi/10.15559/15-VMSTA24 |
| work_keys_str_mv |
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