Estimation of random cycles in persistent time series
File(s)
Published online version
Author(s)
Abadir, Karim M
Bailey, Natalia
Distaso, Walter
Giraitis, Liudas
Type
Journal Article
Abstract
A number of economic, financial, and climatic time series exhibit persistent cycles which are characterized by time-dependence patterns and peaks in the spectrum. In this article, we introduce a class of semiparametric cyclical–memory processes which enable the modeling of random cyclical patterns in stationary and non-stationary time series. We develop a theoretical background and asymptotic estimation theory for the frequency of a cycle represented by the location of a peak in the spectrum. The estimation procedure is easy to implement and allows for the construction of narrow confidence intervals around the location point. Monte Carlo simulations confirm the good finite sample performance of our estimator. We illustrate our method with three empirical applications. We uncover (quasi-)periodic cycles in macroeconomic series, both nominal and real (U.S. nominal GDP and real industrial production), and CO2
concentration levels.
concentration levels.
Date Issued
2026-08-07
Date Acceptance
2026-08-01
Citation
Econometric Theory, 2026, pp.1-28
ISSN
0266-4666
Publisher
Cambridge University Press (CUP)
Start Page
1
End Page
28
Journal / Book Title
Econometric Theory
Copyright Statement
© The Author(s), 2026. Published by Cambridge University Press. This is an Open Access article, distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives licence (https://creativecommons.org/licenses/by-nc-nd/4.0), which permits non-commercial re-use, distribution, and reproduction in any medium, provided that no alterations are made and the original article is properly cited. The written permission of Cambridge University Press or the rights holder(s) must be obtained prior to any commercial use and/or adaptation of the article.
Identifier
10.1017/S0266466626100504
Publication Status
Published online
Date Publish Online
2026-08-07