A quantitative CLT in Wasserstein-1 distance is proved for integrated periodograms of long-memory Gaussian sequences by reducing the problem to variance asymptotics and explicit fourth-cumulant bounds via the fourth-moment theorem.
Hosoya,A limit theory for long-range dependence and statistical inference on related models, Annals of Statistics25(1997), no
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Quantitative central limit theorem for an integrated periodogram via the fourth moment theorem
A quantitative CLT in Wasserstein-1 distance is proved for integrated periodograms of long-memory Gaussian sequences by reducing the problem to variance asymptotics and explicit fourth-cumulant bounds via the fourth-moment theorem.