Asymptotic normality of simultaneous estimators of cyclic long-memory processes

TL;DR

This paper proves the asymptotic normality of estimators for cyclic long-memory processes, extending previous methods with new estimates and including wavelet transformations, supported by numerical results.

Contribution

It advances the understanding of simultaneous estimators for cyclic long-memory processes by establishing their asymptotic normality and proposing new adjusted estimates.

Findings

Asymptotic normality of estimators is established.

New adjusted estimates are introduced and analyzed.

Numerical results support the theoretical findings.

Abstract

Spectral singularities at non-zero frequencies play an important role in investigating cyclic or seasonal time series. The publication [2] 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.