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Article Dans Une Revue Bernoulli Année : 2024

Asymptotic normality for a modified quadratic variation of the Hermite process

Antoine Ayache
Ciprian A Tudor

Résumé

We consider a modified quadratic variation of the Hermite process based on some well-chosen increments of this process. These special increments have the very useful property to be independent and identically distributed up to asymptotically negligible remainders. We prove that this modified quadratic variation satisfies a Central Limit Theorem and we derive its rate of convergence under the Wasserstein distance via Stein-Malliavin calculus. As a consequence, we construct, for the first time in the literature related to Hermite processes, a strongly consistent and asymptotically normal estimator for the Hurst parameter.
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Dates et versions

hal-04076434 , version 1 (20-04-2023)

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Antoine Ayache, Ciprian A Tudor. Asymptotic normality for a modified quadratic variation of the Hermite process. Bernoulli, In press. ⟨hal-04076434⟩
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