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.
Ginovyan,Random Toeplitz functionals and their applications, Frontiers in Probability and the Statistical Sciences, Springer, Cham, [2025]©2025
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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.