Asymptotic normality of randomized periodogram for estimating quadratic variation in mixed Brownian–fractional Brownian model
Azmoodeh, Ehsan; Sottinen, Tommi; Viitasaari, Lauri (2015-05-11)
Azmoodeh, Ehsan
Sottinen, Tommi
Viitasaari, Lauri
VTeX
11.05.2015
Julkaisun pysyvä osoite on
https://urn.fi/URN:NBN:fi-fe2020062645836
https://urn.fi/URN:NBN:fi-fe2020062645836
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©2015 The Author(s). Published by VTeX. Open access article under the CC BY license.
©2015 The Author(s). Published by VTeX. Open access article under the CC BY license.
Tiivistelmä
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.
Kokoelmat
- Artikkelit [3030]