Asymptotic normality of simultaneous estimators of cyclic long-memory processes
journal contributionposted on 2022-05-20, 04:46 authored by A Ayache, M Fradon, Ravindi NanayakkaraRavindi Nanayakkara, Andriy OlenkoAndriy Olenko
Spectral singularities at non-zero frequencies play an impor-tant role in investigating cyclic or seasonal time series. The publication  introduced the generalized filtered method-of-moments approach to simul-taneously 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 in-cludes wavelet transformations as a particular case.