March 2024 ANOPOW for replicated nonstationary time series in experiments
Zeda Li, Yu (Ryan) Yue, Scott A. Bruce
Author Affiliations +
Ann. Appl. Stat. 18(1): 328-349 (March 2024). DOI: 10.1214/23-AOAS1791


We propose a novel analysis of power (ANOPOW) model for analyzing replicated nonstationary time series commonly encountered in experimental studies. Based on a locally stationary ANOPOW Cramér spectral representation, the proposed model can be used to compare the second-order time-varying frequency patterns among different groups of time series and to estimate group effects as functions of both time and frequency. Formulated in a Bayesian framework, independent two-dimensional second-order random walk (RW2D) priors are assumed on each of the time-varying functional effects for flexible and adaptive smoothing. A piecewise stationary approximation of the nonstationary time series is used to obtain localized estimates of time-varying spectra. Posterior distributions of the time-varying functional group effects are then obtained via integrated nested Laplace approximations (INLA) at a low computational cost. The large-sample distribution of local periodograms can be appropriately utilized to improve estimation accuracy since INLA allows modeling of data with various types of distributions. The usefulness of the proposed model is illustrated through two real-data applications: analyses of seismic signals and pupil diameter time series in children with attention deficit hyperactivity disorder. Simulation studies, Supplementary Material (Li, Yue and Bruce (2024a)), and R code (Li, Yue and Bruce (2024b)) for this article are also available.

Funding Statement

Research reported in this publication was supported by the National Institute of General Medical Sciences of the National Institutes of Health under Award Number R01GM140476 and the National Science Foundation under Grant Number CDS&E-MSS-2152950. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health or the National Science Foundation.


Download Citation

Zeda Li. Yu (Ryan) Yue. Scott A. Bruce. "ANOPOW for replicated nonstationary time series in experiments." Ann. Appl. Stat. 18 (1) 328 - 349, March 2024.


Received: 1 September 2022; Revised: 1 May 2023; Published: March 2024
First available in Project Euclid: 31 January 2024

Digital Object Identifier: 10.1214/23-AOAS1791

Keywords: integrated nested Laplace approximations , locally stationary ANOPOW Cramér spectral representation , pupil diameter time series , replicated nonstationary time series , spectral analysis

Rights: Copyright © 2024 Institute of Mathematical Statistics


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Vol.18 • No. 1 • March 2024
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