This paper studies cyclic long‐memory processes with Gegenbauer‐type spectral densities. For a semiparametric statistical model, new simultaneous estimates for singularity location and long‐memory parameters are proposed. This generalized filtered method‐of‐moments approach is based on general filter transforms that include wavelet transformations as a particular case. It is proved that the estimates are almost surely convergent to the true values of parameters. Solutions of the estimation equations are studied, and adjusted statistics are proposed. Monte‐Carlo study results are presented to confirm the theoretical findings.

中文翻译：

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循环长记忆参数的估计

本文研究了具有 Gegenbauer 型谱密度的循环长记忆过程。对于半参数统计模型，提出了新的奇点位置和长记忆参数的同时估计。这种广义滤波矩方法基于包括小波变换作为特殊情况的一般滤波器变换。证明估计几乎肯定会收敛到参数的真实值。研究了估计方程的解，并提出了调整统计量。提供蒙特卡罗研究结果以证实理论发现。