Spectral and cross-spectral analysis of uneven time series with the smoothed Lomb–Scargle periodogram and Monte Carlo evaluation of statistical significance

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dc.contributor.author Pardo Iguzquiza, Eulogio
dc.contributor.author Rodríguez Tovar, Francisco J.
dc.date.accessioned 2020-10-26T11:05:03Z
dc.date.available 2020-10-26T11:05:03Z
dc.date.issued 2012-06-27
dc.identifier.citation Computers & Geosciences, vol.49, 207-216 es_ES
dc.identifier.issn 1873-7803
dc.identifier.uri http://hdl.handle.net/20.500.12468/526
dc.description.abstract Many spectral analysis techniques have been designed assuming sequences taken with a constant sampling interval. However, there are empirical time series in the geosciences (sediment cores, fossil abundance data, isotope analysis,…) that do not follow regular sampling because of missing data, gapped data, random sampling or incomplete sequences, among other reasons. In general, interpolating an uneven series in order to obtain a succession with a constant sampling interval alters the spectral content of the series. In such cases it is preferable to follow an approach that works with the uneven data directly, avoiding the need for an explicit interpolation step. The Lomb–Scargle periodogram is a popular choice in such circumstances, as there are programs available in the public domain for its computation. One new computer program for spectral analysis improves the standard Lomb–Scargle periodogram approach in two ways: (1) It explicitly adjusts the statistical significance to any bias introduced by variance reduction smoothing, and (2) it uses a permutation test to evaluate confidence levels, which is better suited than parametric methods when neighbouring frequencies are highly correlated. Another novel program for cross-spectral analysis offers the advantage of estimating the Lomb–Scargle cross-periodogram of two uneven time series defined on the same interval, and it evaluates the confidence levels of the estimated cross-spectra by a non-parametric computer intensive permutation test. Thus, the cross-spectrum, the squared coherence spectrum, the phase spectrum, and the Monte Carlo statistical significance of the cross-spectrum and the squared-coherence spectrum can be obtained. Both of the programs are written in ANSI Fortran 77, in view of its simplicity and compatibility. The program code is of public domain, provided on the website of the journal (http://www.iamg.org/index.php/publisher/articleview/frmArticleID/112/). Different examples (with simulated and real data) are described in this paper to corroborate the methodology and the implementation of these two new programs es_ES
dc.description.sponsorship Instituto Geológico y Minero de España, España es_ES
dc.description.sponsorship Departamento de Estratigrafía y Paleontología, Universidad de Granada, España es_ES
dc.language.iso en es_ES
dc.publisher Elsevier es_ES
dc.relation CGL2010-15498 es_ES
dc.relation CGL2008-03007 es_ES
dc.relation P08-RNM-03715 es_ES
dc.rights Acceso abierto es_ES
dc.subject cross-spectrum es_ES
dc.subject coherence es_ES
dc.subject phase es_ES
dc.subject irregular data es_ES
dc.subject permutation test es_ES
dc.subject nyquist frequency es_ES
dc.title Spectral and cross-spectral analysis of uneven time series with the smoothed Lomb–Scargle periodogram and Monte Carlo evaluation of statistical significance es_ES
dc.type Postprint es_ES
dc.relation.publisherversion https://reader.elsevier.com/reader/sd/pii/S0098300412002130?token=86423F4070FF46F64E90505445DBDE073E36911E6F50DBB0010D0B80EE85D1D182A56EB196C3AA8B136A1107887B3F1C es_ES
dc.description.funder Ministerio de Economía y Competitividad, España es_ES
dc.description.funder Ministerio de Ciencia e Innovación, España es_ES
dc.description.funder Junta de Andalucía, España es_ES
dc.identifier.doi https://doi.org/10.1016/j.cageo.2012.06.018 es_ES

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