Spectral singularities at non-zero frequencies play an important role in investigating cyclic or seasonal time series. The publication  introduced the generalized filtered method-of-moments approach to simultaneously estimate singularity location and long-memory parameters. This paper continues studies of these simultaneous estimators. A wide class of Gegenbauer-type semi-parametric models is considered. Asymptotic normality of several statistics of the cyclic and long-memory parameters is proved. New adjusted estimates are proposed and investigated. The theoretical findings are illustrated by numerical results. The methodology includes wavelet transformations as a particular case.
Ravindi Nanayakkara and Andriy Olenko were partially supported under the Australian Research Council’s Discovery Projects funding scheme (project DP160101366).
We are thankful to Professor Domenico Marinucci for attracting our attention to this research problem. We also are grateful for the referees’ careful reading of the paper and detailed comments and suggestions, which helped to improve it.
Antoine Ayache is grateful to the Sydney Mathematical Research Institute at the University of Sydney for having financially supported his 7 weeks visit to Australia in 2019, and for the position of visiting researcher at the University of Sydney. Also, he is thankful to the School of Engineering and Mathematical Sciences at the La Trobe University for the honorary visiting professorship for one month at this university.
Andriy Olenko is grateful to Laboratoire d’Excellence, Centre Européen pour les Mathématiques, la Physique et leurs interactions (CEMPI, ANR-11-LABX-0007-01), Laboratoire de Mathématiques Paul Painlevé, France, for support and giving him the opportunity to pursue research at the Université de Lille for two months.
This research includes computations using the Linux computational cluster Gadi of the National Computational Infrastructure (NCI), which is supported by the Australian Government and La Trobe University.
"Asymptotic normality of simultaneous estimators of cyclic long-memory processes." Electron. J. Statist. 16 (1) 84 - 115, 2022. https://doi.org/10.1214/21-EJS1953