Published by the Foundation for Open Access Statistics Editors-in-chief: Bettina Grün, Torsten Hothorn, Edzer Pebesma, Achim Zeileis    ISSN 1548-7660; CODEN JSSOBK
Authors: Adolf Mathias, Florian Grond, Ramon Guardans, Detlef Seese, Miguel Canela, Hans H. Diebner
Title: Algorithms for Spectral Analysis of Irregularly Sampled Time Series
Abstract: In this paper, we present a spectral analysis method based upon least square approximation. Our method deals with nonuniform sampling. It provides meaningful phase information that varies in a predictable way as the samples are shifted in time. We compare least square approximations of real and complex series, analyze their properties for sample count towards infinity as well as estimator behaviour, and show the equivalence to the discrete Fourier transform applied onto uniformly sampled data as a special case. We propose a way to deal with the undesirable side effects of nonuniform sampling in the presence of constant offsets. By using weighted least square approximation, we introduce an analogue to the Morlet wavelet transform for nonuniformly sampled data. Asymptotically fast divide-and-conquer schemes for the computation of the variants of the proposed method are presented. The usefulness is demonstrated in some relevant applications.

Page views:: 17829. Submitted: 2003-02-21. Published: 2004-05-19.
Paper: Algorithms for Spectral Analysis of Irregularly Sampled Time Series     Download PDF (Downloads: 19066)
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DOI: 10.18637/jss.v011.i02

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Code: GNU General Public License (at least one of version 2 or version 3) or a GPL-compatible license.