Abstract
Irregularly sampled time series are common in several different areas, such as astronomy, meteorology, biology, oceanography, cyclostratigraphy, and others. The periodogram is a primary tool to extract meaningful information from irregularly spaced and noisy time series. It is an element of decision theory, meaning the periodogram usually transforms the data, and its ordinates are subsequently submitted to a statistical test compared to a population originating from a known stochastic model (white Gaussian noise). If some ordinate f 0 (usually a local maximum, a peak) fails in this test, we declare that it is a ‘periodicity’ at a frequency f 0 . Besides its full usage, this method until now suffer from numerous theoretical difficulties in adapting to real case situations and shows lack of usefulness for very poorly sampled and high noise cases. All of it implies low usefulness for applying in most sedimentary sequences at our disposal nowadays. The LSTperiod is an application, written in Matlab, conceived to perform spectral analysis of multiple irregularly sampled time series. It combines information from Lomb-Scargle periodogram estimates over different time series sampling the same phenomenon , enabling the recovering of signals from very poorly sampled and noisy time series. The software comprises a set of four Graphical User Interfaces (GUIs) that allow the user to: (1) Have broad choices of the frequency-domain range and density for spectral estimation; (2) Select possible spectral features (i.e., pick T ) for testing as a model [ A ∗ sin ( 2 π t −θ )] T through the visualization of several goodness-of-fit statistics; (3) Visualize the fitting residuals in the time domain, for each time series, for the chosen sinusoidal model. These tools help the user to identify and analyze any suspected feature in the estimated spectra through its related linear system responses. All estimated parameter can be saved on worksheets and the visualizations in several different figure formats. We illustrate the use of the software with a set of Ocean Drilling Program (ODP) data series that show long-period Milankovitch-related spectral features and demonstrate its performance using synthetic time series.
Highlights
Large amounts of data in the form of irregularly sampled time series have emerged from several different areas, such as astronomy, meteorology, biology, oceanography and cyclostratigraphy [Baldysz et al, 2016; Bowdalo et al, 2016; Dawidowicz and Krzan, 2016; Jalón-Rojas et al, 2016; Péron et al, 2016; CAMINHA-MACIEL ET AL.Mortier and Cameron, 2017]
Sampled time series are common in several different areas, such as astronomy, meteorology, biology, oceanography, cyclostratigraphy, and others
Large amounts of data in the form of irregularly sampled time series have emerged from several different areas, such as astronomy, meteorology, biology, oceanography and cyclostratigraphy [Baldysz et al, 2016; Bowdalo et al, 2016; Dawidowicz and Krzan, 2016; Jalón-Rojas et al, 2016; Péron et al, 2016; CAMINHA-MACIEL ET AL
Summary
Large amounts of data in the form of irregularly sampled time series have emerged from several different areas, such as astronomy, meteorology, biology, oceanography and cyclostratigraphy [Baldysz et al, 2016; Bowdalo et al, 2016; Dawidowicz and Krzan, 2016; Jalón-Rojas et al, 2016; Péron et al, 2016; CAMINHA-MACIEL ET AL. Caminha-Maciel and Ernesto [2013] presented a method to address these issues through a Bayesian combination of independent experimental information derived from multiple time series as a stacking procedure applied within the frequency domain aimed to smooth the periodogram and to enhance the signal. We developed this method to study weak signals in LSTPERIOD SOFTWARE short and arbitrarily sampled time series with spectral distortions caused by noise and sampling deficiencies. The remainder of this paper is organized as follows: Section 2 contains the essential background to introduce the LST periodogram; Section 3 contains a description of the LSTperiod software with its main features e mode of operation; Section 4 shows the application to a real set of cyclostratigraphic series with very well known results, and its performance when applied to synthetic time series; and Section 5 presents the final considerations
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