Online spectral density estimation
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Published version (ahead of print)
Author(s)
Kazi, Shahriar Hasnat
Adams, Niall
Cohen, Ed
Type
Journal Article
Abstract
This paper develops the first online algorithms for estimating the spectral density function—a fundamental object of interest in time series analysis—that satisfies the three core requirements of streaming inference: fixed memory, fixed computational complexity, and temporal adaptivity. Our method builds on the concept of forgetting factors, allowing the estimator to adapt to gradual or abrupt changes in the data-generating process without prior knowledge of its dynamics. We introduce a novel online forgetting-factor periodogram and show that, under stationarity, it asymptotically recovers the properties of its offline counterpart. Leveraging this, we construct an online Whittle estimator, and further develop an adaptive online spectral estimator that dynamically tunes its forgetting factor using the Whittle likelihood as a loss. Through extensive simulation studies and an application to ocean drifter velocity data, we demonstrate the method’s ability to track time-varying spectral properties in real-time with strong empirical performance.
Date Issued
2026-04-27
Date Acceptance
2025-11-27
Citation
Journal of Computational And Graphical Statistics (JCGS), 2026
ISSN
1061-8600
Publisher
Taylor and Francis Group
Journal / Book Title
Journal of Computational And Graphical Statistics (JCGS)
Copyright Statement
© 2026 The Author(s). Published with license by Taylor & Francis Group, LLC. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The terms on which this article has been published allow the posting of the Accepted Manuscript in a repository by the author(s) or with their consent.
License URL
Publication Status
Published online
Date Publish Online
2025-12-22